question about finite extension

Question

Gives an example of an algebraics extension which is not a finite extension ?

My attempt : i know that if $K$ be an extesnsion of a field $\mathbb{F}$. An element $a \in K$ is algebraics over $\mathbb{F}$ if and only if $[ F(a) :F]$ is finite

But here i don't know how can i find an algebraic extension

Any hints/solution will be aprreciated

thanks u

Answer 1

How about $$\Bbb Q(\sqrt2,2^{1/3},2^{1/4},\ldots)?$$ This contains $\Bbb Q(2^{1/n})$ which has degree $n$ over $\Bbb Q$ (Eisenstein).