Definition
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Integers:

Integers can be represented by the following set:

I = {..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...}

The set of integers can be broken down to the following:

bulletPositive integers are 1, 2, 3, 4, 5, 6, ...
bulletNegative integers are -1, -2, -3, -4, -5, ...
bulletNon-positive integers are 0, -1, -2, -3, -4, -5, ...
bulletNon-negative integers are 0, 1, 2, 3, 4, 5, ...

Zero is neither positive nor negative.

Notice: the difference between positive integers and non-negative integers is only the zero. The difference between negative integers and non-positive integers is, also, the zero.