Challenge problem:

Let f be a function :

Prove that:

If, a, is not an accumulation point of A,then there exists an mεR,such that for all ε>0 there exists a δ>0 such that :

for all ,x: and $\displaystyle 0<|x-a|<\delta\Longrightarrow |f(x)-m|<\epsilon$

Moderator edit:Approved Challenge question.