Definition

$n \to \infty lim f_{n} = f$

Suppose $f : D \to R$ , is a function, and $(f_{n})$ is a Sequence of Functions whose term has the same domain as the function $f$ If $\forall ϵ > 0, \forall x \in D, \exists N \in N, \forall n \geq N, ∣ f_{n} (x) - f (x) ∣ < ϵ$ , then $(f_{n})$ converges pointwise to $f$ on $D$ , and the function $f$ is said to be the pointwise limit function of the $(f_{n})$