help with proof

**alyssams** · April 11th 2010, 11:51 PM

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?

**tonio** · April 12th 2010, 01:48 AM

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

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