# Thread: Field with Characteristic 0

1. ## Field with Characteristic 0

Prove that every field with characteristic 0 contains a countable subfield.

2. Hint

If the field $F$ has characteristic $0$, prove that $H=\left\{{me/ne:m\in{\mathbb{Z}}},n\in{\mathbb{N}^*}\right\}\su bset F$ is a subfield of $F$ ( $e$ is the unit on $F$). Besides, $H$ is isomorphic to $\mathbb{Q}$.

Regards.

Fernando Revilla