Let A be a non-empty bounded subset of Define: show that sup D = sup A - inf A. I can intuitively understand this however I am not too sure how to go about a rigorous proof. Thanks for any help
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Originally Posted by hmmmm Let A be a non-empty bounded subset of Define: show that sup D = sup A - inf A. Let and . Then which implies or . Can you finish?
errm no sorry, I get that you have shown that it is an upper bound, but i don't know how to show that it is the least upper bound, sorry. thanks for any help
Originally Posted by hmmmm errm no sorry, I get that you have shown that it is an upper bound, but i don't know how to show that it is the least upper bound, sorry. Let suppose that . Use . There must be such that There must be such that Now you show that which is a contradiction. So what does that prove?
It shows that if there is any number less than U-L then you can find a member of the set that is bigger than it and so it is not the supermum. Thanks for the help
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