A proof that Pi does not contain all possible finite combinations

Nobody believes such a result is true. To the contrary, everyone in mathematics expects pi is what is called a normal number: all finite strings of digits should occur infinitely often, and in fact with a positive frequency: there are 10n different strings of n successive decimal digits and each of these strings of digits should occur with limiting frequency 1/10n. For example, the digit string 1234 should occur as successive digits of pi with limiting frequency 1/10000. Note I am saying should occur. There is no proof that pi is a normal number, but everyone believes it, and therefore your proof is almost certainly incorrect. Moreover, a proof about a property of all the digits of pi is almost certainly going to require some serious nontrivial mathematical ideas. In looking over your proof, there's "nothing" there: no deep or substantial ideas at all. This is why it is immediately suspicious that you have achieved anything in your argument.

To take a simpler result, proving pi is an irrational number is pretty hard. All known proofs requires calculus, and the way calculus is used is not an elementary kind of calculation. Irrationality of pi is not proved by mucking around without actually doing something subtle.

/r/math Thread