There are uncountably many (countably) infinite collections of symbols from within a countably infinite set of possible symbols. The set of finite subsets of a

There are uncountably many (countably) infinite collections of symbols from within a countably infinite set of possible symbols. The set of finite subsets of a countably infinite set, is countably infinite. There is a computable bijection between the set of natural numbers and the set of finite sequences of natural numbers.