# The Limit Of Language

Thm. The set of all finite strings is countable.

pf)
Let An be the set of all strings with length n.
Then An is countable.
Therefore A = U An is also countable, since it is a countable unio
n of countable sets.


So we can't even name every real number correctly. Language is cou
ntable, but the set of real numbers is uncountable.

Similarily, we can't see almost every set. We can only deal with f
inite set-defining conditions.