I have the following function f(x)=sin(1/x) I've been told that the function is continuous for any x. I understand that the above function is continuous at (0,infinite) and also at (-infinite,0) but as much as I know the limit of this function while x -->0 does not exist or is undefined so how come the function is still continuous??

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Perhaps it's for all x in its domain?

the function is not continuous at x=0, are you missing something?

it's for \[f(x) \rightarrow R:R\]

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