i need to show that when A is a subset of B and B is a subset of R (A B are non empty sets) then: infB<=infA<=supA<=SupB(adsbygoogle = window.adsbygoogle || []).push({});

here's what i did:

if infA is in A then infA is in B, and by defintion of inf, infB<=infA.

if infA isnt in A then for every e>0 we choose, infA+e is in A and so infA is in B, so infA+e>=infB, we can find e'>0 such that infA+e>=infB+e'>infB

so we have: infA-infB>=e'-e, let e=e'/2 then we have infA-infB>e'/2>0 so we have infA>infB. (is this method correct?).

obviously supA>=infA by defintion.

i think that the same goes for supA and supB, with suitable changes.

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# A review of supremum infimum.

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