If you only allow arbitrarily long, but finite, strings then the set is countable. If you allow infinitely long strings then the cardinality of that set is unc

If you only allow arbitrarily long, but finite, strings then the set is countable. If you allow infinitely long strings then the cardinality of that set is uncountable. For a trivial example consider the string representation of every element in ℝ in the alphabet {0-9,.}