Let $L\supset F$ be a finite field extension of degree $n$ and $K \supset F$ be any extension. I wonder how to prove that the number of embeddings from $L$ to $K$ that restricts to identity on $F$ is bounded by $n$.
If $F=\mathbb Q$ and $K=\mathbb C$, then by primitive element theorem, we can show that the number of embedding is $n$. But I don't know how to deal with this general situation.