Nice.

If you get hooked and end up needing professional psychiatric help, you can always blame it on me.

And don't get me started about transfinite numbers and the different orders of infinity. What's that, you say?

*Different* orders of infinity!? Well, I'm really happy that you asked...

Real numbers are all numbers such as whole numbers, fractions, irrational numbers, etc. Natural numbers are the countable numbers such like the ones we all know on the number line, (1 2 3 4 5 6 7 8 9 10, 11, etc) which, we can all agree, continues into infinity. Now here's the thing... you can take any two numbers (say, 3 & 4) and try to count the fractions between them. 1/2, 1/4, 1/8, 1/16, etc... all the way down the rabbit hole. Now, between any two fractions smaller fractions exist and between them, smaller ones

*ad infinitum*. The infinities of those fractions located between any two arbitrary numbers on the line (like 3 & 4, to repeat myself) constitute an infinity which is larger in numbers than exist on the infinite number line of countable or computational whole numbers. Multiple infinities exist. Using Georg Cantor's method of one-to-one correspondence between all of the whole numbers (1 to infinity) and the fractions between

*any two* whole numbers are termed a correspondence or cardinality (i.e. members of a set) of the set of whole numbers and the set of fractions. Cantor called the set of all natural numbers

*aleph-null* and the set of fractions

*aleph-null+1*. Which is larger? If you're actually still with me, let's take a moment to introduce

*the continuum*. This is the name given to the set of all real numbers and exactly how much more infinite is it than aleph-null? As Georg Cantor showed, there were no sets with a cardinality between that of the set of natural numbers and the set of real numbers. Put another way, the natural numbers were aleph-null, then all the real numbers could be was aleph-one. This became known as the continuum hypothesis and the fraction set (aleph-one) seems to be the larger set; one infinity

*is* larger than another infinity. The "larger" infinity is nested with the "smaller" infinity. And the real kick in the ass is that there are other alephs besides the two I just mentioned.

But, mercifully, I will stop here.

By the way, Cantor ended up going through a series of nervous breakdowns which eventually had him permanently institutionalized in the Bonkers Bungalow where he spent the rest of his life writing essays about William Shakespeare.

*O God, I could be bounded in a nutshell and count myself a king of infinite space*, indeed.

Please don't hate me.