- #1
skate_nerd
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I am given that \(m\) and \(n\) are non zero integers and that \(S=\{k\in N:\,k=mx+ny\) for some integers \(x\) and \(y\}\). (Side note: How do you type the double struck capital N for the set of natural numbers in LaTeX?)
I need to prove that \(S\) is non-empty.
Well I am kind of stuck here thinking that if you had \(x=y=0\) then \(k=0\) making \(k\) not defined in the natural numbers, therefore leaving \(S\) to be none other than the empty set.
I need to prove that \(S\) is non-empty.
Well I am kind of stuck here thinking that if you had \(x=y=0\) then \(k=0\) making \(k\) not defined in the natural numbers, therefore leaving \(S\) to be none other than the empty set.