TITLE: Is every infinite set equipotent to a field?
QUESTION [8 upvotes]: For example, $\mathbb N$ is equipotent to $\mathbb Q$ which is a field.
$\mathbb R$ is equipotent to itself, which is a field.
But what about $\mathbb R^{\mathbb R}$, $P(\mathbb R^{\mathbb R})$ etc.?

REPLY [3 votes]: I think this answer by Gregory Grant is in some ways better than any relying on the Löwenheim–Skolem theorem, since it gives an explicit construction of a field of arbitrary infinite cardinality.