Using the definition of removable discontinuity from Wikipedia, why can't a monotone function have this type of discontinuity?
In other words, if $x_0\in D(f)$ is a point where the monotone function $f$ is discontinuous, and if $$\lim_{x\to x_{0^-}}f(x)=L^-$$ and $$\lim_{x\to x_{0^+}}f(x)=L^+$$ why cannot be $$L^+=L^-$$
I've been baffled by this for far too long now, thanks for any help!