Field
Definition: Suppose $ \mathbb{F} \subseteq \mathbb{E} $ are 2 fields:
1. $ \mathbb{E} $ is a field extention of $ \mathbb{F} $
2. the degree of extention, [ $ \mathbb{E} : \mathbb{F} $ ] is the dimension of the vector space $ \mathbb{E} $ over the coefficient field $ \mathbb{F} $
3. $ \mathbb{E} $ is algebraic over $ \mathbb{F} $ if every element e of IE is the root of a nonzero polynomial in $ \mathbb{F} $[x]. $ \mathbb{E} $ is transcendental if it's not algebraic.
