Proposition 2.21: There exists no integer x such that 0 < x < 1. I am going to s

Question

Proposition 2.21: There exists no integer x such that 0 < x < 1.

I am going to show my attempt, but this was checked by my teacher and he underlined the first error he came to when reading it. I will make the error part shown in red.

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Proof: Assume, to the contrary, that there exists no integer x such that 0 > x > 1.

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I wrote more after the error, but it doesn't matter since I will want to fix the error anyway and thus probably change everything after the red anyway.

What did I do wrong?

Explanation / Answer

First thing: 0>x>1 is the EXACT SAME thing as 01 is not contrary to the proposition- it is an exact restatement of the proposition. Say, assume there DOES exist some integer x s.t. 0

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