Upper bound on cardinality of a field Is there an upper bound on the cardinality of a field?
The "biggest" fields I know are the field of real numbers, or the field of complex numbers. Is there a field with cardinality greater than continuum?

Given any set $X$, you can come up with an integral domain $\mathbb Q[X]$, of polynomials with each $x\in X$ an indeterminate. This ring is an integral domain, so it has a field of fractions, and that field of fractions has at least $X$ elements. 
If $X$ is infinite, I believe the field of fractions will have the same cardinality as $X$, but don't quote me.
