What is Denumerability in Set Theory?

A set is said to be denumerable if it can be put into a one-to-one correspondence with the natural numbers. In other words, if we can pair each element of the set with a unique natural number, then the set is denumerable.

For example, the set of all integers is denumerable because we can pair each integer with a unique natural number: $1$ with the number $1$, $2$ with the number $2$, and so on.

On the other hand, the set of all real numbers is not denumerable because there are uncountably many real numbers, and there is no way to pair each real number with a unique natural number.

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