Does there exist a function f, defined by , which is bounded above and below but does not ever attain the upper bound nor the lower bound? Can anyone give an example of such a function?

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- Feb 1st 2009, 07:45 AMTriAngleContinuous functions
Does there exist a function f, defined by , which is bounded above and below but does not ever attain the upper bound nor the lower bound? Can anyone give an example of such a function?

- Feb 1st 2009, 09:48 AMflyingsquirrel
Hello

Well is bounded above and below by 2 and -2 respectively and never attains these two bounds...

Another example : let . This function is bounded above and below by and respectively but never equals since . - Feb 1st 2009, 10:48 AMTriAngle
That's what I was thinking. It seems like a simple solution should work, but the problem is presented in such a way as to make it seem like it should be harder.