I believe set theory is the only area of mathematics where different orders of infinite actually mean anything. So, in set theory, cardinality is a measure of

I believe set theory is the only area of mathematics where different orders of infinite actually mean anything. So, in set theory, cardinality is a measure of the elements of a set. The cardinality of the infinite set of natural numbers is aleph-0. An infinite set has cardinality aleph-0 if it can be put in one to one correspondence with the naturals. http://en.wikipedia.org/wiki/Bijection http://en.wikipedia.org/wiki/Bijection This counterintuitively includes the rational numbers also. http://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument http://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument The real numbers can't be put into one-to-one correspondence with the rational numbers. So the infinite of the reals truly is bigger than the infinite of the rational numbers. Also see this ppt: http://www.cs.cmu.edu/afs/cs.cmu.edu/academic/class/15251/discretemath/Lectures/cantor.ppt http://www.cs.cmu.edu/afs/cs.cmu.edu/academic/class/15251/di...