Finite means $[L:K]<\infty$; algebraic means every element satisfies a nonzero <polynomial> over $K$. Linear dependence among $1,x,\ldots,x^n$ proves finite implies algebraic. The algebraic closure $\overline{\mathbb Q}/\mathbb Q$ is algebraic but infinite.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 3 / 18F / a / Solution

 Solution (source code)