In an attempt to better understand the definition of an equicontinuous family of continuous functions, I want to find a simple non-example.
My intuition says that the family $\{f_n\colon[0,1]\to\mathbb R\}_{n\in\mathbb N}$ given by $f_n(x)=x^n$ is not equicontinuous, but I do not know how to show this.
Any help is appreciated.