Are numbers countable?

Let’s take the following set:
N = {0, 1, 2, 3, 4, 5, 6, . . . }

This is a set known as the natural numbers, and it represents all possible values that a set’s cardinality can have.

But what is its cardinality?

Think of the largest number you can, then multiply it by itself and then by itself again. . .

You really can’t determine the last element of this set, because it’s infinite. But the set still needs to have a cardinality associated with it.

And so, the cardinality of the natural numbers is what’s known as an infinite cardinal called aleph-zero or aleph-null.

150px-Aleph0.svg

It’s a handy concept to have access to, since many sets have the same cardinality.

More tomorrow. . .

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