1. ## help with proof

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?

2. Originally Posted by alyssams
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 $k\in S\Longrightarrow k-k\in S$

2) So now $\forall\,k\in S\,,\,\,0,\,k\in S\Longrightarrow 0-k\in S$

Tonio