# 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 all real numbers correctly. Language is coun
table, 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.