) Let g : [0; 1] ! R be a continuous function. Let S be a nonempty subset of [0; 1]

and suppose that g(x) = 3 for all x 2 S. Let a = inf(S). Show that g(a) = 3

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- Nov 27th 2011, 09:00 AM #1

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- Nov 27th 2011, 09:52 AM #2

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## Re: need question help

I'm not sure that I understand your question, but if S is a closed set then

and since for all , we conclude that . If is an open set you should find a sequence of numbers that converges to and use the continuity property to prove that (follow this link)

- Nov 27th 2011, 10:06 AM #3

- Nov 27th 2011, 10:10 AM #4

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- Nov 27th 2011, 10:19 AM #5
## Re: need question help

- Nov 27th 2011, 10:22 AM #6

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