Thread: continuity at a point

using the definition: .

f(x)=x if x is an integer.
f(x)=0 if x is not an integer. Prove that f is not continuous at=3 so we use the negation of the above definition.

how do we know Is there a general method?

Thanks

Let . Then for all , . In this case, its probably easier to look at the one-sided limits at an integer: since f is 0 as you approach an integer, the limit of f at any integer is 0, but f is not zero there, so it is discontinuous.