How many $p$-adic numbers are there? Let $\mathbb Q_p$ be $p$-adic numbers field. I know that the cardinal of $\mathbb Z_p$ (interger $p$-adic numbers) is continuum, and every $p$-adic number $x$ can be in form $x=p^nx^\prime$, where $x^\prime\in\mathbb Z_p$, $n\in\mathbb Z$. 
So the cardinal of $\mathbb Q_p$ is continuum or more than that?

Well, $\mathbb{Q}_p\subset \mathbb{C}$ ...
