Is an irrational number, such as $\pi$ or $\sqrt2$, guaranteed to contain every possible digit sequence somewhere within it? Is there no proof for this? Is there any clue as to whether this is so? It seems logical to me, seeing that irrational numbers continue infinitely and are essentially patternless.
If it is true that every possible digit sequence can be found in any irrational number, that would imply that one could find any set of data (such as an encoded version of the Human Genome Project or something like that) within an irrational number, which would be quite intriguing in a philosophical context.