**Question:**

Let $B[0,1]$ be the normed space of bounded real-valued functions on $[0,1]$ with the norm $\|f\| =\sup\left\{\left|f(x)\right| : x\in [0,1]\right\}$. Is this metric space separable?

My problem is that I have no real intuition about this metric space. I have a solution for the problem that uses the "characteristic equation" but do not know how I would come up with this solution. Any insight as well as different solutions would be appreciated.

The characteristic equation is $\mathcal{X}\_x(s) = 1$ if $s=x$ , $0$ otherwise

Sorry, I'm not sure how to do a piecewise function.