Can any finite set of integers be closed under addition? Prove your answer.

I kind of have an understanding of what this means but don't know how to prove this?

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- Sep 4th 2010, 02:51 AMacevipaFinite set of integers closed under addition
Can any finite set of integers be closed under addition? Prove your answer.

I kind of have an understanding of what this means but don't know how to prove this? - Sep 4th 2010, 03:49 AMundefined
- Sep 4th 2010, 04:24 AMSoroban
Hello, acevipa!

Quote:

Can any finite set of integers be closed under addition? Prove your answer.

Suppose the set is: .$\displaystyle S \:=\:\{a,\:b,\:c,\:\hdots\:n\}$ . . . in increasing order.

. . $\displaystyle \text{If }n\text{ is positive: }\:n+n\;\notin S$

. . $\displaystyle \text{If }a\text{ is negative: }\:a+a\;\notin S$

The set isclosed under addition.*not*

The only such set is a trivial one: .$\displaystyle \{0\}$

Edit: too slow . . . again !