This is the Question:

Let $\displaystyle x_n(t) = \begin{cases} nt & 0 \leq t \leq \frac{1}{n} \\ 2-nt & \frac{1}{n}<t\leq\frac{2}{n} \\0 & \frac{2}{n}<t\leq1 \end{cases}$

Show that$\displaystyle \{x_n\}$ is NOT compact set in $\displaystyle C([0,1])$

My idea is to show that $\displaystyle \mbox{\{x_n(t)\}}$ converge pointwise to $\displaystyle x(t)$, and $\displaystyle x(t) \notin C([0,1])$

Where $\displaystyle x(t) = \lim_{n\to \infty}x_n(t) = \begin{cases}1&t=0\\0&0<t\leq1\end{cases}$

Is this enough to show $\displaystyle \{x_n\}$ is NOT compact set in $\displaystyle C([0,1])$???

And how do I state formally that $\displaystyle \mbox{\{x_n(t)\}}$ converge pointwise to $\displaystyle x(t)$???