Definition. degree of field extensions [1203] 1. degree [1203A]If $K$ is a field extension of $F$, then $K$ can be viewed as an $F$-vector space. Exegesis. vector space [1203AA]TODO The degree of $K / F$ is $$ [K : F] := \dim_{F}K .$$ 2. finiteness [1203B]A field extension $K / F$ is called finite if $[K : F] < \infty$.