Finite set of integers closed under addition

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• September 4th 2010, 03:51 AM
acevipa
Finite 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?
• September 4th 2010, 04:49 AM
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Quote:

Originally Posted by acevipa
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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• September 4th 2010, 05:24 AM
Soroban
Hello, acevipa!

Quote:

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

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

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

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

The set is not closed under addition.

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

Edit: too slow . . . again !