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Let $E/K$ and $E'/K$ be two extensions. If $[E:K] =n$ then to prove that $|Emb_K(E,E')| \leq n$, where $Emb_K(E,E')$ denotes the field homomorphism from $E \to E'$ fixing $K$ point-wise.

I can see that it is a generalization of If $L/K$ is a field extension then $|Aut(L/K)| < [L:K]$.

I am stuck with the problem. Hints are welcomed!

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    use induction on $n$ – 2017-02-08
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    Isn't somehow given that $\;E'\;$ is algebraically closed, an algebraic closure of $\;K\;$ or something? Not that otherwise it isn't true, it is just the usual way it appears many times... – 2017-02-08
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    no no such asumtions are given – 2017-02-08
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    I'm troubled by the expression *denotes **the** field homomorphism* as if there is only one. This is not always true let $F = \Bbb Q$ and $a, b, c$ the roots of $x^3+x+1$. If $E = \Bbb Q(a)$ and $E' = \Bbb Q(a,b,c)$, the splitting field, then there is an embedding that maps $a \mapsto a$, one that $a \mapsto b$ and one that $a \mapsto c$. – 2017-02-08

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