Definition:Field Extension/Degree

Definition
Let $E / F$ be a field extension.

The degree of $E / F$, denoted $\left[{E : F}\right]$, is the dimension of $E / F$ when $E$ is viewed as a vector space over $F$.

If $\left[{E : F}\right]$ is finite, then $E / F$ is a finite extension

Otherwise $E / F$ is an infinite extension.