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specific example would be good

which means that f exists at c, and that the two sided limit exists, and they are equal

How do you know that f(x) doesn't have a hole?

because if f has a "hole" then the function doesn't exist there

right, so how does \[\lim_{x \rightarrow c} f(x) = f(c)\] explain that f(c) is where it should be?

|dw:1327164250426:dw|
example of function existing, but not continuous because limit does not exist

"where it should be" is a good english way to think about it, but the math is what is written above.

I mean, say \[\lim_{x \rightarrow 4} = 5\] that doesn't mean that f(x) necessarily is continuous

oops forgot the f(x)

\[\lim_{x\rightarrow 4}f(x)=5=f(4)\] and your function is continuous at 4.

oh i mis understood.

ok, I'm gonna think about this all over again. Maybe I just need to rethink. Thanks so far though ^^

Well thanks guys for helping me get rid of this self-induced confusion :P