I am not sure about how to prove this:
Show that any nonempty set of integers that is closed under subtraction must also be closed under addition.
Basic axioms of maths.
Recall that subtraction is just the addition of a negative number, so if subtraction is closed, then so is addition.
Let S be your set, and suppose that a â S; then 0 = a - a â S (because S is closed under subtraction); this implies that, if b â S, then -b = 0 - b â S; so, if a,b â S, then a + b = a - (-b) â S.
Comments
Basic axioms of maths.
Recall that subtraction is just the addition of a negative number, so if subtraction is closed, then so is addition.
Let S be your set, and suppose that a â S; then 0 = a - a â S (because S is closed under subtraction); this implies that, if b â S, then -b = 0 - b â S; so, if a,b â S, then a + b = a - (-b) â S.