The only possible counterexample is to pick the integer 0. It is neither positive nor negative. Counterexamples go against the claim to prove it false.
So the claim "if a number is an integer, then it is either positive or negative" is proven false. To fix the claim, you would have to say something like "if a number is an integer, then it is either positive, negative, or zero".
The set of integers is { ..., -3, -2, -1, 0, 1, 2, 3, ... } basically any positive or negative whole number, including zero as well.
Zero (0) which is an integer that is neither positive nor negative is a counterexample for the conditional.
By definition, an integer is any number that doesn't have a fraction part. In other words, they are whole numbers.
Numbers that have no fraction part, and have positive sign or negative sign attached to their values are all integers.
Therefore, Zero (0) which is an integer that is neither positive nor negative is a counterexample for the conditional.
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