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 set $S_n$ of the English words with length $n$ is finite (this is almost obvious). So it's also countable. Why is it finite? The set $A_n$ of all sequences with length $n$ made up of latin characters is finite as it contains $26^n$ elements. Only some of these sequences are meaningful/actual English words. So $S_n \subset A_n$. So $S_n$ is also finite.
The set $T$ for which you have to prove that it is countable is:
$T = S_1 \cup S_2 \cup S_3 \cup ...  $ 
Now you have this theorem:
"A countable union of countable sets is also countable"  
Applying it you get that T is also countable.
Thus your statement has been proved.
