Why this function is not uniformly continuous? Let a function $f: \mathbb R \rightarrow \mathbb R$ be such that $f(n)=n^2$ for $n \in \mathbb N$. 
Why $f$ is not uniformly continuous?
Thanks

Recall that $f$ is uniformly continuous if and only if: for every sequences $(x_n)$ and $(y_n)$ such that $\lim_{n\to\infty}x_n-y_n=0$ we have $\lim_{n\to\infty}f(x_n)-f(y_n)=0$.
Now for counterexample: take $x_n=n+\frac{1}{n}$ and $y_n=n$. 
