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In saying that something doesn't exist, is it unusual to use the ga particle
(が) and a negative verb? For example, would "(Uchi ni) Terebi ga arimasen" be
an unusual way to say "There isn't a TV (at my house)"?

The reason I'm wondering is that lesson 8 of Japanese For Busy People, which
introduces the ga particle and the existence of people and things, teaches
"place ni noun ga arimasu/imasu" to say "The object exists at this location!".
(If you were talking about a noun whose existance was already known, and you
were just providing additional information, it currently suggests using "wa"
and "desu" - eg "terebi wa ookii desu" - "the television is big")

Also, at the start of chapter 9, it teaches "place ni noun ga arimasu ka", and
tells you how to do the positive answer "Hai, noun ga arimasu".

However, it doesn't teach "noun ga arimasen/imasen" to say "The object doesn't
exist!". The only time it mentions the negative form is with "Nani mo
arimasen" and "Dare mo imasen", which is to say that nothing or no-one exists
at a specific location.

Since it doesn't teach "noun ga arimasen/imasen", I'm wondering if it's
because that's not grammatically correct.
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negation particle-が
Is it unusual to have the ga particle with a negative verb?
I'd say using が particle with negative verbs is not unusual at all especially
if it is [exhaustive が
usage](http://en.wikipedia.org/wiki/Japanese_grammar#Exhaustive_ga).

Consider if the question was: "I think you said before that your house doesn't
have this one electrical appliances I've forgotten which one was it, was it
TV, fridge or microwave?" To answer this question, you need to say something
that say TV, out of electrical appliances, is the one you don't have at your
house: "it is the TV that my house doesn't have" - 僕の家にはテレビがありません. That is to
say that you use が to single out the topic from some set of choices or even
the whole 'universe', and it works similarly for both positive and negative
verbs.

If the topic is not coming from a set of choices, meaning your statement does
not imply anything about the rest of the world, you would use は instead:
テレビはありません - "There is no TV (and I imply nothing about whether other things
exist or not).
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'Ga' has nothing to do with negation. Your example 'テレビがありません' is completely
fine.

The reason you need 'mo' in those examples is because Japanese uses a category
of words called indeterminates (which includes 'なに' and 'だれ'), which can be
used as a universal quantifier (which translates to English as 'any ...'),
existential quantifier (which translates to English as 'some ...') or an
interrogative quantifier (which translates to English as 'wh...').
Indeterminates take 'も' to function as a universal quantifier or 'か' to
function as an existential quantifier or take neither to function as an
interrogative quantifier.

> 何でもあります  
> 'There is anything.'
>
> 何もありません  
> 'There isn't anything.'
>
> 何かあります  
> 'There is something.'
>
> 何がありますか  
> 'What is there?'
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> Since it doesn't teach "noun ga arimasen/imasen", I'm wondering if it's
> because that's not grammatically correct.

It is correct. For example,

```

    どうしてさみしいんですか？ (Why are you sad?)  
    彼氏がいないので、さみしいんです。 (I'm sad because I don't have a boyfriend)
    
```

or

```

    最近忙しくて、友達に会う時間がない。 (I've been too busy recently to see my mates)
    
```

However, very often, when you state your negation, you emphasise your
subject/topic. It is therefore common to turn が into は.

```

    家にテレビがありますか？ (Do you have a telly at home?)  
    いいえ、家にテレビはありません。(A telly? No, I don't have one at home.)
    
```
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To complement other answers, let me state why が is less often used with
negation.

One of the roles of が is to introduce a new thing into the [universe of
discourse](https://japanese.stackexchange.com/questions/22/whats-the-
difference-between-wa-and-ga/51#51), whereas は is used when the thing you are
talking about is already in the universe of discourse. It should be
understandable that it is rare that one introduces a new subject and the first
thing to say about it is what it is _not_ like.
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