Let f : R -> R be a continuous function such that f(x + 1) = f(x), for all x. Then f

attains its supremum. Is this statement true or false?? Give reasons...???

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- Feb 16th 2013, 03:36 AMtejasnatuIts an entrance exam problem based on Calculus
Let f : R -> R be a continuous function such that f(x + 1) = f(x), for all x. Then f

attains its supremum. Is this statement true or false?? Give reasons...??? - Feb 16th 2013, 06:15 AMemakarovRe: Its an entrance exam problem based on Calculus
Well, f attains its supremum on [0,1]...

- Feb 16th 2013, 07:31 AMtejasnatuRe: Its an entrance exam problem based on Calculus
could you please elaborate

- Feb 16th 2013, 07:34 AMemakarovRe: Its an entrance exam problem based on Calculus
See the extreme value theorem. And the values of f on are the same as on [0, 1].