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If there is a closed interval I = [a,b] then is it appropriate to assume that b = supI and a = infI ? Does it need to be shown? because I'm not sure it is written explicitly anywhere. | If there is a closed interval I = [a,b] then is it appropriate to assume that b = supI and a = infI ? Does it need to be shown? because I'm not sure it is written explicitly anywhere. | ||
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| + | '''Prof. Alekseenko:''' It is actually a theorem that <math> b=\sup{(a,b)} </math> and <math> a=\inf{(a,b)} </math>. You may assume that this theorem is given, however, it seems unusual that you need a statement like that. Intervals are rather simple. Do we have to use <math> \sup </math> and <math> \inf </math> on them? | ||
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If there is a closed interval I = [a,b] then is it appropriate to assume that b = supI and a = infI ? Does it need to be shown? because I'm not sure it is written explicitly anywhere.
Prof. Alekseenko: It is actually a theorem that $ b=\sup{(a,b)} $ and $ a=\inf{(a,b)} $. You may assume that this theorem is given, however, it seems unusual that you need a statement like that. Intervals are rather simple. Do we have to use $ \sup $ and $ \inf $ on them?
