I was reading the Wikipedia pages for normal numbers and disjunctive sequences (hadn't come across either of these terms before so I'm not an expert or anything, pls be nice. Just going on a tangent on pi stuff). Saw it mentioned that "A normal sequence is disjunctive, but a disjunctive sequence need not be normal". There didn't seem to be a citation for the claim that a normal sequence is disjunctive, is there a proof for this? Or some super obvious thing I'm missing (besides the fact that it seems intuitively correct)? I don't see why a number having equally distributed digits means it must contain any finite sequence of digits. (This might not make a lot of sense because I'm sort of flipping between sets and numbers but it's because I'm trying to contextualize this for myself using pi which I see as more sort of concrete (I have not studied anything to do with sets)).
note - as far as I am aware this is not a question about disjunctive normal form - I think that's something else.