Question

Which sets are not closed under subtraction

Answer 1

If you're referring to the different sets of real numbers, it's the ones that you could try to do subtraction and not get an answer that still in that set.

For example, natural numbers (aka 1, 2, 3, 4, ...) are not, because 7 - 11 = -4 and -4 is not a natural number.

Also, whole numbers (aka 0, 1, 2, 3, 4, ...) has the same issue.

Basically any set of real numbers that doesn't include negative numbers will have this issue.