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Possible Duplicate:
How can I prove sup(A+B)=supA+supB if A+B={a+b}

How would I go about proving that the supremum of A + B (where A and B are each subsets if $\mathbb{R}$) is equal to the supremum of A plus the supremum of B?

I was thinking of using variables to represent the sup of A and the sup of B (say a & b), showing that a + b is an upper bound of A + B, and finally showing that no matter how small some other variable, e, is, that a + b - e cannot represent an upper bound for A + B.

Any idea how I might go about formalizing the proof? Thanks!

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    I'll try! Thanks for the input guys! Great resource we've got here.2011-04-04

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