Schlieffen Plan and the First Battle of the Marne

WEBVTT
Kind: captions
Language: en

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Ever since the Franco-Prussian
War in 1870 to 1871,

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the Germans recognized
that they were

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likely to face another
war with France.

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That was the war that
allowed Germany to unify.

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They humiliated France.

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They were able to capture
some very valuable territory

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from France, in particular
Alsace and Lorraine,

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which is very mineral rich.

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And so the Germans were
plotting too, well,

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what are we going to do if we
get into another war with them?

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At the same time, once France
and Russia had this alliance,

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Germany fully recognized if
there is a war with France,

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it's likely to not
be just with France.

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It's likely to be
a two front war.

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On the Western Front, they'll
be in conflict with France.

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And on the Eastern
Front, they'll

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be in conflict with Russia.

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And so to deal with
this eventuality--

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this is all the
scheming that Germany

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did in the decades
going up to World War

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I-- they came up with
the Schlieffen Plan.

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And I'm sure I'm
mispronouncing it.

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Named for Alfred
von Schlieffen, he

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was chief of the German
Empire's general staff

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from 1891 to 1905.

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And it was based on how do
you deal with a two front war?

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And the general ides
here were that Russia

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had a large and almost
inexhaustible army.

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But because it was so large it
would take a long time for it

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to mobilize.

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And the Germans are actually
able to approximate it

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correctly because
this is how long it

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did take the
Russians to mobilize

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at the beginning of World War
I. They estimated that it would

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take them about six weeks.

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So the Schlieffen Plan called
for enough German troops

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on the Eastern Front,
initially, in order

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to keep the Russians at bay.

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But then the main fighting
force of the Germans,

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while the Russians
are mobilizing,

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is to go after France and try
to essentially knock France out

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of commission, so that
they're not facing a two front

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war anymore.

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And then have those
troops go back

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to fight against the Russians.

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And the way that
they wanted to do it

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is by rolling through Belgium in
a wheel like pattern like this.

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And the reason why they wanted
to do this wheel like pattern

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is that they correctly
predicted that the French were

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very eager to get this
territory right over here.

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And the French
actually had a plan--

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they called it
Plan 17- for going

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after Alsace and Lorraine.

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It was an offensive plan.

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And the view is if
the French army is

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going in that direction,
if the German army

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rolls through Belgium and is
able to get them from the rear,

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they could put the French
army out of commission.

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So in early August
1914, the Germans,

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once they declared war
on France and on Russia,

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the Germans tried to put the
Schlieffen Plan into action.

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And they frankly,
almost succeeded.

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So through August
and early September,

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the Germans were able
to essentially roll

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through Belgium and keep the
combined, mainly French forces,

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but there was also some
assistance from British,

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to keep them on their heels.

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And this happened all the
way until early September

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when they get near the
Marne, or a little bit

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past the Marne River in France.

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And it was here that
the Sixth French Army--

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and when we talk
about armies we're

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talking about huge
numbers of troops.

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The Sixth French Army had
over 200,000 troops in it.

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When we're talking about
the Battle of the Marne--

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which I'm about to talk to you.

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We're talking about the
first Battle of the Marne.

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We're talking
about a battle that

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involves two million troops.

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So these are battles that are
occurring on an epic scale.

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Just each of these
armies-- this army

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or this one, or even the
German armies-- we're

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talking about tens to hundreds
of thousands of troops.

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In general, an army
characterize you're

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talking about over
50,000, 60,000 troops.

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So what happens as you go to
early September, especially

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September 5, 1914,
the Sixth French Army

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recognizes a mistake that
the First German Army made.

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By trying to roll
around like this,

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they exposed their right flank.

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So right over here would be the
right flank of the German army.

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And just as most
mammals, our flanks

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are our weak spot, that
area between your ribs

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and your hips, the same
thing is true for armies.

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The front of the
army tends to be

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where you have the
strongest forces.

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And then you have your
supply routes going back.

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So if you can outflank
an army-- and that's

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what a lot of military
strategy is designed around--

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you can hit an army
in its weaker points.

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So by September 5, the First
German Army recognized this,

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but it was too late.

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By September 6, they
were essentially

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being confronted by
the Sixth French Army.

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And by essentially
turning to meet them

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they created an opening between
them and the Second German

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Army.

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And that opening was able--
the French and the British

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were able to take advantage
of that to essentially put

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the Germans on their heels
after a month of advancing.

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And so right over here, you
have the various French armies.

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And they were assisted by the
British expeditionary force.

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And so from the Battle
of the Marne, which

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was essentially, most historians
would say, between September 6,

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or September 5, September
6 and September 12,

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they were able to put the
Germans on the retreat.

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The Germans retreated
past the Aisne River.

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And then once you
get into November

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and the end of the year of
1914, the Germans essentially

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entrenched themselves.

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They were literally
building deep trenches

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in northern France and a
little bit of western Belgium.

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And what I have
right over here-- let

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me see if I can draw it.

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What I have right over here,
what the boundaries are

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eventually happened
after the Germans

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suffered, essentially,
their first big defeat.

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They had to retreat and they
had to literally retrench.

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And this is what the
borders would then be like.

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And these were literally
trenches getting dug here.

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This first stage of the
war was hugely dynamic.

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You had armies
moving fairly rapidly

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over a period of
weeks and months.

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But then once the
Germans retrenched,

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you have roughly this position
being static for the next three

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years and the famous trench
warfare of the Western front

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that you might have
seen movies on.

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And I want to emphasize
this was a big deal.

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The first Battle of
the Marne-- sometimes

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it's called the
Miracle of the Marne--

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if the French,
with British help,

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were not able to push
the Germans back,

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they might have accomplished
the Schlieffen Plan

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and actually maybe would
have won World War I,

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or at least been able to win the
Western front fairly quickly.

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And then been able to
deal with the Russians

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a little bit better.

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But because of the
Miracle at the Marne--

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which was hugely bloody.

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We're talking about 500,000
casualties on both sides.

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We're talking 100,000 to
200,000 dead on both sides.

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But because of that, that was
able to hold off the Germans.

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But it got the Western front
into this ugly three year

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long trench warfare.


Assassination of Franz Ferdinand

WEBVTT
Kind: captions
Language: en

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We're now ready
to talk about one

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of the most famous events
in all of world history

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that really was the
trigger for World War I,

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or the Great War, as it
was called back then.

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So just as a little
bit of backdrop,

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in 1908, the Austro-Hungarian
Empire formally

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annexes Bosnia and Herzegovina.

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It had already been occupying
it since the late 1800s,

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since the Ottomans
were being pushed out.

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But then in 1908, it
formally annexes it.

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And just as a little
bit more backdrop,

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as the Ottomans were being
pushed out of the Balkans,

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it helped rekindle or
bring about more hope

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of unifying the Yugoslavic
people, the southern Slavic

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people.

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When people talk about
Yugoslav, they're

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literally talking about
the southern Slavs.

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So that literally
means southern.

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So you had these
nationalistic hopes.

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But now in 1908, it was
already being occupied.

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A significant
state, that would be

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part of a potential
future Yugoslav,

00:01:07.090 --> 00:01:11.550
was now formally annexed
by the Austro-Hungarians.

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Now, you also had an independent
kingdom of Serbia right here.

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And you can imagine
that this was the home

00:01:17.230 --> 00:01:20.120
base of the
nationalistic movement.

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If only they could add the other
southern Slavic states to this,

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it could one day turn
into a greater Yugoslavia.

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So in that context,
we get to 1914.

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So let me draw a
little line here.

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So we're getting to 1914.

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June 28, which is one of
the most famous dates in all

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of history.

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And you have the Archduke Franz
Ferdinand and his wife, Sophie.

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They're visiting Sarajevo
which is now in annexed Bosnia.

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And when they are
there, there is a ploy.

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There is a scheme
to assassinate them,

00:01:56.930 --> 00:02:00.190
from a group-- they're
called the Young Bosnians.

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They have ties to
the Black Hand,

00:02:02.960 --> 00:02:06.320
which is this
nationalistic group.

00:02:06.320 --> 00:02:08.930
That has ties, many,
many people say--

00:02:08.930 --> 00:02:11.450
all these things are all very
shady and behind the back,

00:02:11.450 --> 00:02:12.580
behind the scenes.

00:02:12.580 --> 00:02:17.440
But it has ties to elements
in the kingdom of Serbia.

00:02:17.440 --> 00:02:21.750
They attempt to assassinate
Archduke Franz Ferdinand.

00:02:21.750 --> 00:02:24.050
And it's actually
a fascinating story

00:02:24.050 --> 00:02:26.350
because the initial
assassination attempt

00:02:26.350 --> 00:02:28.750
is completely,
completely botched.

00:02:28.750 --> 00:02:31.150
There's even one case of
a guy, one of the guys

00:02:31.150 --> 00:02:33.290
who tried to be an assassin
when it gets botched,

00:02:33.290 --> 00:02:35.310
he tries to bite on
a cyanide capsule

00:02:35.310 --> 00:02:37.240
and then jump into a river.

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The cyanide capsule
had gone bad.

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The river was only
10 inches deep.

00:02:40.730 --> 00:02:42.990
And so they were able to
get their hands on him.

00:02:42.990 --> 00:02:46.010
And one of the conspirators,
Gavrilo Princip--

00:02:46.010 --> 00:02:48.010
at this point, once the
whole thing was botched,

00:02:48.010 --> 00:02:50.920
he gives up on the whole
assassination attempt.

00:02:50.920 --> 00:02:55.360
And he's having, literally, a
sandwich at a cafe in Sarajevo,

00:02:55.360 --> 00:02:58.580
thinking about how botched
their whole attempt was.

00:02:58.580 --> 00:03:01.040
And while that was
happening, a mistake

00:03:01.040 --> 00:03:05.790
on the part of those planning
Archduke Franz Ferdinand's

00:03:05.790 --> 00:03:08.830
route as he was
traveling within Sarajevo

00:03:08.830 --> 00:03:11.510
has them driving right
near Gavrilo Princip.

00:03:11.510 --> 00:03:13.367
So he sees, all of a
sudden, that they've

00:03:13.367 --> 00:03:15.700
taken the wrong route, that
they're driving right by him

00:03:15.700 --> 00:03:16.600
again.

00:03:16.600 --> 00:03:17.570
Remember, his
people already knew

00:03:17.570 --> 00:03:19.486
that there was an
assassination attempt on him

00:03:19.486 --> 00:03:20.810
earlier in the day.

00:03:20.810 --> 00:03:22.760
So they should have
been more careful.

00:03:22.760 --> 00:03:25.910
Now, Gavrilo Princip gets
up, puts his sandwich down,

00:03:25.910 --> 00:03:29.030
and starts walking over to
where he sees Archduke Franz

00:03:29.030 --> 00:03:31.160
Ferdinand and
Sophie's car going.

00:03:31.160 --> 00:03:33.244
Now, the drivers,
once they realized

00:03:33.244 --> 00:03:34.660
that they had made
a mistake, they

00:03:34.660 --> 00:03:36.320
had taken a less safe route.

00:03:36.320 --> 00:03:38.990
They tried to back up, which
makes things even worse

00:03:38.990 --> 00:03:40.780
because then the
car starts stalling.

00:03:40.780 --> 00:03:43.650
And Gavrilo Princip
literally walks up to the car

00:03:43.650 --> 00:03:47.191
and is able to shoot Archduke
Franz Ferdinand and Sophie.

00:03:47.191 --> 00:03:49.440
And just to give you a sense
of how important this is,

00:03:49.440 --> 00:03:52.110
Archduke Franz Ferdinand
of Austria is the heir.

00:03:52.110 --> 00:03:58.330
He's the nephew of
Franz Josef, who

00:03:58.330 --> 00:04:00.680
was the ruler of
Austria-Hungary.

00:04:00.680 --> 00:04:02.980
And so he is the
heir to the empire.

00:04:02.980 --> 00:04:06.850
And so he gets assassinated
by Gavrilo Princip.

00:04:06.850 --> 00:04:20.410
So Franz Ferdinand assassinated
by Gavrilo Princip.

00:04:20.410 --> 00:04:22.970
And we have right over
here a picture right

00:04:22.970 --> 00:04:24.870
after Gavrilo
Princip-- I believe

00:04:24.870 --> 00:04:27.030
this is Gavrilo Princip
right over here,

00:04:27.030 --> 00:04:31.000
right after he was arrested.

00:04:31.000 --> 00:04:32.560
And just to get a
little sense of how

00:04:32.560 --> 00:04:37.080
this was tied to this
whole Yugoslavian

00:04:37.080 --> 00:04:38.560
nationalistic movement.

00:04:38.560 --> 00:04:41.100
This is what he said
once he was arrested.

00:04:41.100 --> 00:04:43.320
"I am a Yugoslav
nationalist, aiming

00:04:43.320 --> 00:04:46.350
for the unification
of all Yugoslavs,

00:04:46.350 --> 00:04:48.800
and I do not care
what form of state,

00:04:48.800 --> 00:04:52.180
but it must be free of Austria."

00:04:52.180 --> 00:04:56.250
So this act, this
assassination motivated

00:04:56.250 --> 00:04:58.870
by a nationalistic movement,
motivated by a desire

00:04:58.870 --> 00:05:02.045
to maybe merge Bosnia and
Herzegovina with Serbia

00:05:02.045 --> 00:05:04.238
and maybe eventually
Croatia, with Bosnia

00:05:04.238 --> 00:05:06.040
and Herzegovina and Serbia.

00:05:06.040 --> 00:05:08.850
This assassination, as
we'll see in the next video,

00:05:08.850 --> 00:05:11.630
is the trigger for
all of World War I.

00:05:11.630 --> 00:05:14.799
And the reason why it triggers
it is because, well, there's

00:05:14.799 --> 00:05:15.840
many things you can cite.

00:05:15.840 --> 00:05:18.990
You could argue that many
of the empires in Europe

00:05:18.990 --> 00:05:21.360
were already
militarizing, already

00:05:21.360 --> 00:05:22.970
had a desire for conflict.

00:05:22.970 --> 00:05:25.260
But then you also had all
of these alliances that

00:05:25.260 --> 00:05:28.154
essentially allowed the dominoes
to fall in all of Europe.

00:05:28.154 --> 00:05:30.320
And because they had these
empires, essentially much

00:05:30.320 --> 00:05:33.720
of the world to be at
war with each other.


The Great War begins

WEBVTT
Kind: captions
Language: en

00:00:00.580 --> 00:00:03.470
In the last video, we left
off with the assassination

00:00:03.470 --> 00:00:08.520
of Archduke Franz Ferdinand
of Austria, the heir

00:00:08.520 --> 00:00:11.970
to the Austro-Hungarian empire.

00:00:11.970 --> 00:00:15.360
And so you could imagine,
the Austro-Hungarian empire

00:00:15.360 --> 00:00:16.650
did not take that well.

00:00:16.650 --> 00:00:21.120
They already did not enjoy the
kingdom of Serbia trying to,

00:00:21.120 --> 00:00:24.470
essentially, provoke this
nationalistic movement.

00:00:24.470 --> 00:00:27.880
And they viewed them as this
small, little, weak country

00:00:27.880 --> 00:00:29.480
right below them.

00:00:29.480 --> 00:00:31.690
And so they use this
to, essentially,

00:00:31.690 --> 00:00:32.690
issue an ultimatum.

00:00:32.690 --> 00:00:34.600
Essentially say,
look, immediately

00:00:34.600 --> 00:00:37.460
bring all the people
who did this to justice,

00:00:37.460 --> 00:00:40.330
all the people who might have
conspired with the Gavrilo

00:00:40.330 --> 00:00:43.700
Princips to allow
this assassination

00:00:43.700 --> 00:00:46.870
attempt to occur,
and do it or else,

00:00:46.870 --> 00:00:48.890
and accept full responsibility.

00:00:48.890 --> 00:00:51.240
And actually, the
kingdom of Serbia

00:00:51.240 --> 00:00:55.780
was in no mood to get into
a war with Austria-Hungary,

00:00:55.780 --> 00:00:57.860
and so they tried
their best to comply,

00:00:57.860 --> 00:00:59.410
but their best wasn't enough.

00:00:59.410 --> 00:01:03.630
So then July 28,
a month later, you

00:01:03.630 --> 00:01:06.930
have the Austrians declaring
war on the Serbians.

00:01:15.860 --> 00:01:19.057
Now up until this point,
the Austro-Hungarian empire

00:01:19.057 --> 00:01:21.390
is thinking, OK, Serbia is a
small, little kingdom here.

00:01:21.390 --> 00:01:24.290
It has some ties and
obviously, it's a Slavic nation

00:01:24.290 --> 00:01:27.310
so it has some linguistic
ties with the Russian empire.

00:01:27.310 --> 00:01:29.850
The Russian empire also had
some political ties to it,

00:01:29.850 --> 00:01:32.350
but Russia is not going to get
into a war with us over this.

00:01:32.350 --> 00:01:33.990
We're justified
in attacking them.

00:01:33.990 --> 00:01:36.187
They've just killed
the heir to our throne.

00:01:36.187 --> 00:01:38.520
So we're going to go in there
and Russia is probably not

00:01:38.520 --> 00:01:43.020
interested in actually creating
a larger skirmish here.

00:01:43.020 --> 00:01:48.290
That was a severe miscalculation
on the part of the Austrians.

00:01:48.290 --> 00:01:50.510
The Russians were
not happy about this.

00:01:50.510 --> 00:01:52.740
They felt close
ties to the Serbians

00:01:52.740 --> 00:01:55.020
and they felt a need to
protect the Serbians,

00:01:55.020 --> 00:01:57.560
or you could argue,
that maybe they

00:01:57.560 --> 00:02:00.349
wanted to mobilize just
to scare the Austrians.

00:02:00.349 --> 00:02:02.140
Whatever it might be,
whether it was Russia

00:02:02.140 --> 00:02:03.950
wanted to get into a war,
whether they were really

00:02:03.950 --> 00:02:06.491
looking to protect the Serbians,
or whether they were looking

00:02:06.491 --> 00:02:09.720
to mobilize to scare the
Austrians from actually

00:02:09.720 --> 00:02:12.610
attacking, the Russians
began to mobilize.

00:02:12.610 --> 00:02:16.820
So the Russians began
to gather their troops.

00:02:16.820 --> 00:02:20.280
So the Russians mobilize.

00:02:23.060 --> 00:02:25.720
And now, this is where
all of the alliances

00:02:25.720 --> 00:02:28.570
start to come into effect.

00:02:28.570 --> 00:02:30.710
If you remember
about the alliances

00:02:30.710 --> 00:02:36.180
we talked about several
videos ago, if you go to 1879,

00:02:36.180 --> 00:02:38.070
you have the Dual
Alliance Treaty

00:02:38.070 --> 00:02:40.220
between Germany
and Austria-Hungary

00:02:40.220 --> 00:02:42.830
to protect each other if
Russia attacks and actually,

00:02:42.830 --> 00:02:45.230
if Russia attacks or mobilizes.

00:02:45.230 --> 00:02:47.260
So now, Germany is
like, hey, maybe I

00:02:47.260 --> 00:02:50.130
am obligated to protect
Austria-Hungary from Russia.

00:02:50.130 --> 00:02:54.260
You also have to remember
in 1892, the Franco-Russian

00:02:54.260 --> 00:02:55.620
Military Convention.

00:02:55.620 --> 00:02:59.720
Military assistance both
ways in the event of attack.

00:02:59.720 --> 00:03:02.650
So Germany is thinking,
look, we signed this treaty

00:03:02.650 --> 00:03:05.410
and we, to some degree,
are maybe eager for war

00:03:05.410 --> 00:03:08.190
because we've been
militarizing so much.

00:03:08.190 --> 00:03:10.080
And I can't just fight Russia.

00:03:10.080 --> 00:03:11.900
I also know that
France and Russia

00:03:11.900 --> 00:03:14.040
have this alliance
right over here.

00:03:14.040 --> 00:03:17.500
So Germany in quite
surprising quickness

00:03:17.500 --> 00:03:19.990
decides to declare war on both.

00:03:19.990 --> 00:03:26.470
So on August 1, Germany
declares war on Russia.

00:03:31.650 --> 00:03:42.764
And then on August 3, Germany
declares war on France

00:03:42.764 --> 00:03:44.180
because they know
or at least they

00:03:44.180 --> 00:03:46.470
feel that they can't declare
war on only one of them.

00:03:46.470 --> 00:03:48.845
And they wanted to do it very
quickly because they didn't

00:03:48.845 --> 00:03:51.557
want Russia a chance
to mobilize too much.

00:03:51.557 --> 00:03:53.890
And the fact that they were
able to do this so quickly--

00:03:53.890 --> 00:03:57.639
we're talking three days after
Austria declares war on Serbia

00:03:57.639 --> 00:03:59.180
and then another
two days declare war

00:03:59.180 --> 00:04:01.800
on France-- kind of shows
that Germany was already

00:04:01.800 --> 00:04:02.540
in a war footing.

00:04:02.540 --> 00:04:04.850
It's not a joke to
all of a sudden invade

00:04:04.850 --> 00:04:06.330
or declare war on countries.

00:04:06.330 --> 00:04:08.380
So Germany was, essentially,
preparing for this.

00:04:08.380 --> 00:04:11.680
And this right
over here gave them

00:04:11.680 --> 00:04:15.310
the excuse to,
essentially, declare war.

00:04:15.310 --> 00:04:18.709
So they declare war on both
of these characters, Germany

00:04:18.709 --> 00:04:19.880
against Russia.

00:04:19.880 --> 00:04:22.140
Germany is declaring
war on France.

00:04:22.140 --> 00:04:25.702
Now, the easiest way for
them to move into France--

00:04:25.702 --> 00:04:27.410
so they're literally
going on the offense

00:04:27.410 --> 00:04:30.025
here-- is for them to
go through Belgium.

00:04:34.650 --> 00:04:36.093
But the Germans were aware.

00:04:36.093 --> 00:04:39.600
They're aware that there's this
75-year-old treaty, the Treaty

00:04:39.600 --> 00:04:42.110
of London in 1839,
Article 7 said

00:04:42.110 --> 00:04:46.070
that Britain was to protect
the neutrality of Belgium.

00:04:46.070 --> 00:04:48.140
And Germany was in
no interest to get

00:04:48.140 --> 00:04:49.940
into a war with the British.

00:04:49.940 --> 00:04:52.340
The British had a
powerful military,

00:04:52.340 --> 00:04:55.585
especially a very powerful navy.

00:04:55.585 --> 00:04:56.960
The Germans said,
hey, let's just

00:04:56.960 --> 00:04:58.962
take on the Russians
and the French for now.

00:04:58.962 --> 00:05:00.920
And so they actually
reached out to the British

00:05:00.920 --> 00:05:03.045
and said, hey, this little
treaty that you got here

00:05:03.045 --> 00:05:04.967
from 1839, this
75-year-old treaty,

00:05:04.967 --> 00:05:06.800
you don't really take
this seriously, right?

00:05:06.800 --> 00:05:08.560
I mean if we have to
go through Belgium,

00:05:08.560 --> 00:05:11.840
you're not really going to
hold true to this treaty?

00:05:11.840 --> 00:05:13.600
And the British
said, no, we actually

00:05:13.600 --> 00:05:15.040
take that very seriously.

00:05:15.040 --> 00:05:17.284
Obviously, the
British didn't want

00:05:17.284 --> 00:05:18.700
the Germans to be
aggressive here.

00:05:18.700 --> 00:05:20.760
The British didn't
want the Germans

00:05:20.760 --> 00:05:22.840
to be able to invade France.

00:05:22.840 --> 00:05:31.170
And so on August 4 when
Germany, essentially,

00:05:31.170 --> 00:05:33.890
rolls through Belgium,
Germany invades

00:05:33.890 --> 00:05:40.760
Belgium to get to France, this
gave the legal justification

00:05:40.760 --> 00:05:42.795
for the British to
declare war on Germany.

00:05:52.370 --> 00:05:54.980
And so in a matter of only--
I mean not even, we're

00:05:54.980 --> 00:05:58.560
talking a few months here from
the assassination of Franz

00:05:58.560 --> 00:06:01.080
Ferdinand of Austria,
you essentially

00:06:01.080 --> 00:06:03.830
have all of the major
powers of Europe.

00:06:03.830 --> 00:06:07.610
And then as we'll see because
they had these empires, in not

00:06:07.610 --> 00:06:11.840
too long most of the world
is at war with each other.


Language and religion of the former Yugoslavia

WEBVTT
Kind: captions
Language: en

00:00:00.660 --> 00:00:03.430
Understanding the ethnic
and religious commonalities

00:00:03.430 --> 00:00:06.310
and differences in the
state or the region that

00:00:06.310 --> 00:00:08.277
used to be Yugoslavia
can be quite confusing.

00:00:08.277 --> 00:00:10.860
What I want to do in this video
is try to give a primer on it.

00:00:10.860 --> 00:00:14.230
It's really key to understanding
some of the triggers of World

00:00:14.230 --> 00:00:16.990
War I. And to, obviously,
understand the breakup

00:00:16.990 --> 00:00:21.100
of Yugoslavia which was
quite ugly during the fall

00:00:21.100 --> 00:00:24.476
of Communism in the late
'80s and early '90s.

00:00:24.476 --> 00:00:25.850
So first of all,
it's a good idea

00:00:25.850 --> 00:00:30.960
to just understand where the
word Yugoslavia comes from.

00:00:30.960 --> 00:00:34.000
It's literally referring to
the southern Slavic states.

00:00:34.000 --> 00:00:36.190
So Yugo- is referring
to southern.

00:00:36.190 --> 00:00:38.610
And -slavia, we're talking
about the Slavic states.

00:00:38.610 --> 00:00:40.624
And when people talk
about Slavic languages,

00:00:40.624 --> 00:00:42.290
they're talking about
the languages that

00:00:42.290 --> 00:00:45.700
are spoken in this region, but
also much of Eastern Europe,

00:00:45.700 --> 00:00:49.070
and in what is now Russia.

00:00:49.070 --> 00:00:52.410
Now, what we have
here in blue is,

00:00:52.410 --> 00:00:56.080
we have shaded in
where Serbo-Croatian

00:00:56.080 --> 00:01:02.210
is spoken, which is the dominant
Slavic language in this region.

00:01:05.510 --> 00:01:07.430
And there are multiple dialects.

00:01:07.430 --> 00:01:10.060
Some people will say, oh,
it's Croatian or Montenegrin

00:01:10.060 --> 00:01:12.204
or Serbian or
whatever it might be.

00:01:12.204 --> 00:01:13.870
But mostly, linguists
say, well, they're

00:01:13.870 --> 00:01:15.260
pretty close to each other.

00:01:15.260 --> 00:01:20.810
And you can categorize them as
one language as Serbo-Croatian.

00:01:20.810 --> 00:01:24.536
And you see that it's now spoken
in modern day Croatia, Bosnia

00:01:24.536 --> 00:01:28.330
and Herzegovina,
Serbia and Montenegro.

00:01:28.330 --> 00:01:31.430
And that is the
commonality here,

00:01:31.430 --> 00:01:33.710
the thing that ties
together this region.

00:01:33.710 --> 00:01:36.490
Now on top of that,
the Slovenian language

00:01:36.490 --> 00:01:39.180
is also Slavic language
that is closely related

00:01:39.180 --> 00:01:40.800
to Serbo-Croatian.

00:01:40.800 --> 00:01:43.290
In Macedonia, they also
speak a Slavic language.

00:01:43.290 --> 00:01:44.830
It's closer to Bulgarian.

00:01:44.830 --> 00:01:46.320
But it has some close ties.

00:01:46.320 --> 00:01:48.950
It's not completely different
than Serbo-Croatian.

00:01:48.950 --> 00:01:51.150
So you have this
linguistic connection

00:01:51.150 --> 00:01:53.220
throughout this area.

00:01:53.220 --> 00:01:57.730
Now, what divides this area is
really religion and history.

00:01:57.730 --> 00:02:01.060
So this area, if you look,
go back hundreds of years,

00:02:01.060 --> 00:02:03.640
it was under the control
of various empires,

00:02:03.640 --> 00:02:06.220
the Austro-Hungarian
Empire, the Ottoman Empire.

00:02:06.220 --> 00:02:08.634
Different-- the
Austro-Hungarian Empire,

00:02:08.634 --> 00:02:10.550
you're dealing with the
Roman Catholic Empire.

00:02:10.550 --> 00:02:11.880
When you're talking
about the Ottomans,

00:02:11.880 --> 00:02:13.710
you're dealing with
the Muslim Empire.

00:02:13.710 --> 00:02:16.180
And they held in different
parts of this territory

00:02:16.180 --> 00:02:18.570
for hundreds of years.

00:02:18.570 --> 00:02:22.510
And so what you end up, is
really a mix of religions.

00:02:22.510 --> 00:02:26.220
And that often gets tied to
people's-- what they perceive

00:02:26.220 --> 00:02:28.450
as also their ethnicities.

00:02:28.450 --> 00:02:31.110
And so what I have
here is a break down,

00:02:31.110 --> 00:02:34.230
the religious
breakdown of the state,

00:02:34.230 --> 00:02:36.380
the former state of Yugoslavia.

00:02:36.380 --> 00:02:38.570
So in this pinkish
color right over here,

00:02:38.570 --> 00:02:41.500
I have the areas that are
predominately Roman Catholic.

00:02:41.500 --> 00:02:44.190
And I say, predominantly,
because it really is all mixed

00:02:44.190 --> 00:02:44.690
together.

00:02:44.690 --> 00:02:48.470
So Slovenia, Croatia,
primarily Roman Catholic.

00:02:48.470 --> 00:02:51.510
If you look at Serbia
and Montenegro,

00:02:51.510 --> 00:02:54.170
primarily Eastern Orthodox.

00:02:54.170 --> 00:03:00.950
Kosovo, you have a strong Muslim
majority right over there.

00:03:00.950 --> 00:03:04.240
And it really gets-- and
Kosovo, before its break up,

00:03:04.240 --> 00:03:07.520
was kind of part of
Serbia and Montenegro.

00:03:07.520 --> 00:03:10.770
Despite it having this very
different religious makeup.

00:03:10.770 --> 00:03:12.360
And then, Bosnia
and Herzegovina is

00:03:12.360 --> 00:03:14.740
where things get
really, really mixed up.

00:03:14.740 --> 00:03:16.740
Roughly half of the
population, and it's

00:03:16.740 --> 00:03:19.650
been moving over the centuries.

00:03:19.650 --> 00:03:23.380
But the dominant
religion there is Islam.

00:03:23.380 --> 00:03:25.630
And in general, and this is
where it can be confusing,

00:03:25.630 --> 00:03:28.420
when people talk
about a Bosniak,

00:03:28.420 --> 00:03:30.250
when they're talking
about a Bosniak,

00:03:30.250 --> 00:03:32.080
they're talking about
a Bosnian Muslim.

00:03:36.550 --> 00:03:40.710
But Bosnia and Herzegovina
also has significant fractions

00:03:40.710 --> 00:03:44.020
of Serbs who are
Eastern Orthodox.

00:03:44.020 --> 00:03:45.840
So that's why I put
the brown here as well.

00:03:45.840 --> 00:03:47.410
It's about a third
of the population.

00:03:47.410 --> 00:03:50.580
And it also has a pretty sizable
Roman Catholic population.

00:03:50.580 --> 00:03:53.025
Or we could say Bosnian Croats.

00:03:53.025 --> 00:03:55.150
So just to be clear here,
it can be very confusing.

00:03:55.150 --> 00:03:56.980
Even when you when
you hear history of it

00:03:56.980 --> 00:03:58.490
or when you've heard
it on the news.

00:03:58.490 --> 00:04:00.340
I remember the '90s
hearing this on the news

00:04:00.340 --> 00:04:02.060
and getting very confused.

00:04:02.060 --> 00:04:04.970
If someone's referring to a
Bosnian Muslim or Bosniak,

00:04:04.970 --> 00:04:06.780
that's a Muslim
living in Bosnia.

00:04:06.780 --> 00:04:09.070
That's they tend
to be referring to.

00:04:09.070 --> 00:04:16.709
If they say a
Bosnian Croats, this

00:04:16.709 --> 00:04:20.440
would be an ethnically Croat
who is living in Bosnia.

00:04:20.440 --> 00:04:24.600
And they are-- it would
tend to be Roman Catholic.

00:04:24.600 --> 00:04:29.320
And then if you
have a Bosnian Serb,

00:04:29.320 --> 00:04:32.760
this is someone who ethnically
identifies themselves

00:04:32.760 --> 00:04:35.870
as a Serbian or as
a Serb who lives

00:04:35.870 --> 00:04:38.330
in Bosnia and Herzegovina.

00:04:38.330 --> 00:04:42.210
But is probably going
to be Eastern Orthodox.

00:04:42.210 --> 00:04:46.070
So you can imagine, you have
the strong linguistic and even

00:04:46.070 --> 00:04:48.160
ethnic ties.

00:04:48.160 --> 00:04:52.040
But at some point, because
of the religion and dialect

00:04:52.040 --> 00:04:54.510
changes, there's also
significant amount

00:04:54.510 --> 00:04:55.380
of differences here.

00:04:55.380 --> 00:04:57.780
Especially when things
got ugly, as you

00:04:57.780 --> 00:04:58.927
have the fall of Communism.

00:04:58.927 --> 00:05:00.510
So hopefully, this
lays the groundwork

00:05:00.510 --> 00:05:03.030
of the commonalities and
the differences here.

00:05:03.030 --> 00:05:06.272
And it'll help us understand
what got us into World War I,

00:05:06.272 --> 00:05:08.480
or at least what triggered
World War I. And also some

00:05:08.480 --> 00:05:12.590
of the ugliness that was
seen in the early '90s.

00:05:12.590 --> 00:05:15.100
And just to finish up with
a little bit of context,

00:05:15.100 --> 00:05:19.010
this was not a unified
state until-- World War

00:05:19.010 --> 00:05:21.380
I, to some degree, was
precipitated by a desire

00:05:21.380 --> 00:05:24.455
to make this a unified state.

00:05:24.455 --> 00:05:28.600
This ethnic grouping,
this linguistic grouping

00:05:28.600 --> 00:05:31.150
tended to be broken up with
the Austro-Hungarian Empire,

00:05:31.150 --> 00:05:32.454
the Ottoman Empire.

00:05:32.454 --> 00:05:34.120
Entering into a World
War I, you started

00:05:34.120 --> 00:05:35.850
to have the decline
of the Ottoman Empire

00:05:35.850 --> 00:05:39.170
which started to allow
these people to start

00:05:39.170 --> 00:05:43.780
to have more energy behind their
desire to form a unified state.

00:05:43.780 --> 00:05:45.850
World War I was
essentially the catalyst

00:05:45.850 --> 00:05:49.970
that allowed the state
of Yugoslavia to unify.

00:05:49.970 --> 00:05:51.850
And in different
forms, it stayed

00:05:51.850 --> 00:05:54.600
unified until the
fall of Communism.

00:05:54.600 --> 00:05:56.435
And even though it
was a socialist state,

00:05:56.435 --> 00:05:59.320
a communist state
during the Cold War,

00:05:59.320 --> 00:06:03.030
it actually always had a
strange and distant relationship

00:06:03.030 --> 00:06:04.360
with the Soviet Union.

00:06:04.360 --> 00:06:06.320
But after the fall
of Communism, that

00:06:06.320 --> 00:06:09.170
was kind of holding it
together, these, especially

00:06:09.170 --> 00:06:11.590
these religious
differences, frankly,

00:06:11.590 --> 00:06:15.732
and these ethnic and religious
differences broke it apart.


Alliances leading to World War I

WEBVTT
Kind: captions
Language: en

00:00:00.520 --> 00:00:04.880
One of the reasons that's
most cited as to a cause

00:00:04.880 --> 00:00:08.550
or the cause of why World War
I turned into a world war,

00:00:08.550 --> 00:00:11.490
as opposed to just a regional
conflict in southeast Europe,

00:00:11.490 --> 00:00:15.180
is the alliance system that
was developing in the decades

00:00:15.180 --> 00:00:18.170
leading up to World War
I. And to understand

00:00:18.170 --> 00:00:20.630
that, I've distilled a bunch
of the alliances that occurred

00:00:20.630 --> 00:00:22.549
in those decades leading
up to World War I.

00:00:22.549 --> 00:00:24.090
And this is just a
distilled version.

00:00:24.090 --> 00:00:26.780
There were many other alliances
that were tangentially related.

00:00:26.780 --> 00:00:29.405
But I tried to distill down the
ones that were directly related

00:00:29.405 --> 00:00:33.070
to all of the dominoes
falling in 1914 that

00:00:33.070 --> 00:00:35.340
led to all of Europe
being essentially at war

00:00:35.340 --> 00:00:36.650
with each other.

00:00:36.650 --> 00:00:39.780
So to understand that, we
have to rewind 75 years.

00:00:39.780 --> 00:00:42.240
So World War I starts in 1914.

00:00:42.240 --> 00:00:47.280
75 years before that, in 1839,
you have the Treaty of London.

00:00:47.280 --> 00:00:49.680
And the Treaty of
London did many things.

00:00:49.680 --> 00:00:52.780
But Article 7 is what's relevant
to the beginning of World War

00:00:52.780 --> 00:00:55.450
I, where Britain
agrees to protect

00:00:55.450 --> 00:00:57.810
the neutrality of Belgium.

00:00:57.810 --> 00:00:59.930
And if you're skeptical,
you might say, hey,

00:00:59.930 --> 00:01:01.660
this is a 75-year-old treaty.

00:01:01.660 --> 00:01:02.980
Why does this matter anymore?

00:01:02.980 --> 00:01:05.000
And that, actually,
would be a good question.

00:01:05.000 --> 00:01:06.600
Really, all of these
alliances-- it's

00:01:06.600 --> 00:01:08.320
a very healthy debate
you can have as to

00:01:08.320 --> 00:01:10.865
whether these are the
direct causes of why

00:01:10.865 --> 00:01:13.440
one of these powers
declared war on the other.

00:01:13.440 --> 00:01:15.000
Or whether these
were just excuses.

00:01:15.000 --> 00:01:17.336
These were a legal
pretext for saying,

00:01:17.336 --> 00:01:18.710
oh, I need to
declare war on you.

00:01:18.710 --> 00:01:20.170
When in reality,
they really did want

00:01:20.170 --> 00:01:21.960
to declare war for a
whole set of reasons

00:01:21.960 --> 00:01:24.650
to keep the other
person's empire in check,

00:01:24.650 --> 00:01:26.380
to flex their
military muscle, to go

00:01:26.380 --> 00:01:28.410
after more territory
in their empires.

00:01:28.410 --> 00:01:30.210
Who knows what it might be?

00:01:30.210 --> 00:01:33.880
But needless to say,
1839 was the legal basis

00:01:33.880 --> 00:01:39.540
for the British Empire
to protect Belgium.

00:01:39.540 --> 00:01:43.940
Now, you fast-forward 40
years, you get to 1879.

00:01:43.940 --> 00:01:46.840
You have a newly
born German Empire

00:01:46.840 --> 00:01:50.440
out of the Franco-Prussian
War in 1871.

00:01:50.440 --> 00:01:53.520
That newly born German empire,
they just had-- essentially,

00:01:53.520 --> 00:01:57.370
it's an extension of
Prussia, fundamentally,

00:01:57.370 --> 00:01:58.807
a German kingdom.

00:01:58.807 --> 00:02:00.140
They just had a war with France.

00:02:00.140 --> 00:02:02.700
They took some very valuable
territory from France.

00:02:02.700 --> 00:02:05.290
They're paranoid that France
wants to get back at them.

00:02:05.290 --> 00:02:08.800
They're paranoid
about the Russians.

00:02:08.800 --> 00:02:12.540
And they have some connection
with the Austrians--

00:02:12.540 --> 00:02:14.710
the Austro-Hungarians,
I should say.

00:02:14.710 --> 00:02:19.370
And so in 1879, they sign
the Dual Alliance Treaty

00:02:19.370 --> 00:02:21.870
between Germany
and Austria-Hungary

00:02:21.870 --> 00:02:24.700
to protect each other
if Russia attacks.

00:02:24.700 --> 00:02:27.900
They have this common enemy
right over here, Russia.

00:02:27.900 --> 00:02:30.770
So they are going to-- let me
do this in a different color.

00:02:30.770 --> 00:02:32.870
They are going to
protect each other.

00:02:32.870 --> 00:02:35.990
So this makes the new German
Empire feel a little bit better

00:02:35.990 --> 00:02:37.930
about its position
in Europe, in case

00:02:37.930 --> 00:02:41.380
they were to get into a war
with either of these characters.

00:02:41.380 --> 00:02:43.900
Then in 1892--
you could imagine,

00:02:43.900 --> 00:02:45.840
if you ever play a game
of Risk or if you ever

00:02:45.840 --> 00:02:47.714
play the game of Diplomacy,
which is actually

00:02:47.714 --> 00:02:49.740
based on what
happened in World War

00:02:49.740 --> 00:02:52.550
I. If you see some
people that you might be

00:02:52.550 --> 00:02:54.265
at war with starting
to become friends,

00:02:54.265 --> 00:02:56.390
you want to look for other
friends, other alliances

00:02:56.390 --> 00:02:59.400
that you can form in case
they declare war on you.

00:02:59.400 --> 00:03:02.030
So in 1892, you have an
alliance between the French

00:03:02.030 --> 00:03:04.400
and the Russians, the
Franco-Russian Military

00:03:04.400 --> 00:03:05.470
Convention.

00:03:05.470 --> 00:03:07.080
So this is an alliance.

00:03:07.080 --> 00:03:10.670
Let me do this in the
magenta color again.

00:03:10.670 --> 00:03:16.250
You have an alliance
between France and Russia.

00:03:16.250 --> 00:03:20.520
And then finally, in the
early 1900s, 1904 to 1907,

00:03:20.520 --> 00:03:22.410
you have a series of agreements.

00:03:22.410 --> 00:03:24.350
"Entente" essentially
means agreements.

00:03:24.350 --> 00:03:26.780
Agreements between the
British Empire and France,

00:03:26.780 --> 00:03:29.410
between the British Empire
and the Russian Empire,

00:03:29.410 --> 00:03:32.630
to essentially get on good
terms with each other.

00:03:32.630 --> 00:03:34.027
These weren't as
formally bonding

00:03:34.027 --> 00:03:35.860
that, hey, if someone's
going to attack you,

00:03:35.860 --> 00:03:37.460
I'm going to attack them.

00:03:37.460 --> 00:03:39.400
But they were, essentially,
able to resolve

00:03:39.400 --> 00:03:41.390
a lot of their issues
on what's going on

00:03:41.390 --> 00:03:43.850
in their other
imperial conquests.

00:03:43.850 --> 00:03:46.950
And they formed what is
called the Triple Entente,

00:03:46.950 --> 00:03:50.070
the triple agreement
between Britain,

00:03:50.070 --> 00:03:52.580
between the British Empire--
and right here, I just

00:03:52.580 --> 00:03:57.370
circled the United Kingdom--
France, and Russia.

00:03:57.370 --> 00:04:00.070
And on the other side of that,
you had the Triple Alliance.

00:04:00.070 --> 00:04:00.830
You have Germany.

00:04:00.830 --> 00:04:02.300
You have Austria-Hungary.

00:04:02.300 --> 00:04:06.130
And you also have Italy.

00:04:06.130 --> 00:04:09.100
Now, the reason why, even though
entering into World War I,

00:04:09.100 --> 00:04:11.570
Italy was formerly part
of the Triple Alliance.

00:04:11.570 --> 00:04:14.140
And there were treaties
between Italy and Germany

00:04:14.140 --> 00:04:16.209
to become part of
this Triple Alliance.

00:04:16.209 --> 00:04:18.810
The reason I don't focus on
those is once the war started,

00:04:18.810 --> 00:04:24.280
Italy did not go on the side
of Germany and Austria-Hungary.

00:04:24.280 --> 00:04:26.570
It went on the
side of the Allies,

00:04:26.570 --> 00:04:29.294
on the side of the
Triple Entente.

00:04:29.294 --> 00:04:30.960
But this will give
you a good background

00:04:30.960 --> 00:04:36.360
for why what would seem like a
regional skirmish in southeast

00:04:36.360 --> 00:04:42.457
Europe turns into a pan-Europe
and eventually pan-global war.


Empires before World War I

WEBVTT
Kind: captions
Language: en

00:00:00.660 --> 00:00:03.220
A lot of people,
including myself,

00:00:03.220 --> 00:00:04.650
have found the
study of World War

00:00:04.650 --> 00:00:07.520
I to be a little bit
confusing sometimes.

00:00:07.520 --> 00:00:09.180
And I think the
reason is is the world

00:00:09.180 --> 00:00:12.690
was very different leading up
to World War I than it is today.

00:00:12.690 --> 00:00:14.970
And to some degree, the
modern world we live in

00:00:14.970 --> 00:00:16.930
was shaped to a large
degree by Word War

00:00:16.930 --> 00:00:18.471
I and then later World War II.

00:00:18.471 --> 00:00:20.970
And just to get a sense of what
our modern world looks like,

00:00:20.970 --> 00:00:23.240
and especially what
modern Europe looks like,

00:00:23.240 --> 00:00:26.460
this is a map of modern Europe.

00:00:26.460 --> 00:00:28.660
But the interesting
thing about this map

00:00:28.660 --> 00:00:30.660
is instead of being the
traditional map that you

00:00:30.660 --> 00:00:32.951
normally see where you just
see the country boundaries,

00:00:32.951 --> 00:00:35.471
the state boundaries, this
has the state boundaries right

00:00:35.471 --> 00:00:35.970
here.

00:00:35.970 --> 00:00:37.870
And these little gray
lines, these show

00:00:37.870 --> 00:00:41.080
where France ends and, say,
Switzerland or Germany or Italy

00:00:41.080 --> 00:00:41.870
begins.

00:00:41.870 --> 00:00:44.410
But overlain on
top of that we see

00:00:44.410 --> 00:00:46.262
where the languages are spoken.

00:00:46.262 --> 00:00:47.970
So this is actually
much more focused on,

00:00:47.970 --> 00:00:49.178
where do people speak French.

00:00:49.178 --> 00:00:50.770
Where do people speak German?

00:00:50.770 --> 00:00:53.210
And the thing that you will
notice is, for the most part,

00:00:53.210 --> 00:00:56.030
throughout most of Europe,
today's boundaries,

00:00:56.030 --> 00:00:59.000
the modern boundaries
closely, closely match

00:00:59.000 --> 00:01:01.210
up to where
languages are spoken.

00:01:01.210 --> 00:01:03.330
There are a few
areas where there

00:01:03.330 --> 00:01:05.650
is more of a disconnect
with Catalan and Spanish.

00:01:05.650 --> 00:01:08.680
And actually, that is
leading to some issues.

00:01:08.680 --> 00:01:11.270
But for the most part,
in modern Europe,

00:01:11.270 --> 00:01:13.970
the country boundaries and
the linguistic boundaries

00:01:13.970 --> 00:01:17.710
or the national boundaries
kind of match up.

00:01:17.710 --> 00:01:21.600
If we rewind to the world of
entering into World War I,

00:01:21.600 --> 00:01:23.250
things were very different.

00:01:23.250 --> 00:01:24.930
Some of the boundaries
we recognize.

00:01:24.930 --> 00:01:29.020
We recognize the United Kingdom.

00:01:29.020 --> 00:01:31.580
Well, Ireland has
since been carved out.

00:01:31.580 --> 00:01:33.820
But we recognize it
as not being that

00:01:33.820 --> 00:01:34.994
different than it is today.

00:01:34.994 --> 00:01:36.160
Spain is not that different.

00:01:36.160 --> 00:01:37.410
France is not that different.

00:01:37.410 --> 00:01:39.380
Italy is not that different.

00:01:39.380 --> 00:01:41.490
Germany is a good bit different.

00:01:41.490 --> 00:01:45.210
In fact, if you take Germany,
the German Empire entering

00:01:45.210 --> 00:01:47.760
into World War I,
or the early 1900s,

00:01:47.760 --> 00:01:51.230
around 1914, between them
and the Russian Empire,

00:01:51.230 --> 00:01:58.200
they essentially were swallowing
up a bunch of linguistic groups

00:01:58.200 --> 00:02:01.970
right over here that now have
their own independent states.

00:02:01.970 --> 00:02:03.880
The other thing that
you might notice

00:02:03.880 --> 00:02:08.270
is this huge state called
Austria-Hungary, or often

00:02:08.270 --> 00:02:10.509
called the
Austro-Hungarian Empire.

00:02:10.509 --> 00:02:13.639
And people say, well, there's--
I'm familiar with some of these

00:02:13.639 --> 00:02:15.930
nations that have the word
Austria and Hungary in them,

00:02:15.930 --> 00:02:19.360
but I'm not-- what is this
Austro-Hungarian Empire?

00:02:19.360 --> 00:02:21.940
And what's interesting about
it is it really was an empire.

00:02:21.940 --> 00:02:24.350
It was really trying
to cobble together

00:02:24.350 --> 00:02:26.782
all of these folks that
spoke all different-- all

00:02:26.782 --> 00:02:28.240
the different types
of ethnicities.

00:02:28.240 --> 00:02:33.050
This is kind of a zoom-in of the
Austro-Hungarian Empire leading

00:02:33.050 --> 00:02:34.500
into World War I.

00:02:34.500 --> 00:02:38.240
And the Austro-Hungarian Empire
is probably the most important

00:02:38.240 --> 00:02:39.700
thing to understand
if we're trying

00:02:39.700 --> 00:02:43.800
to get a sense of how World War
I started, because leading up

00:02:43.800 --> 00:02:46.780
to World War I, in 1908,
the Austro-Hungarian

00:02:46.780 --> 00:02:50.530
Empire formally annexed
Bosnia and Herzegovina.

00:02:50.530 --> 00:02:52.670
And that's another confusing
thing for many of us,

00:02:52.670 --> 00:02:54.390
that that's actually
one country.

00:02:54.390 --> 00:02:56.390
It's called Bosnia
and Herzegovina,

00:02:56.390 --> 00:02:59.090
or I guess for the
Austro-Hungarians that was now

00:02:59.090 --> 00:03:01.700
one region that they annexed.

00:03:01.700 --> 00:03:03.700
And what's
interesting about that

00:03:03.700 --> 00:03:06.080
is if you look at
the linguistic map,

00:03:06.080 --> 00:03:08.310
you see that this whole
region right over here

00:03:08.310 --> 00:03:10.430
speaks a very similar--
essentially, they're

00:03:10.430 --> 00:03:12.990
dialects of Serbian,
Croatian, Bosnian.

00:03:12.990 --> 00:03:16.160
They're all very linguistically
and ethnically connected,

00:03:16.160 --> 00:03:19.440
so this whole region
right over here

00:03:19.440 --> 00:03:22.950
is linguistically and
ethnically connected.

00:03:22.950 --> 00:03:25.080
And what we'll see is,
is that this desire

00:03:25.080 --> 00:03:31.050
to connect people with similar
ethnic or linguistic roots--

00:03:31.050 --> 00:03:34.510
linguistic backgrounds is what
led to a lot of what happened

00:03:34.510 --> 00:03:37.490
in World War-- or at
least was the spark that

00:03:37.490 --> 00:03:38.940
fueled, that people
sometimes say,

00:03:38.940 --> 00:03:41.780
the powder keg of World War I.

00:03:41.780 --> 00:03:43.980
The other thing that
was a very different

00:03:43.980 --> 00:03:47.100
or the other country
or nation or empire

00:03:47.100 --> 00:03:51.260
that we are not used to
today is the Ottoman Empire.

00:03:51.260 --> 00:03:53.880
So if we go today,
we see the country

00:03:53.880 --> 00:03:56.770
of Turkey, which is on
the Anatolian Peninsula.

00:03:56.770 --> 00:03:59.900
So this is Turkey
right over here.

00:03:59.900 --> 00:04:01.460
This is modern-day Turkey.

00:04:01.460 --> 00:04:05.070
But entering into
World War I in 1914,

00:04:05.070 --> 00:04:07.870
Turkey was essentially part
of the remnants of the Ottoman

00:04:07.870 --> 00:04:09.230
Empire.

00:04:09.230 --> 00:04:11.920
So this right over here is what
the Ottoman Empire looked like.

00:04:11.920 --> 00:04:14.970
This right over here is
roughly modern-day Turkey.

00:04:14.970 --> 00:04:17.790
But the Ottoman Empire
consisted of modern-day Turkey

00:04:17.790 --> 00:04:20.200
and much of the
modern Middle East.

00:04:20.200 --> 00:04:23.530
So much of-- especially,
much of the Arab-- especially

00:04:23.530 --> 00:04:28.080
the Arab world around
Syria, Iraq, Lebanon,

00:04:28.080 --> 00:04:30.250
much of what where
modern-day Israel is,

00:04:30.250 --> 00:04:32.160
some of Saudi Arabia.

00:04:32.160 --> 00:04:35.010
And this was really the dying
state of the Ottoman Empire.

00:04:35.010 --> 00:04:37.390
At its peak, it controlled
much of the Muslim world.

00:04:37.390 --> 00:04:40.220
It controlled Northern Africa
as well as all the stuff

00:04:40.220 --> 00:04:43.760
you see here and even
a little bit of Persia

00:04:43.760 --> 00:04:46.310
and actually a good bit of
the Balkans, southeast Europe,

00:04:46.310 --> 00:04:48.720
and even Greece at the
peak of its Ottoman Empire.

00:04:48.720 --> 00:04:51.310
And now I'm talking about going
hundreds and hundreds of years

00:04:51.310 --> 00:04:52.770
back into the past.

00:04:52.770 --> 00:04:54.570
So when we enter
into World War II,

00:04:54.570 --> 00:04:57.190
we don't have a world
where people are,

00:04:57.190 --> 00:04:59.790
where states are defined
by linguistic boundaries

00:04:59.790 --> 00:05:00.930
or by ethnic boundaries.

00:05:00.930 --> 00:05:03.050
To a large degree,
we had these empires

00:05:03.050 --> 00:05:06.670
that had existed as we
exited out of the 1800s.

00:05:06.670 --> 00:05:08.750
And these empires were
not just in Europe,

00:05:08.750 --> 00:05:12.650
like the Austro-Hungarian Empire
or not just in the Middle East,

00:05:12.650 --> 00:05:14.420
like the Ottoman Empire.

00:05:14.420 --> 00:05:20.090
Right over here is an empire map
at around that point in time.

00:05:20.090 --> 00:05:23.040
And you see, probably the
most dominant feature here

00:05:23.040 --> 00:05:24.530
is the British Empire.

00:05:24.530 --> 00:05:25.970
That's in this pink color.

00:05:25.970 --> 00:05:28.360
So British, that's
the United Kingdom.

00:05:28.360 --> 00:05:31.230
Great Britain would just
be this right over here.

00:05:31.230 --> 00:05:32.250
You throw in Ireland.

00:05:32.250 --> 00:05:34.220
You get the United Kingdom.

00:05:34.220 --> 00:05:37.320
Great Britain was in
control of the Indian,

00:05:37.320 --> 00:05:41.290
the entire Indian subcontinent. It was essentially

00:05:41.290 --> 00:05:44.517
although nominally Egypt
was somewhat independent,

00:05:44.517 --> 00:05:46.600
Great Britain had a huge
amount of influence here.

00:05:46.600 --> 00:05:52.570
Obviously places like Canada
and Australia and New Zealand

00:05:52.570 --> 00:05:55.984
were under control of or a
part of the British Empire.

00:05:55.984 --> 00:05:57.400
What a lot of
people don't realize

00:05:57.400 --> 00:06:00.670
is a significant amount
of Africa as well.

00:06:00.670 --> 00:06:07.240
A significant amount of Africa
was also under British control.

00:06:07.240 --> 00:06:10.330
And what we have running
up into World War

00:06:10.330 --> 00:06:14.490
I is kind of a race
for empire, an arms

00:06:14.490 --> 00:06:17.370
race between the major
powers of Europe.

00:06:17.370 --> 00:06:21.060
In particular, you have Great
Britain, or the United Kingdom,

00:06:21.060 --> 00:06:22.972
that obviously
had a vast empire.

00:06:22.972 --> 00:06:24.680
The sun never sets on
the British Empire.

00:06:24.680 --> 00:06:26.440
And it wasn't ever
setting on this empire

00:06:26.440 --> 00:06:27.810
that we just saw here.

00:06:27.810 --> 00:06:31.450
And the German Empire was also
starting to flex its muscle

00:06:31.450 --> 00:06:33.751
and starting to militarize.

00:06:33.751 --> 00:06:36.000
And the more that the German
saw that the British were

00:06:36.000 --> 00:06:38.770
militarizing, the more
that the British--

00:06:38.770 --> 00:06:41.546
the more that the Germans would
want to militarize and vice

00:06:41.546 --> 00:06:43.170
versa, and you just
had this arms race.

00:06:43.170 --> 00:06:45.420
And they were all trying
to build their empires.

00:06:45.420 --> 00:06:48.690
So the Germans, they
were present in Africa.

00:06:48.690 --> 00:06:51.741
You have the French who were
present in much of Africa.

00:06:51.741 --> 00:06:53.740
And you have to remember
all of this in context.

00:06:53.740 --> 00:06:57.140
Some of this empire building
was, frankly, just about ego

00:06:57.140 --> 00:06:59.340
and just about spreading
someone's influence,

00:06:59.340 --> 00:07:01.190
spreading their power.

00:07:01.190 --> 00:07:06.490
A lot of it was based on ethnic
beliefs about civilization.

00:07:06.490 --> 00:07:08.680
I guess these were
rationalization to take control

00:07:08.680 --> 00:07:10.420
of other people's resources.

00:07:10.420 --> 00:07:12.640
And a lot of it was
we were in a world

00:07:12.640 --> 00:07:15.700
where access to resources--
in particular, access

00:07:15.700 --> 00:07:19.380
to raw materials and especially
oil-- could, to some degree,

00:07:19.380 --> 00:07:24.580
define whether a power
was a power at all.

00:07:24.580 --> 00:07:27.250
And so with that, I think
we have a pretty good basis

00:07:27.250 --> 00:07:33.930
for the state of affairs as
we enter into World War I.


Bringing the set operations together

WEBVTT
Kind: captions
Language: en

00:00:00.550 --> 00:00:02.380
Let's now use our
understanding of some

00:00:02.380 --> 00:00:06.210
of the operations on sets
to get some blood flowing

00:00:06.210 --> 00:00:07.670
to our brains.

00:00:07.670 --> 00:00:09.031
So I've defined some sets here.

00:00:09.031 --> 00:00:10.530
And just to make
things interesting,

00:00:10.530 --> 00:00:12.238
I haven't only put
numbers in these sets.

00:00:12.238 --> 00:00:15.580
I've even put some colors and
some little yellow stars here.

00:00:15.580 --> 00:00:16.970
And what I want
you to figure out

00:00:16.970 --> 00:00:19.890
is what would this set
be, this crazy thing that

00:00:19.890 --> 00:00:23.660
involves relative complements,
intersections, unions,

00:00:23.660 --> 00:00:24.957
absolute complements.

00:00:24.957 --> 00:00:26.540
So I encourage you
to pause it and try

00:00:26.540 --> 00:00:30.336
to figure out what
this set would be.

00:00:30.336 --> 00:00:31.460
Well, let's give it a shot.

00:00:31.460 --> 00:00:33.790
And the key here is to
really break it down, work

00:00:33.790 --> 00:00:35.945
on the stuff in the
parentheses first,

00:00:35.945 --> 00:00:37.570
just as you would do
if you were trying

00:00:37.570 --> 00:00:40.010
to parse a traditional
mathematical statement.

00:00:40.010 --> 00:00:42.720
And then it should hopefully
make a little bit of sense.

00:00:42.720 --> 00:00:44.740
So a good place
to start might be

00:00:44.740 --> 00:00:48.415
to try to figure out what is the
relative complement of C in B.

00:00:48.415 --> 00:00:51.220
Or another way of thinking
about it is what is B minus C?

00:00:51.220 --> 00:00:53.850
What is B if you take out
all the stuff with C in it?

00:00:53.850 --> 00:00:55.240
So let me write this down.

00:00:55.240 --> 00:00:57.830
The relative complement
of C and B or you

00:00:57.830 --> 00:01:01.380
could call this B minus C.
This is all the stuff in B

00:01:01.380 --> 00:01:04.019
with all the stuff
in C taken out of it.

00:01:04.019 --> 00:01:05.880
So let's think about
what this would be.

00:01:05.880 --> 00:01:06.950
B has a 0.

00:01:06.950 --> 00:01:08.370
Does C have a 0?

00:01:08.370 --> 00:01:11.180
No, so we don't have
to take out the 0.

00:01:11.180 --> 00:01:12.300
B has a 17.

00:01:12.300 --> 00:01:13.270
Does C have a 17?

00:01:13.270 --> 00:01:13.980
Yes, it does.

00:01:13.980 --> 00:01:15.640
So we take out the 17.

00:01:15.640 --> 00:01:17.920
B has a 3, but c has a 3.

00:01:17.920 --> 00:01:19.340
So we take that out.

00:01:19.340 --> 00:01:21.410
B has a Blue.

00:01:21.410 --> 00:01:22.930
C does not have a blue.

00:01:22.930 --> 00:01:24.490
So we leave the Blue in.

00:01:24.490 --> 00:01:27.790
So let me write down--
we leave the blue in.

00:01:27.790 --> 00:01:30.020
And then B has a gold star.

00:01:30.020 --> 00:01:31.410
C also has a gold star.

00:01:31.410 --> 00:01:33.340
So we take the gold star out.

00:01:33.340 --> 00:01:38.270
So the relative complement of
C in B is just the set of 0

00:01:38.270 --> 00:01:40.160
and this Blue written in blue.

00:01:40.160 --> 00:01:42.510
So let me write this down.

00:01:42.510 --> 00:01:44.999
Let me write that down.

00:01:44.999 --> 00:01:46.040
Now, it gets interesting.

00:01:46.040 --> 00:01:48.360
We're going to take the
absolute complement,

00:01:48.360 --> 00:01:50.530
the absolute complement of that.

00:01:50.530 --> 00:01:51.613
So let me write this down.

00:01:51.613 --> 00:01:57.880
So B-- the absolute
complement of this business

00:01:57.880 --> 00:02:01.920
is going to be-- let me write
it this-- the set of all things

00:02:01.920 --> 00:02:21.450
in our universe that are
neither a 0 or a-- and I'll

00:02:21.450 --> 00:02:24.757
write it in blue-- or a Blue.

00:02:24.757 --> 00:02:26.840
That's the only way I could
describe it right now.

00:02:26.840 --> 00:02:28.679
I haven't really defined
the universe well.

00:02:28.679 --> 00:02:30.470
We already see that
our universe definitely

00:02:30.470 --> 00:02:32.790
contains some integers,
it contains colors,

00:02:32.790 --> 00:02:34.307
it contains some stars.

00:02:34.307 --> 00:02:35.640
So this is all I can really say.

00:02:35.640 --> 00:02:38.223
This is the set of all things
in the universe that are neither

00:02:38.223 --> 00:02:39.240
a 0 or a Blue.

00:02:39.240 --> 00:02:39.940
So fair enough.

00:02:39.940 --> 00:02:44.690
So we so far we figured
out all of this stuff.

00:02:44.690 --> 00:02:45.850
Let me box this off.

00:02:45.850 --> 00:02:48.390
So that is that
right over there.

00:02:48.390 --> 00:02:51.310
And now we want to
find the intersection.

00:02:51.310 --> 00:02:56.065
We need to find the intersection
of A and this business.

00:02:58.782 --> 00:02:59.740
Let me write that down.

00:02:59.740 --> 00:03:02.710
So it's going to
be A intersected

00:03:02.710 --> 00:03:06.010
with the relative
complement of C and B

00:03:06.010 --> 00:03:08.660
and the absolute
complement of that.

00:03:08.660 --> 00:03:11.030
So this is going to be the
intersection of the set

00:03:11.030 --> 00:03:15.070
A and the set of all things in
the universe that are neither

00:03:15.070 --> 00:03:17.460
a 0 or a Blue.

00:03:17.460 --> 00:03:19.000
So it's essentially
the things that

00:03:19.000 --> 00:03:23.030
satisfy both of these
that has to be in set A

00:03:23.030 --> 00:03:25.290
and it has to be in
the set of all things

00:03:25.290 --> 00:03:28.270
in the universe that are
neither a 0 or a blue.

00:03:28.270 --> 00:03:30.140
So let's think
about what this is.

00:03:30.140 --> 00:03:33.500
So the number 3 is in set A and
it's in the set of all things

00:03:33.500 --> 00:03:35.650
in the universe that
are neither a 0 or Blue.

00:03:35.650 --> 00:03:37.450
So let's throw a 3 in there.

00:03:37.450 --> 00:03:39.590
The number 7, it's in
A and it's in the set

00:03:39.590 --> 00:03:42.750
of all things in the universe
that are neither a 0 or a Blue.

00:03:42.750 --> 00:03:44.470
So let's put a 7 there.

00:03:44.470 --> 00:03:48.120
Negative 5 also meets
that constraint.

00:03:48.120 --> 00:03:50.540
A 0 does not meet
that constraint.

00:03:50.540 --> 00:03:52.804
A 0 is in A but
it's not in the set

00:03:52.804 --> 00:03:54.720
of all things in the
universe that are neither

00:03:54.720 --> 00:03:56.500
a 0 or blue because it is a 0.

00:03:56.500 --> 00:03:58.650
So we're not going
to throw 0 in there.

00:03:58.650 --> 00:04:00.940
And then a 13 is in
A and it's in the set

00:04:00.940 --> 00:04:04.010
of all things in the universe
that are neither a 0 or a Blue.

00:04:04.010 --> 00:04:06.650
So we could throw a 13 in there.

00:04:06.650 --> 00:04:08.680
So we've simplified
things a good bit.

00:04:08.680 --> 00:04:12.210
This whole crazy business,
all of this crazy business,

00:04:12.210 --> 00:04:15.570
has simplified to this
set right over here.

00:04:15.570 --> 00:04:19.660
Now we want to find the relative
complement of this business

00:04:19.660 --> 00:04:22.140
in A. So let me pick
another color here.

00:04:22.140 --> 00:04:25.110
So we want to find the relative
complement of this business

00:04:25.110 --> 00:04:31.645
in A. And I'll just write out
the set-- 3, 7, negative 5, 13.

00:04:31.645 --> 00:04:33.270
Actually, let me
write out both of them

00:04:33.270 --> 00:04:36.880
just so that we can
really visualize

00:04:36.880 --> 00:04:38.030
them both right over here.

00:04:38.030 --> 00:04:40.910
So A is this.

00:04:40.910 --> 00:04:48.460
It is 3, 7, negative
5, 0, and 13.

00:04:48.460 --> 00:04:50.420
And I could write the
relative complement sign.

00:04:50.420 --> 00:04:51.560
Or actually, let me
just write m-- well

00:04:51.560 --> 00:04:52.934
let me write
relative complement.

00:04:52.934 --> 00:04:54.280
I was going to write minus.

00:04:54.280 --> 00:04:56.800
And so in all of this business,
we already figured out,

00:04:56.800 --> 00:05:01.550
is a 3, a 7, a
negative 5, and a 13.

00:05:01.550 --> 00:05:03.621
So it's essentially,
start with this set

00:05:03.621 --> 00:05:05.620
and take out all the stuff
that are in this set.

00:05:05.620 --> 00:05:07.660
So this is going to
be equal to-- so you

00:05:07.660 --> 00:05:10.884
see we're going to have to
take out a 3 out of this set.

00:05:10.884 --> 00:05:12.050
We're going to take out a 7.

00:05:12.050 --> 00:05:13.270
We're going to get a negative 5.

00:05:13.270 --> 00:05:14.750
And we're going
to take out a 13.

00:05:14.750 --> 00:05:18.560
So we're just left with
the set that contains a 0.

00:05:18.560 --> 00:05:20.470
So all of this business
right over here

00:05:20.470 --> 00:05:25.500
has simplified to a set
that only contains a 0.

00:05:25.500 --> 00:05:30.590
Now let's think about
what B intersect C is.

00:05:30.590 --> 00:05:34.170
These are all the things
that are in both B and C.

00:05:34.170 --> 00:05:38.340
So this is going to be B
intersect C. Let's see,

00:05:38.340 --> 00:05:40.250
0 is not in both of them.

00:05:40.250 --> 00:05:42.260
17 is in both of them.

00:05:42.260 --> 00:05:44.240
So we'll throw 17 in there.

00:05:44.240 --> 00:05:47.419
The number 3 is in both
of them, the number 3

00:05:47.419 --> 00:05:48.210
is in both of them.

00:05:48.210 --> 00:05:50.840
Blue is not in both of them.

00:05:50.840 --> 00:05:53.000
The star is in both of them.

00:05:53.000 --> 00:05:55.450
So I'll put the little
gold star right over there.

00:05:55.450 --> 00:05:57.077
And so that's B intersect C.

00:05:57.077 --> 00:05:58.660
And so we're essentially
going to take

00:05:58.660 --> 00:06:00.785
the union of this crazy
thing-- which ended up just

00:06:00.785 --> 00:06:03.310
being a set with a 0 in it--
we're taking the union of that

00:06:03.310 --> 00:06:06.850
and B intersect C. We
deserve a drum roll now.

00:06:06.850 --> 00:06:09.490
This is all going to be
equal to-- we're just

00:06:09.490 --> 00:06:10.910
going to combine these two sets.

00:06:10.910 --> 00:06:15.550
It's going to be the set
with a 0, a 17, a three,

00:06:15.550 --> 00:06:16.930
and our gold star.

00:06:19.440 --> 00:06:24.950
And we are-- I should make the
brackets in a different color--

00:06:24.950 --> 00:06:27.380
and we are done.


Subset, strict subset, and superset

WEBVTT
Kind: captions
Language: en

00:00:00.680 --> 00:00:02.740
Let's define
ourselves some sets.

00:00:02.740 --> 00:00:08.530
So let's say the set A is
composed of the numbers 1.

00:00:08.530 --> 00:00:09.510
3.

00:00:09.510 --> 00:00:13.880
5, 7, and 18.

00:00:13.880 --> 00:00:16.980
Let's say that
the set B-- let me

00:00:16.980 --> 00:00:18.640
do this in a different
color-- let's

00:00:18.640 --> 00:00:26.010
say that the set B is
composed of 1, 7, and 18.

00:00:26.010 --> 00:00:38.522
And let's say that the set C is
composed of 18, 7, 1, and 19.

00:00:38.522 --> 00:00:40.730
Now what I want to start
thinking about in this video

00:00:40.730 --> 00:00:42.950
is the notion of a subset.

00:00:42.950 --> 00:00:48.752
So the first question
is, is B a subset of A?

00:00:48.752 --> 00:00:50.960
And there you might say,
well, what does subset mean?

00:00:50.960 --> 00:00:53.590
Well, you're a subset if
every member of your set

00:00:53.590 --> 00:00:56.410
is also a member
of the other set.

00:00:56.410 --> 00:01:01.976
So we actually can write
that B is a subset--

00:01:01.976 --> 00:01:03.600
and this is a notation
right over here,

00:01:03.600 --> 00:01:08.647
this is a subset-- B is a
subset of A. B is a subset.

00:01:08.647 --> 00:01:09.730
So let me write that down.

00:01:09.730 --> 00:01:19.260
B is subset of A. Every
element in B is a member of A.

00:01:19.260 --> 00:01:21.040
Now we can go even further.

00:01:21.040 --> 00:01:23.950
We can say that B is
a strict subset of A,

00:01:23.950 --> 00:01:26.830
because B is a subset
of A, but it does not

00:01:26.830 --> 00:01:29.850
equal A, which means that there
are things in A that are not

00:01:29.850 --> 00:01:32.680
in B. So we could
even go further

00:01:32.680 --> 00:01:34.750
and we could say
that B is a strict

00:01:34.750 --> 00:01:37.245
or sometimes said a
proper subset of A.

00:01:37.245 --> 00:01:39.690
And the way you do that
is, you could almost

00:01:39.690 --> 00:01:42.380
imagine that this is kind of
a less than or equal sign,

00:01:42.380 --> 00:01:44.590
and then you kind of
cross out this equal part

00:01:44.590 --> 00:01:46.080
of the less than or equal sign.

00:01:46.080 --> 00:01:48.440
So this means a
strict subset, which

00:01:48.440 --> 00:01:51.770
means everything that
is in B is a member A,

00:01:51.770 --> 00:01:54.060
but everything that's in
A is not a member of B.

00:01:54.060 --> 00:01:55.050
So let me write this.

00:01:55.050 --> 00:02:03.920
This is B. B is a
strict or proper subset.

00:02:03.920 --> 00:02:09.475
So, for example, we can write
that A is a subset of A.

00:02:09.475 --> 00:02:12.350
In fact, every set is
a subset of itself,

00:02:12.350 --> 00:02:16.330
because every one of its
members is a member of A.

00:02:16.330 --> 00:02:21.480
We cannot write that A
is a strict subset of A.

00:02:21.480 --> 00:02:26.310
This right over here is false.

00:02:26.310 --> 00:02:29.250
So let's give ourselves a
little bit more practice.

00:02:29.250 --> 00:02:37.082
Can we write that
B is a subset of C?

00:02:40.639 --> 00:02:41.305
Well, let's see.

00:02:41.305 --> 00:02:45.320
C contains a 1, it contains
a 7, it contains an 18.

00:02:45.320 --> 00:02:47.940
So every member of
B is indeed a member

00:02:47.940 --> 00:02:51.640
C. So this right
over here is true.

00:02:51.640 --> 00:02:54.380
Now, can we write
that C is a subset?

00:02:54.380 --> 00:03:00.665
Can we write that
C is a subset of A?

00:03:00.665 --> 00:03:04.490
Can we write C is a subset of A?

00:03:04.490 --> 00:03:05.700
Let's see.

00:03:05.700 --> 00:03:09.940
Every element of C needs
to be in A. So A has an 18,

00:03:09.940 --> 00:03:11.940
it has a 7, it has a 1.

00:03:11.940 --> 00:03:13.910
But it does not have a 19.

00:03:13.910 --> 00:03:20.196
So once again, this
right over here is false.

00:03:20.196 --> 00:03:21.570
Now we could have
also added-- we

00:03:21.570 --> 00:03:23.710
could write B is a subset
of C. Or we could even

00:03:23.710 --> 00:03:28.260
write that B is a
strict subset of C.

00:03:28.260 --> 00:03:32.145
Now, we could also reverse
the way we write this.

00:03:32.145 --> 00:03:34.270
And then we're really just
talking about supersets.

00:03:34.270 --> 00:03:36.110
So we could reverse
this notation,

00:03:36.110 --> 00:03:43.015
and we could say that
A is a superset of B,

00:03:43.015 --> 00:03:45.640
and this is just another way of
saying that B is a subset of A.

00:03:45.640 --> 00:03:49.400
But the way you could
think about this is,

00:03:49.400 --> 00:03:53.570
A contains every
element that is in B.

00:03:53.570 --> 00:03:55.100
And it might contain more.

00:03:55.100 --> 00:03:56.970
It might contain
exactly every element.

00:03:56.970 --> 00:03:59.452
So you can kind of view
this as you kind of

00:03:59.452 --> 00:04:00.660
have the equals symbol there.

00:04:00.660 --> 00:04:02.870
If you were to view this
as greater than or equal.

00:04:02.870 --> 00:04:04.837
They're note quite
exactly the same thing.

00:04:04.837 --> 00:04:06.420
But we know already
that we could also

00:04:06.420 --> 00:04:13.320
write that A is a strict
superset of B, which

00:04:13.320 --> 00:04:17.140
means that A contains
everything B has and then some.

00:04:17.140 --> 00:04:21.690
A is not equivalent to B. So
hopefully this familiarizes you

00:04:21.690 --> 00:04:31.130
with the notions of subsets and
supersets and strict subsets.


Universal set and absolute complement

WEBVTT
Kind: captions
Language: en

00:00:00.454 --> 00:00:01.870
What I want to do
in this video is

00:00:01.870 --> 00:00:04.610
introduce the idea
of a universal set,

00:00:04.610 --> 00:00:07.870
or the universe that we care
about, and also the idea

00:00:07.870 --> 00:00:10.674
of a complement, or an
absolute complement.

00:00:10.674 --> 00:00:12.340
If we're for doing
it as a Venn diagram,

00:00:12.340 --> 00:00:14.690
the universe is usually
depicted as some type

00:00:14.690 --> 00:00:16.820
of a rectangle right over here.

00:00:16.820 --> 00:00:18.930
And it itself is a set.

00:00:18.930 --> 00:00:21.110
And it usually is denoted
with the capital U--

00:00:21.110 --> 00:00:24.700
U for universe-- not to be
confused with the union set

00:00:24.700 --> 00:00:25.780
notation.

00:00:25.780 --> 00:00:27.490
And you could say
that the universe

00:00:27.490 --> 00:00:30.530
is all possible things
that could be in a set,

00:00:30.530 --> 00:00:34.500
including farm animals
and kitchen utensils

00:00:34.500 --> 00:00:38.450
and emotions and
types of Italian food

00:00:38.450 --> 00:00:40.770
or even types of food.

00:00:40.770 --> 00:00:43.780
But then that just
becomes somewhat crazy,

00:00:43.780 --> 00:00:46.650
because you're thinking
of all possible things.

00:00:46.650 --> 00:00:49.164
Normally when people talk
about a universal set,

00:00:49.164 --> 00:00:51.830
they're talking about a universe
of things that they care about.

00:00:51.830 --> 00:00:54.910
So the set of all people or
the set of all real numbers

00:00:54.910 --> 00:00:57.390
or the set of all countries,
whatever the discussion

00:00:57.390 --> 00:00:58.560
is being focused on.

00:00:58.560 --> 00:01:00.915
But we'll talk about in
abstract terms right now.

00:01:00.915 --> 00:01:08.750
Now, let's say you have a subset
of that universal set, set A.

00:01:08.750 --> 00:01:11.910
And so set A literally
contains everything

00:01:11.910 --> 00:01:13.680
that I have just shaded in.

00:01:13.680 --> 00:01:15.140
What we're going
to talk about now

00:01:15.140 --> 00:01:20.867
is the idea of a complement, or
the absolute complement of A.

00:01:20.867 --> 00:01:22.450
And the way you could
think about this

00:01:22.450 --> 00:01:31.110
is this is the set of all
things in the universe that

00:01:31.110 --> 00:01:35.360
aren't in A. And
we've already looked

00:01:35.360 --> 00:01:37.190
at ways of expressing this.

00:01:37.190 --> 00:01:39.770
The set of all things in the
universe that aren't in A,

00:01:39.770 --> 00:01:43.240
we could also write as
a universal set minus A.

00:01:43.240 --> 00:01:45.890
Once again, this is a
capital U. This is not

00:01:45.890 --> 00:01:48.110
the union symbol
right over here.

00:01:48.110 --> 00:01:51.370
Or we could literally
write this as U,

00:01:51.370 --> 00:01:56.640
and then we write that little
slash-looking thing, U slash A.

00:01:56.640 --> 00:01:58.710
So how do we represent
that in the Venn diagram?

00:01:58.710 --> 00:02:05.389
Well, it would be all the stuff
in U that is not in A. One way

00:02:05.389 --> 00:02:07.180
to think about it, you
could think about it

00:02:07.180 --> 00:02:10.104
as the relative complement
of A that is in U.

00:02:10.104 --> 00:02:12.020
But when you're taking
the relative complement

00:02:12.020 --> 00:02:14.020
of something that is
in the universal set,

00:02:14.020 --> 00:02:16.364
you're really talking about
the absolute complement.

00:02:16.364 --> 00:02:18.280
Or when people just talk
about the complement,

00:02:18.280 --> 00:02:19.100
that's what they're saying.

00:02:19.100 --> 00:02:21.250
What's the set of all
the things in my universe

00:02:21.250 --> 00:02:25.139
that are not in A.

00:02:25.139 --> 00:02:27.180
Now, let's make things a
little bit more concrete

00:02:27.180 --> 00:02:28.860
by talking about
sets of numbers.

00:02:28.860 --> 00:02:31.360
Once again, our sets-- we could
have been talking about sets

00:02:31.360 --> 00:02:34.210
of TV personalities
or sets of animals

00:02:34.210 --> 00:02:35.210
or whatever it might be.

00:02:35.210 --> 00:02:38.050
But numbers are a nice,
simple thing to deal with.

00:02:38.050 --> 00:02:40.850
And let's say that
our universe that we

00:02:40.850 --> 00:02:45.040
care about right over here
is the set of integers.

00:02:45.040 --> 00:02:47.880
So our universe is
the set of integers.

00:02:47.880 --> 00:02:49.900
So I'll just write
U-- capital U--

00:02:49.900 --> 00:02:51.370
is equal to the set of integers.

00:02:51.370 --> 00:02:53.090
And this is a little
bit of an aside,

00:02:53.090 --> 00:02:57.410
but the notation for the set of
integers tends to be a bold Z.

00:02:57.410 --> 00:03:01.294
And it's Z for Zahlen, from
German, for apparently integer.

00:03:01.294 --> 00:03:02.710
And the bold is
this kind of weird

00:03:02.710 --> 00:03:05.290
looking- they call
it blackboard bold.

00:03:05.290 --> 00:03:07.820
And it's what mathematicians
use for different types of sets

00:03:07.820 --> 00:03:08.550
of numbers.

00:03:08.550 --> 00:03:10.570
In fact, I'll do a little
aside here to do that.

00:03:10.570 --> 00:03:14.740
So for example, they'll
write R like this

00:03:14.740 --> 00:03:17.140
for the set of real numbers.

00:03:20.020 --> 00:03:23.710
They'll write a Q in that
blackboard bold font,

00:03:23.710 --> 00:03:25.880
so it looks something like this.

00:03:25.880 --> 00:03:28.900
They'll write the Q; it might
look something like this.

00:03:28.900 --> 00:03:30.900
This would be the set
of rational numbers.

00:03:30.900 --> 00:03:32.567
And you might say,
why Q for a rational?

00:03:32.567 --> 00:03:33.983
Well, there's a
couple of reasons.

00:03:33.983 --> 00:03:35.590
One, the R is already taken up.

00:03:35.590 --> 00:03:37.090
And Q for quotient.

00:03:37.090 --> 00:03:38.510
A rational number
can be expressed

00:03:38.510 --> 00:03:40.520
as a quotient of two integers.

00:03:40.520 --> 00:03:45.920
And we just saw you
have your Z for Zahlen,

00:03:45.920 --> 00:03:50.520
or integers, the
set of all integers.

00:03:50.520 --> 00:03:52.032
So our universal
set-- the universe

00:03:52.032 --> 00:03:54.150
that we care about
right now-- is integers.

00:03:54.150 --> 00:03:56.990
And let's define a subset of it.

00:03:56.990 --> 00:03:58.980
Let's call that
subset-- I don't know.

00:03:58.980 --> 00:04:01.220
Let me use a letter that I
haven't been using a lot.

00:04:01.220 --> 00:04:04.240
Let's call it C,
the set C. Let's say

00:04:04.240 --> 00:04:09.500
it's equal to negative
5, 0, and positive 7.

00:04:09.500 --> 00:04:11.250
And I'm obviously not
drawing it to scale.

00:04:11.250 --> 00:04:12.750
The set of all
integers is infinite,

00:04:12.750 --> 00:04:15.060
while the set C is a finite set.

00:04:15.060 --> 00:04:16.940
But I'll just kind
of just to draw

00:04:16.940 --> 00:04:20.440
it, that's our set
C right over there.

00:04:20.440 --> 00:04:22.390
And let's think about
what is a member of C,

00:04:22.390 --> 00:04:26.880
and what is not a member of
C. So we know that negative 5

00:04:26.880 --> 00:04:31.310
is a member of our set C.

00:04:31.310 --> 00:04:36.230
This little symbol right
here, this denotes membership.

00:04:36.230 --> 00:04:38.570
It looks a lot like the
Greek letter epsilon,

00:04:38.570 --> 00:04:40.360
but it is not the
Greek letter epsilon.

00:04:40.360 --> 00:04:43.450
This just literally means
membership of a set.

00:04:43.450 --> 00:04:50.460
We know that 0 is a
member of our set.

00:04:50.460 --> 00:04:55.120
We know that 7 is a
member of our set.

00:04:55.120 --> 00:04:56.800
Now, we also know
some other things.

00:04:56.800 --> 00:05:04.530
We know that the number negative
8 is not a member of our set.

00:05:04.530 --> 00:05:12.160
We know that the number 53
is not a member of our set.

00:05:12.160 --> 00:05:14.540
And 53 is sitting
someplace out here.

00:05:14.540 --> 00:05:19.090
We know the number 42 is
not a member of our set.

00:05:19.090 --> 00:05:22.460
42 might be sitting
someplace out there.

00:05:22.460 --> 00:05:24.790
Now let's think
about C complement,

00:05:24.790 --> 00:05:27.810
or the complement
of C. C complement,

00:05:27.810 --> 00:05:31.250
which is the same thing as
our universe minus C, which

00:05:31.250 --> 00:05:33.600
is the same thing
as universe, or you

00:05:33.600 --> 00:05:36.090
could say the relative
complement of C

00:05:36.090 --> 00:05:37.145
in our universe.

00:05:37.145 --> 00:05:39.820
These are all
equivalent notation.

00:05:39.820 --> 00:05:41.850
What is this, first of
all, in our Venn diagram?

00:05:41.850 --> 00:05:43.960
Well, it's all
this stuff outside

00:05:43.960 --> 00:05:48.520
of our set C right over here.

00:05:48.520 --> 00:05:51.880
And now, all of a sudden,
we know that negative 5

00:05:51.880 --> 00:05:55.180
is a member of C, so it can't
be a member of C complement.

00:05:55.180 --> 00:05:59.750
So negative 5 is not a
member of C complement.

00:05:59.750 --> 00:06:03.310
0 is not a member
of C complement.

00:06:03.310 --> 00:06:07.500
0 sits in C, not
in C complement.

00:06:07.500 --> 00:06:12.990
I could say 53-- 53 is a
member of C complement.

00:06:12.990 --> 00:06:17.940
It's outside of C. It's in the
universe, but outside of C. 42

00:06:17.940 --> 00:06:22.400
is a member of C complement.

00:06:22.400 --> 00:06:26.380
So anyway, hopefully that helps
clear things up a little bit.


Relative complement or difference between sets

WEBVTT
Kind: captions
Language: en

00:00:00.522 --> 00:00:01.980
What we're now
going to think about

00:00:01.980 --> 00:00:04.829
is finding the
differences between sets.

00:00:04.829 --> 00:00:06.370
And the first way
that we will denote

00:00:06.370 --> 00:00:08.760
this is we'll start with
set A. I've already defined

00:00:08.760 --> 00:00:11.650
set A. Let me do it in
that same shade of green.

00:00:11.650 --> 00:00:13.410
I've already defined set A here.

00:00:13.410 --> 00:00:17.160
And in both cases, I've defined
these sets with numbers.

00:00:17.160 --> 00:00:19.830
Instead of having numbers as
being the objects in the set,

00:00:19.830 --> 00:00:22.380
I could have had farm animals
there or famous presidents,

00:00:22.380 --> 00:00:25.460
but numbers hopefully
keep things fairly simple.

00:00:25.460 --> 00:00:28.610
So I'm going to start with
set A. And from set A,

00:00:28.610 --> 00:00:33.620
I'm going to subtract set B.
So this is one way of thinking

00:00:33.620 --> 00:00:36.210
about the difference
between set A and set B.

00:00:36.210 --> 00:00:37.960
And when I've
written it this way,

00:00:37.960 --> 00:00:41.550
this essentially says give me
the set of all of the objects

00:00:41.550 --> 00:00:43.740
that are in A with
the things that

00:00:43.740 --> 00:00:46.239
are in B taken out of that set.

00:00:46.239 --> 00:00:47.780
So let's think about
what that means.

00:00:47.780 --> 00:00:51.560
So what's in set A with the
things that are in B taken out?

00:00:51.560 --> 00:00:56.610
Well, that means-- let's take
set A and take out a 17, a 19--

00:00:56.610 --> 00:01:00.040
or take out the 17s,
the 19s, and the 6s.

00:01:00.040 --> 00:01:03.660
So we're going to be left with--
we're going to have the 5.

00:01:03.660 --> 00:01:05.080
We're going to have the 3.

00:01:05.080 --> 00:01:08.415
We're not going to have the
17 because we subtracted out

00:01:08.415 --> 00:01:12.970
set B. 17 is in set B, so take
out anything that is in set B.

00:01:12.970 --> 00:01:14.300
So you get the 5, the 3.

00:01:14.300 --> 00:01:17.820
See, the 12 is not in set B,
so we can keep that in there.

00:01:17.820 --> 00:01:20.340
And then the 19 is
in set B, so we're

00:01:20.340 --> 00:01:22.690
going to take out
the 19 as well.

00:01:22.690 --> 00:01:25.190
And so that is this
right over here

00:01:25.190 --> 00:01:29.880
is-- you could view it as
set B subtracted from set A.

00:01:29.880 --> 00:01:32.210
So one way of thinking
about it, like we just said,

00:01:32.210 --> 00:01:34.480
these are all of
the elements that

00:01:34.480 --> 00:01:37.601
are in set A that
are not in set B.

00:01:37.601 --> 00:01:39.100
Another way you
could think about it

00:01:39.100 --> 00:01:42.260
is, these are all of the
elements that are not in set B,

00:01:42.260 --> 00:01:45.160
but also in set A. So
let me make it clear.

00:01:45.160 --> 00:01:55.130
You could view this as
B subtracted from A.

00:01:55.130 --> 00:02:02.090
Or you could view this as
the relative complement--

00:02:02.090 --> 00:02:05.450
I always have trouble
spelling things--

00:02:05.450 --> 00:02:14.960
relative complement
of set B in A.

00:02:14.960 --> 00:02:17.170
And we're going to talk a
lot more about complements

00:02:17.170 --> 00:02:18.160
in the future.

00:02:18.160 --> 00:02:20.880
But the complement is the
things that are not in B.

00:02:20.880 --> 00:02:22.560
And so this is
saying, look, what

00:02:22.560 --> 00:02:25.490
are all of the things that are
not in B-- so you could say

00:02:25.490 --> 00:02:31.300
what are all of the things
not in B but are in A?

00:02:31.300 --> 00:02:33.925
So once again, if you said all
of the things that aren't in B,

00:02:33.925 --> 00:02:35.800
then you're thinking
about all of the numbers

00:02:35.800 --> 00:02:38.809
in the whole universe
that aren't 17, 19, or 6.

00:02:38.809 --> 00:02:40.600
And actually, you could
even think broader.

00:02:40.600 --> 00:02:42.433
You're not even just
thinking about numbers.

00:02:42.433 --> 00:02:44.590
It could even be the color
orange is not in set B,

00:02:44.590 --> 00:02:48.340
so that would be in the
absolute complement of B.

00:02:48.340 --> 00:02:49.860
I don't see a zebra
here in set B,

00:02:49.860 --> 00:02:51.240
so that would be its complement.

00:02:51.240 --> 00:02:53.531
But we're saying, what are
the things that are not in B

00:02:53.531 --> 00:02:55.540
but are in A?

00:02:55.540 --> 00:02:59.280
And that would be the
numbers 5, 3, and 12.

00:02:59.280 --> 00:03:02.859
Now, when we visualized
this as B subtracted from A,

00:03:02.859 --> 00:03:04.650
you might be saying,
hey, wait, look, look.

00:03:04.650 --> 00:03:05.150
OK.

00:03:05.150 --> 00:03:07.520
I could imagine you
took the 17 out.

00:03:07.520 --> 00:03:09.310
You took the 19 out.

00:03:09.310 --> 00:03:10.680
But what about taking the 6 out?

00:03:10.680 --> 00:03:12.054
Shouldn't you have
taken a 6 out?

00:03:12.054 --> 00:03:13.875
Or in traditional
subtraction, maybe we

00:03:13.875 --> 00:03:15.950
would end up with a negative
number or something.

00:03:15.950 --> 00:03:19.650
And when you subtract a set, if
the set you're subtracting from

00:03:19.650 --> 00:03:22.270
does not have that element, then
taking that element out of it

00:03:22.270 --> 00:03:23.270
doesn't change it.

00:03:23.270 --> 00:03:26.890
If I start with set A, and if
I take all the 6s out of set A,

00:03:26.890 --> 00:03:27.952
it doesn't change it.

00:03:27.952 --> 00:03:29.160
There was no 6 to begin with.

00:03:29.160 --> 00:03:31.260
I could take all the
zebras out of set A;

00:03:31.260 --> 00:03:33.390
it will not change it.

00:03:33.390 --> 00:03:36.950
Now, another way to denote
the relative complement

00:03:36.950 --> 00:03:40.810
of set B in A or B
subtracted from A,

00:03:40.810 --> 00:03:43.190
is the notation that
I'm about to write.

00:03:43.190 --> 00:03:44.685
We could have
written it this way.

00:03:44.685 --> 00:03:47.760
A and then we would have had
this little figure like this.

00:03:47.760 --> 00:03:52.440
That looks eerily
like a division sign,

00:03:52.440 --> 00:03:56.380
but this also means the
difference between set A

00:03:56.380 --> 00:03:58.222
and B where we're
talking about-- when

00:03:58.222 --> 00:03:59.680
we write it this
way, we're talking

00:03:59.680 --> 00:04:02.580
about all the things in
set A that are not in

00:04:02.580 --> 00:04:06.900
set B. Or the things in
set B taken out of set A.

00:04:06.900 --> 00:04:10.061
Or the relative
complement of B in A.

00:04:10.061 --> 00:04:11.810
Now, with that out of
the way, let's think

00:04:11.810 --> 00:04:13.660
about things the
other way around.

00:04:13.660 --> 00:04:19.510
What would B slash--
I'll just call it

00:04:19.510 --> 00:04:20.990
a slash right over here.

00:04:20.990 --> 00:04:25.640
What would B minus A be?

00:04:25.640 --> 00:04:28.170
So what would be B minus A?

00:04:28.170 --> 00:04:37.890
Which we could also
write it as B minus A.

00:04:37.890 --> 00:04:41.920
What would this be equal to?

00:04:41.920 --> 00:04:44.170
Well, just going
back, we could view

00:04:44.170 --> 00:04:46.490
this as all of the
things in B with all

00:04:46.490 --> 00:04:48.820
of the things in
A taken out of it.

00:04:48.820 --> 00:04:52.022
Or all of the things--
the complement of A

00:04:52.022 --> 00:04:55.270
that happens to
be in B. So let's

00:04:55.270 --> 00:04:56.930
think of it as
the set B with all

00:04:56.930 --> 00:04:58.760
of the things in
A taken out of it.

00:04:58.760 --> 00:05:01.900
So if we start with
set B, we have a 17.

00:05:01.900 --> 00:05:05.360
But a 17 is in set A, so
we have to take the 17 out.

00:05:05.360 --> 00:05:06.110
Then we have a 19.

00:05:06.110 --> 00:05:09.690
But there's a 19 in set A, so
we have to take the 19 out.

00:05:09.690 --> 00:05:11.547
Then we have a 6.

00:05:11.547 --> 00:05:13.380
Oh, well, we don't have
to take a 6 out of B

00:05:13.380 --> 00:05:17.680
because the 6 is not in set A.
So we're left with just the 6.

00:05:17.680 --> 00:05:22.420
So this would be just the set
with a single element in it,

00:05:22.420 --> 00:05:24.020
set 6.

00:05:24.020 --> 00:05:26.140
Now let me ask another question.

00:05:26.140 --> 00:05:35.220
What would the relative
complement of A in A be?

00:05:35.220 --> 00:05:38.170
Well, this is the same
thing as A minus A.

00:05:38.170 --> 00:05:41.170
And this is literally
saying, let's take set A

00:05:41.170 --> 00:05:44.910
and then take all of the things
that are in set A out of it.

00:05:44.910 --> 00:05:46.074
Well, I start with the 5.

00:05:46.074 --> 00:05:47.240
Oh, but there's already a 5.

00:05:47.240 --> 00:05:49.230
There's a 5 in set A. So
I have to take the 5 out.

00:05:49.230 --> 00:05:50.680
Well, there's a 3, but
there's a 3 in set A,

00:05:50.680 --> 00:05:51.720
so I have to take a 3 out.

00:05:51.720 --> 00:05:53.595
So I'm going to take
all of these things out.

00:05:53.595 --> 00:06:00.640
And so I'm just going to
be left with the empty set,

00:06:00.640 --> 00:06:02.350
often called the null set.

00:06:02.350 --> 00:06:04.130
And sometimes the
notation for that

00:06:04.130 --> 00:06:08.670
will look like this, the
null set, the empty set.

00:06:08.670 --> 00:06:14.230
There's a set that has
absolutely no objects in it.