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.