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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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 .
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.
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