$E$ is an extension field of a field $F$ and $A$ is the subset of $E$ containing all the members algebraic over $F$. "To prove that $A$ is a subfield of $E$ it is enough to show that any two elements $u,v$ of $A$ lies in some finite extension $L$ of $F$." I'm missing something simple, I know, but why is the quoted sentence correct?
2026-03-31 10:09:27.1774951767
Why does this criterion imply that $A$ is a subfield of $E$?
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