proving that the set of all english words is countble. This is the question :
Prove that the set of all the words in the English language is countble (the set's cardinality is אo)
A word is defined as a finite sequence of letters in the English language.
I'm not really sure how to start this. I know that a finite union of countble sets is countble and i think this is the way to start.
Thanks in advance !

The easiest way to show a set is countable is to provide a way of counting it - ie a rule to determine the position of any member within the set.
In this case we can start with all 1-letter "words", from a to z - there are 26 of these. Then we can continue with the two-letter words aa, ab, ... az, ba, bb .... zy, zz. There are 26^2 of these. And so on. 
Any finite-length word will be assigned a unique position in this sequence, therefore the sequence is countable.
