it says: Suppose S is a subset of Z which is closed under subtraction, and k is an element of S. Prove that 0 is an element of S and then use that to prove that -k is an element of S.
Any ideas on how to start?
it says: Suppose S is a subset of Z which is closed under subtraction, and k is an element of S. Prove that 0 is an element of S and then use that to prove that -k is an element of S.
Any ideas on how to start?
1) There exists some element $\displaystyle k\in S\Longrightarrow k-k\in S$
2) So now $\displaystyle \forall\,k\in S\,,\,\,0,\,k\in S\Longrightarrow 0-k\in S$