using the definition: $\displaystyle \forall \epsilon >0, \exists \delta >0, \forall h, \ |h|<\delta \ : |f(a+h)-f(a)|<\epsilon$.

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 $\displaystyle h=\min(\delta/2,0.5)$ Is there a general method?

Thanks