Why does aleph-null multiplied by aleph-null equal aleph-null?

In mathematics, the equation ${\aleph }_0·{\aleph }_0={\aleph }_0$ holds true because the set of all ordered pairs of natural numbers is equivalent to the set of natural numbers themselves.12

While arithmetic with transfinite numbers often deviates from the rules governing finite natural numbers, it remains consistent with the definition of cardinality as a measure of the size of a set. Aleph-null (${\aleph }_0$) represents the cardinality of the set of natural numbers. Because one can establish a one-to-one correspondence between the set of natural numbers and the set of ordered pairs of natural numbers, the product of these two infinite sets does not result in a "larger" infinity, but rather remains ${\aleph }_0$.12