Existence of proper field extension

Question

I am wondering whether the following statement is true or not?

Given any field $F$, there exists a proper field extension $K$ of $F$.

Answer 1

If you talk about the existence of field contain strictly F as sub field , the answer is yes, as indicated in the comments, with for example $K = F (t)$ rational field of polinomial ring $F[t]$.

If you talk about finite extension $K$ over $F$,then $K$ exist if and only if $F$ is not algebraically closed.

if you talk about a proper sub extension $K$ of $F$ , then $K$ exist if and only if $F$ is not prime field ($\neq\Bbb{Q}$ and $\neq\Bbb{F}_p$)