Originally Posted by

**SpringFan25** BTW, i never studied this and i am basically guessing.

I'm not sure whether the questioner is really interested in the specific case of "is a part of e inside pi", or the general question of "will an irrational number contain an arbitrary finite sequence if you go through enough digits".

If the interest is in the second question, read on...

The answer to the second question is no, it is not necessary. The simplest way to prove it is to show that an irrational number can be constructed without containing a sequence, x.

Define:

x = the finite sequence you are looking for

y = all but the last digit in that sequence

Then the following number is irrational because it never repeats:

z=y0y00y000y0000y00000y00000y000000y0000000y...

(if the last digit of x was zero, youd need to use a different number as a spacer, obviously!)