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In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers. A countable set is either a finite set or a countably infinite set. Whether finite or infinite, the elements of a countable set can always be counted one at a time and...
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What is a countable set? In Wikipedia we read this definition: … Now, what is the cardinality of $\mathbb{N}$? $\mathbb{N}$ contains an infinity of numbers so its cardinality should be $\infty$, isn't it?
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A countable set is an infinite set that has a bijection with the natural numbers. Each natural number can be associated with an element of a countable set. Thus, any element in the set can be "reached" simply by counting long enough. A subset of a countable set is either finite or countable.
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