What is a countable set?
In Wikipedia we read this definition:
In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.
Now, what is the cardinality of \mathbb{N}? \mathbb{N} contains an infinity of numbers so its cardinality should be \infty, isn't it? So a countable set could contain an infinity of elements? In this case, in which way is it countable?
