Two sets can be put into a *one-to-one correspondence* if and only if they have
exactly the same number of elements. For example:

{red, yellow, green, blue} | | | | {apple, banana, cucumber, plum}

You probably learned to count by putting things into a one-to-one correspondence with
your fingers. Now you count by putting things into a one-to-one correspondence with a
subset of the *natural numbers* (the numbers 1, 2, 3, ...). Like so:

{red, yellow, green, blue} | | | | { 1, 2, 3, 4 }

In calculus you probably learned that "infinity" is not a number.
They lied. Infinity, as a number, is represented by the symbol _{0}
pronounced "aleph-null."

A set is *denumerable* if its elements can be put into a one-to-one correspondence
with the natural numbers. Denumerable sets have _{0}
elements.

Copyright © 1996 by David Matuszek

Last modified Mar 31, 1996