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I am confused by 「二番」vs.「二番目」、「三番」vs.「三番目」etc.

While **「一番速い人。」** seems grammatically correct and sounds ok to me,
**「二番速い人。」** sounds so unnatural to me I am thinking the grammar might be
wrong. But, if 「一番速い」 is correct, certainly 「二番速い」 must also correct, right?

With regard to modifying nouns with adjectives such as "second", "third", etc.
this is how I've heard it done:  
「それは、二番目に高い建物です。」  
「三番目の好きな日本料理はお好み焼きです。」  
「四番目に速い人は、田中さんです。」 ...

Personally, but for 「一番」、 I never just say 「＿番」. I say 「＿番目」. But in forums
such as this, I observe 「＿番」 used more often than 「＿番目」。 So, I am getting
worried / confused about this.

Also, in this context. 「目」 must be consider a counter right? It is the counter
of positions in an ordered list. If it's not officially a counter, what is it?
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counters
「二番」 vs. 「二番目」 confusion
I think that the sequence beginning `一番・二番・三番` corresponds roughly to _number
one, number two, number three_. Each word in this sequence is formed from the
combination of a numeral (`一・二・三`) with a counter meaning _number_ (`番`).

You can take this list and add the ordinal suffix `目` to each word, producing
the list `一番目・二番目・三番目`, corresponding roughly to _first, second, third_.

What may be confusing here is that an adverb has been derived from `一番`, but
not from the other words formed with `番`. As a result, `一番` can represent
either _number one_ or _first/most_ , but `二番` and `三番` mean _number two_ and
_number three_. You can see this if you compare dictionary entries; the
entries for [一番](http://kotobank.jp/word/%E4%B8%80%E7%95%AA) in 大辞林 and 大辞泉
list it as both a noun and an adverb, while the corresponding entries for
[二番](http://kotobank.jp/word/%E4%BA%8C%E7%95%AA) don't list a derived
adverbial sense.

So, if you're talking about the tallest, second tallest, and third tallest
buildings, I think the list naturally looks like this:

  * 一番高い建物
  * 二番目に高い建物
  * 三番目に高い建物

And your example `二番速い人` is, I think, ungrammatical.

As for whether `〜目` is a counter, I don't think so. It doesn't combine
directly with numbers like counters do. Instead, it's a suffix that attaches
to words that consist of a number and a counter. If we check
[大辞林](http://kotobank.jp/word/%E7%9B%AE%E3%83%BB%E7%9C%BC), we find the
following:

> 二 （ 接尾 ）  
>  ① **数を表す語に付いて，順序を表す。** 「一つ目」 「三番目」

You'll notice that it says this is a 接尾語 ( _suffix_ ). I've bolded the actual
definition, which I'll translate here as "attaches to words that express
number, and expresses ordinality."

You'll note the definition includes an example where `目` attaches to a word
with `つ`, as well as another example where it attaches to a word with `番`.
With `目` attached, both `一つ目・二つ目・三つ目` and `一番目・二番目・三番目` express _first,
second, third_ , but of course the `つ` list can only count to nine, while the
`番` list can be used to express arbitrary positions in a list.
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2013-10-05T14:20:31.863
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2013-10-05T14:27:33.637
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answer