Difference between "じゃない" and "ない"


I would like to ask what is the difference between "じゃない" and "ない"?

I know that "ない" is an i-adjective (info from dictionary).

But we have a sentence for example:

> 近くも遠くも **ない** です。

Can we say:

> 近くも遠くも **じゃない** です。

If not, please explain why.  
  

I've also found here this information:

> "You may be aware that ない is the negative form of ある".

How does it come???

Is "ない" i-adjective or negative conjugation of verb "ある"?  
  

I think that now I do not understand nothing.

Thank you very much in advance.




ある is a verb which means "to be located" (It also means 'to have', but that is
not relevant here).

The negative conjugation of ある is ない. Which behaves grammatically like an
i-adjective. Whether it is strictly correct to call it in i-adjective, I do
not know.

So ない means 'is not located'. Therefore your sentence can translate as "It is
located neither near nor far _from here_ ".

じゃない means 'is not'. But it denotes the lack of equality of two things. e.g
."A cat is not a vegetable". 猫は野菜じゃない. Can you see how this is different from
the "is not" in "He is not here"? In the latter we are talking about a
location and not about the equivalence between "him" and "here".

**Note, that I am confident about the things above this line, but less so
about the things below.**

Unfortunately things can get more complicated. If you wanted to say "It is not
here" you could say ここにない but you could also say ここじゃない. I'm starting to
speculate now, but I think the latter could just be an abbreviation of
あるところはここじゃない. That is to say that the equivalence we are comparing is, **the
place where it is located** , and **here**. Which makes more sense than
comparing **it** (which maybe a cabbage) and **here** , which is a place.

For this reason, as a non-native speaker, I'm not sure if 近くも遠くもじゃない is
grammatical. It sounds weird to me though.




ある is a verb which means "to be located" (It also means 'to have', but that is
not relevant here).

The negative conjugation of ある is ない. Which behaves grammatically like an
i-adjective. Whether it is strictly correct to call it in i-adjective, I do
not know.

So ない means 'is not located'. Therefore your sentence can translate as "It is
located neither near nor far _from here_ ".

じゃない means 'is not'. But it denotes the lack of equality of two things. e.g
."A cat is not a vegetable". 猫は野菜じゃない. Can you see how this is different from
the "is not" in "He is not here"? In the latter we are talking about a
location and not about the equivalence between "him" and "here".

**Note, that I am confident about the things above this line, but less so
about the things below.**

Unfortunately things can get more complicated. If you wanted to say "It is not
here" you could say ここにない but you could also say ここじゃない. I'm starting to
speculate now, but I think the latter could just be an abbreviation of
あるところはここじゃない. That is to say that the equivalence we are comparing is, **the
place where it is located** , and **here**. Which makes more sense than
comparing **it** (which maybe a cabbage) and **here** , which is a place.

For this reason, as a non-native speaker, I'm not sure if 近くも遠くもじゃない is
grammatical. It sounds weird to me though.

