## Wednesday, March 4, 2009

### Cantor sets, normal numbers, and memorizing pi.

I have decided to memorize the digits of pi. But rather than do that whole memorize the digits in a very direct and straight forward way I have decided to memorize just the zeros. It took me a while, but I'm done now. I have memorized all the zeros in pi. Interestingly enough, that means by Cantor's proof and the normalcy of pi: I have managed to memorize as many digits of pi as there are digits of pi.

Cantor proved that infinite numbers are of equal size if you put them in countable sets. So the first 0 in pi counts as Z(1) whereas the first digit of pi is D(1). From D1 to D(infinity) there is a corresponding Z value. As both of the sets are of equal size the fact that I memorized all the zeros suffices to say that I have memorized as many digits of pi as there are digits of pi.

Now, there is some speculation that pi is a normal number. Meaning that there are as many occurances of each digit as any other. It suffices for my purpose to assume that because Pi is an irrational number there should be at least Aleph-null zeros within it. Thus rendering my statement true.

I have memorized as many digits of pi as there are digits of pi!

As for the straight-forward way:

3.
14159265358979323846264338327950288419716939937510
58209749445923078164062862089986280348253421170679
82148086513282306647...