• Mar 10th 2013, 01:33 PM
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,

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 :)
• Mar 10th 2013, 02:58 PM
Plato
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 $f(x) = \left\lceil x \right\rceil - 1\;\& \;g(x) = \left\lfloor x \right\rfloor$
• Mar 10th 2013, 09:32 PM
oneminiketchup
Well then for.. x0=1 for instance.. left-sided limit for f is 0-1=-1 and for g it's 0 ..
• Mar 11th 2013, 04:07 AM
Plato
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: ${\lim _{x \to {1^ - }}}\left\lceil x \right\rceil - 1 = 0$