Note: According to my high school math teacher, people have seriously gone insane because of musing over stuff to do with infinity, so unless you are fine with going insane, or are sure not to ponder too much, stop reading now :P
Relatively basic mathemetics is that irrational numbers, such as Pi, have an infinite number of decimals that do not repeat forever. Numbers with an infinite number of decimals that do repeat, however, are considered rational(such as 10 / 3).
Another relatively basic piece of mathemetics is that any irrational number contains any possible combination of numbers, so given that you keep calculating for long enough, your birth date, your credit card number, all of your passwords in binary, and basically every possible series of numbers is somewhere in Pi.
But think about this: Does that mean that the same goes for e, the square root of 2, the square root of 3, and all irrational numbers? And if every possible combination of numbers is in Pi, then is Pi in Pi? And what about 10 / 3, which is rational? And if Pi is in Pi, would that mean that it repeats, so it is no longer irrational - but 10 / 3 would also be in Pi, along with Pi itself, then it would not repeat, meaning that it is irrational AND rational at the same time?
Now, since you have read this, make sure you do everything you have ever wanted to do in your life before you go insane. :P