) 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

Results 1 to 6 of 6

- Nov 27th 2011, 08:00 AM #1

- Joined
- Nov 2011
- Posts
- 16

- Nov 27th 2011, 08:52 AM #2

- Joined
- Nov 2011
- Posts
- 14

## 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, 09:06 AM #3

- Nov 27th 2011, 09:10 AM #4

- Joined
- Nov 2011
- Posts
- 14

- Nov 27th 2011, 09:19 AM #5
## Re: need question help

- Nov 27th 2011, 09:22 AM #6

- Joined
- Nov 2011
- Posts
- 14