Negative math sets

Question

Say X belongs to natural numbers, If i were to negate this statement, hence X does not belong to natural numbers, then exactly what is X? is X gonna be a fractional number, a negative number etc. Can it still be a positive integer, because it may belong to integers, and the integer set also contains positive integers just like natural numbers. I am really confused.

Answer 1

If x does not belong to a set S, we say that it belongs to X's complement. The complement is, however, always determined by the context: you can imagine that it is the universe of the scenario in question, one in which S is itself contained. The complement of S, then, is everything in the universe and NOT in S.

To answer your question, X cannot be a positive integer. Depending on what you set the universe to be it can be a negative integer, a rational, an irrational...