This is a topic that has bothered me for a while. Countable infinities. The concept is simple enough -- if you can provide a given set a one-to-one correspondence with the the natural numbers, you have a countable infinity (Aleph Null). So, the number of digits in Pi, e, etc. are countable infinities. Now, the argument goes that if Pi is a "normal" number (if the digits 0-9 are distributed randomly), then in an infinite sequence, any given sequence of numbers must, at some point, appear. It's easy enough to imagine that your birthday appears somewhere in Pi -- 01-09-72 for instance -- but the idea is expanded for arbitrarily large sequences. Your personal genetic code, for instance, boiled down to a numerical sequence is present somewhere deep in the bowels of Pi. The collected works of Shakespear, along with the genetic makeup of the monkeys that could have typed it are present in the far reaches of infinity. But let's consider this. If it is true that in an infinite, random sequence of digits every possible combination of numbers must appear at some point, then that means that Pi itself would exist in that sequence. The astute reader instantly objects that that makes Pi repeating, and we know that it does not. But is that true? If Pi can be found somewhere in Pi, does it repeat? Pi is an infinite sequence... So it never ends and cannot repeat. The real question becomes what is the cardinality of an infinite set containing an infinite set? If it is still a countable infinity, it seems possible that Pi could contain Pi and not repeat. So, let's look at the even numbers. The even numbers can very easily be placed in one to one correspondence with the natural numbers (1=2, 2=4, 3=6, 4=8 and so on). So the set of even numbers is a countable infinity just as the set of natural numbers are. And the even numbers are contained within the set of natural numbers. So a countably infinite set can contain another countably infinite set -- they have the same cardinality. So, to me, it seems possible that Pi could contain Pi. But that's not the fruit filling I am after here. The real prize is that Pi could contain another famous transcendental number: e. Get it? Pi contains e. Pie. Lordy, I kill myself.