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Question about two functions..

Is the following statement true?

If two functions, f and g (both R -> R) have the same one-sided limit (left-sided limit, for isntance) in every real point, then f=g. In other words,

http://i46.tinypic.com/29fwi0m.jpg

Is it true? If it is.. is there a proof? If it isn't could you give me a counter-example? ..

Thanks :)

Re: Question about two functions..

Quote:

Originally Posted by

**oneminiketchup** Is the following statement true?

If two functions, f and g (both R -> R) have the same one-sided limit (left-sided limit, for isntance) in every real point, then f=g. In other words, Is it true? If it is.. is there a proof? If it isn't could you give me a counter-example? ..

Consider $\displaystyle f(x) = \left\lceil x \right\rceil - 1\;\& \;g(x) = \left\lfloor x \right\rfloor$

Re: Question about two functions..

Well then for.. x0=1 for instance.. left-sided limit for f is 0-1=-1 and for g it's 0 ..

Re: Question about two functions..

Quote:

Originally Posted by

**oneminiketchup** Well then for.. x0=1 for instance.. left-sided limit for f is 0-1=-1 and for g it's 0 ..

No that is not correct: $\displaystyle {\lim _{x \to {1^ - }}}\left\lceil x \right\rceil - 1 = 0$