Prove that each field of characteristic zero contains a copy of the rational number field?

Question

Linear Alebra

Answer 1

The proof for this is in most abrstract algebra texts. Basically a field of char 0 means that it is an infinite field (you can add 1 as many times as you want), so you can get all of the integers. Since it is a field, you have all of the quotients, in other words you have a subset that is isomorphic to the set of rational numbers.