My infinity’s bigger than yours
By Murray Bourne, 17 Aug 2007
An article from Scientific American (no longer available) explains how Infinity Comes in Different Sizes.
According to the article, the 19th century German mathematician Georg Cantor showed ...
... there are more real numbers packed in between zero and one than there are numbers in the entire range of naturals.
I remember being blown away by the concepts of "countably infinite" (for example, the whole numbers 0, 1, 2, 3, ... is a countably infinite set) and "uncountably infinite" (for example, the number of all numbers - that's all the rationals, irrationals, complex numbers, etc.)
Cantor created Set Theory, a topic that was used and abused in secondary schools for many years. According to this Wikipedia article, after developing the concept of transfinite numbers, Cantor took himself a little too seriously and died a seriously depressed man.
I can't resist concluding with Einstein's profound quote:
Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.
See the 3 Comments below.