User blog comment:MachineGunSuper/My problem with pi/@comment-30754445-20171217195220/@comment-1605058-20171217231455

If pi contains every pattern at least once, then it contains every pattern infinitely many times - for example, if we pick a pattern, say, 25678015689, then if all of the patterns 256780156891, 2567801568901, 25678015689001, 256780156890001,... (appending 00...01 at the end) appear at least once, then the sub-pattern 25678015689 must appear infinitely often.