I have some revision questions in my maths books and I'm a bit stuck on this one.
Is $S=\{n^2:n \in \mathbb{Z}\}$ closed under the usual addition.
I know that for it to be closed the sum of any 2 elements of $S$ must also be in $S$
The solution says it isn't closed but doesn't say why, could anyone help me with this?
Much appreciated
Hints:
Does $1^2+2^2 \in S$? ${}{}{}{}{}$