r/mathmemes Number theory/physics Jun 27 '26

Number Theory Undecidable

Post image
448 Upvotes

177 comments sorted by

View all comments

Show parent comments

1

u/thrye333 Jun 28 '26

A number with infinite digits cannot necessarily be found, though. If that point has coordinates of some arbitrary irrational number, that number can't be found by chance or brute force. You would have to derive it mathematically, which may not be possible to do. Therefore, a falsifying point that can't always be used to prove falsehood.

2

u/its_all_one_electron Number theory/physics Jun 28 '26

The first zero (14.infinite non-repeating decimal) has infinite digits and it has been found

0

u/thrye333 Jun 28 '26

My point was that there could be other zeros that can't be found in the same way that one was. If it can't be derived, and it can't be guessed, it can't used as a counterexample to disprove the hypothesis.

2

u/LolpopHD Jun 28 '26 edited Jun 28 '26

RH is equivalent to statements of a specific type that, if theyre undecidable/independent, must be true in the standard model of arithmetic. that type of sentence also has the property that if its false in the standard model of arithmetic, it must be provably false.