Proving Finite Extension is Algebraic & Example of Converse

[luciasiti]

Hi everyone
I 'm having difficulty in proving the following theorem
theorem: If L/K ( L is a field extension of K) is a finite extension then it is algebraic. Show, by an example, that the converse of this theorem is not true, in general.
Can you help me to find an example in this case?
Thanks for your help!

 

[micromass]

What algebraic extensions do you know of \mathbb{Q}??

 

[HallsofIvy]

Let L be the set of rational numbers and K the set of all algebraic numbers.

 

[luciasiti]

What algebraic extensions do you know of \mathbb{Q}??

\mathbb{Q(\sqrt{2})} is an algebraic extension of \mathbb{Q}