(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If Sup A<Sup B Then show that there exists a b[tex]\in[/tex]B which serves as an upper bound for A.

First off, I am not looking for a complete solution but rather a hint.

2. Relevant equations

SupA-[tex]\epsilon[/tex]<a for some a[tex]\in[/tex]A

SupB-[tex]\epsilon[/tex]<b for some b[tex]\in[/tex]B

3. The attempt at a solution

The only thing I have succeeded in so far is "locating one element of each set"

SupA-[tex]\epsilon[/tex]<a[tex]\leq[/tex]SupA for some a[tex]\in[/tex]A

SupB-[tex]\epsilon[/tex]<b[tex]\leq[/tex]SupB for some b[tex]\in[/tex]B

I know that if I can demonstrate that SupA[tex]\leq[/tex]SupB-[tex]\epsilon[/tex], then I can be done. Equivalently, if I can show that b[tex]\geq[/tex]SupA for some b[tex]\in[/tex]B I will also be done. However, right now this has me caught.

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# SupA<SupB, What can you say?

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