TITLE: What is a countable set?
QUESTION [8 upvotes]: 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?

REPLY [2 votes]: If we said countable set we mean that the set is in one-to-one corresponding with set of Natural numbers, so  we can arrangment the element of the countable set is a sequence form and easy we can deal with it.