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Does a positive integer include a negative number?

How can a positive integer contain negative numbers? Isn't this a joke?

1. positive integer, that is, an integer greater than 0, such as 1, 2,3, …, n, …

2.0

It is neither a positive integer nor a negative integer, but a number between positive and negative integers.

3. Negative integers, that is, integers less than 0, such as-1, -2, -3, …, -n, …