Transcendental number that can be writen without "symbols"

Question

I know that : $e$ and $\pi$ are transcendental numbers, yet I was wondering is there transcendental numbers that are written without any "symbols" ?

I mean we use the symbol $\pi$ to denote the real number : $3.14...$ and $e$ the real number : $2.71$

Answer 1

We don't necessarily need $e$ and $\pi$ to denote those numbers, they just come up enough that it's convenient to denote them as such. For example, we could also write $$e = \sum_{n = 0}^{\infty}\frac{1}{n!}$$ or $$e = \lim_{n\to\infty}\left(1+\frac{1}{n}\right)^{n}.$$

Answer 2

It seems that : $2^{\sqrt{2}}$ is irrational