Yes, the set of integers is closed under subtraction.
The set of positive numbers, the set of negative numbers are two examples. Any subsets of these will also not be closed.
The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.
negetive integers are not closed under addition but positive integers are.
Yes.
No, they are not.
yes
No.
That is correct, the set is not closed.
Yes!
Yes it is.
Yes!
The set of integers is not closed under multiplication and so is not a field.