Let $f_1, f_2, f_3, \dots : [0, 1] \to \mathbb{R}$ each be a D4364: Real function such that

(i)	$f_n(x) = x^n$ for all $x \in [0,1]$ and $n \in \mathbb{N} + 1$

Then

(1)	$f_1, f_2, f_3, \dots$ are each a D2943: Continuous function
(2)	$\lim_{n \to \infty} f_n(x) \neq \emptyset$ is not a D2943: Continuous function