I'm just learning about Dedekind cuts and I've been shown how the $\displaystyle \sqrt{2}$ is can be a cut and can infer how all algebraic numbers have cuts.

A question popped into my mind that I can't seem to get is how do you get transcendential numbers like $\displaystyle \pi$ and $\displaystyle e$ as cuts. Could someone give me a hint as how to prove this?