) 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

Printable View

- Nov 27th 2011, 08:00 AMsbacon1991inf(S)
) 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 - Nov 27th 2011, 08:52 AMuasacRe: 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 AMPlatoRe: need question help
- Nov 27th 2011, 09:10 AMuasacRe: need question help
If is open then .

If is closed then .

I think... - Nov 27th 2011, 09:19 AMPlatoRe: need question help
- Nov 27th 2011, 09:22 AMuasacRe: need question help
Right... thanks for the correction.