I only took the first undergraduate abstract algebra course, so i don't know (at all) what Galois theory is about.
I'm asking this question since i'm not sure of the definition of inner product space and normed space.
Generally, they are defined on a vector space over $\mathbb{R}$ or $\mathbb{C}$, but some contexts define them on a vector space over a subfield of $\mathbb{C}$.
Are $\mathbb{Q},\mathbb{R},\mathbb{C}$ all the subfields of $\mathbb{C}$?
Best Answer
There are lots of subfields of $\mathbb{C}$. Some typical examples:
Using the axiom of choice, one can even construct "arbitrary complicated" subfields of $\mathbb{C}$. Generally speaking, many fields may be embedded into $\mathbb{C}$. They only have to be of characteristic zero and should have cardinality $\leq |\mathbb{C}|$.