"Let A and B be bounded nontempty sets of real numbers. Let C={ab:a in A, b in B}. Prove that sup(C)=sup(A)sup(B)."(adsbygoogle = window.adsbygoogle || []).push({});

Here's what I've done so far:

By the completeness axiom/theorem A and B have suprema. Let sup(A)=z and sup(B)=y. For all e>0, there exists a in A and b in B such that z-e<a and y-e<b. Multiplying the two inequalities and we have

zy-ze-ye+e^2 < ab

I'm stuck here.

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# Homework Help: Completeness axiom/theorem and supremum

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