I have a group of questions where I basically need to show that $f(x)$ is continuous from $\Bbb{R}^n$ to $\Bbb{R}$.
Honestly, I'm not sure how to approach this generally.
The first one seems to obvious: $f(x_1,x_2,...,x_j,...,x_n)=x_j$ but I have no idea on how to write a proof for this.
The next one: $f(\mathbf{x})=|\mathbf{x}|$. I know that $|x|$ is continuous from $\Bbb{R}$ to $\Bbb{R}$, but how do I prove this here?