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?
Hello, acevipa!
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 is not closed under addition.
The only such set is a trivial one: .$\displaystyle \{0\}$
Edit: too slow . . . again !