/sci/ - Science & Math

>>8309220
Considering the hypothesis can either be true or false its a safe bet (50/50) to assume its true

>>8309220

Several already-proven theorems of the form

"If RH is true, then this other thing P(x) is also true"

would, in the event that RH is actually true, immediately establish that the various P(x)'s in theorems of the above form are in fact also true.

Furthermore, several already-proven theorems of the form

"RH is true IFF Q(x) is true"

would similarly (though in a logically distinct fashion) establish the various Q(x)'s to actually be true, because they really say the same thing as RH, albeit in sometimes very, very different language - Farey sequences are one example of this. In this latter formulation, RH and a given Q(x) rise and fall together. If RH is false, then all Q(x)'s are immediately scuppered. In contrast with this state of affairs, some of the above P(x)'s might yet in principle be salvaged (that is, proven true) even if RH is false - a false thing may imply some one given true thing, but it can never happen that a true thing implies a false thing, unless a human has goofed their work somewhere, which isn't the same thing. Thus RH being true would immediately vindicate all established P(x)'s, whereas RH's falsity does not necessarily of itself banish all P(x)'s into falsity.

There is furthermore something stronger/larger/closely related called the generalized Riemann Hypothesis, certain sections of which have been established. GRH is also attended by a series of established theorems which are of the same form as the above two, and establishing RH would presumably at a bare minimum be an important insight to establishing GRH itself, if such is possible. One example of a purported (though apparently not yet wholly settled) P(x) in this case: something very similar to Goldbach's conjecture called Goldbach's weak conjecture is said to follow from GRH.

What I wonder about at this point is whether RH might be shown to be undecidable/somehow unprovable. This would have very strange, abstruse consequences for all of the above entailed statements.

>>8309232

>half the M&Ms are poison, it's okay, eat up!

5/10 for managing to phrase something that dumb on purpose, and getting me to reply.

>>8309232
This is well done.

You combined pic related meme with something even stupider.

>>8309349
That's not a real quote, right? Often people confuse a possible event with its probability.

>>8309232
>this is what Bayesians actually believe

>>8309365
What do you think?

>>8309232
Alright GV

>>8309365
>Stephen Wolfram speaking without praising Stephen Wolfram. Fat chance, kid.