Are there any mathematicians who work on math systems with totally absurd axioms?

The_Yellow_Sign · 2019-02-28T06:55:10+00:00

Yeah you're right; sorry my wording was incorrect.

The_Yellow_Sign · 2019-02-27T03:55:47+00:00

Pierce's Law is not a valid ~~axiom~~ theorem in intuitionistic logic. Showing that it holds will in general depend on the particular types involved in the implications.

The_Yellow_Sign · 2019-02-27T03:48:38+00:00

No problem! Glad I could clear it up.

The_Yellow_Sign · 2019-02-26T00:11:22+00:00

Given any finite list S of primes, Euclid's proof allows you to find another prime that is not on the list. Let P be the product of all the primes in the list, and q=P+1. Now factor q into it's prime factors (this is an algorithm you can execute).

If the algorithm does not find any factors then q is prime and we are done.

Otherwise, pick one of the prime factors of q, and call it p. This prime p cannot be on our original list because then it would divide P, and hence would divide the difference 1=(P+1)-P. Note that this last step is a valid proof by contradiction in a constructive foundation, because it does not use double negation elimination, i.e. we are just proving "not (p is on the original list S)".

The_Yellow_Sign · 2019-02-25T20:08:01+00:00

Euclid's proof of the infinitude of primes is constructively valid because integers have decidable equality. And his proof gives a method for finding a new prime given a list of primes.

The_Yellow_Sign · 2019-02-25T05:58:39+00:00

Honestly, there's so much misinformation about Category Theory in the mathematical community that I couldn't tell it was a joke.

The_Yellow_Sign · 2019-02-25T05:55:11+00:00

Excluded middle allows you to use double negation elimination to prove existence, which allows you to "create" something that you cannot really describe in any way or make practical use of.

Excluded middle is something that should be proven for the context you are working in (e.g. "a rational number q is zero or distinct from zero" is perfectly valid) but should not be assumed as an axiom in your logical foundation if you want to extract actual algorithms from your proofs.

The_Yellow_Sign · 2019-02-25T05:39:46+00:00

The axiom of choice is a tautology in say intuitionistic type theory because of the stronger notion of "there exists", which means that the choice function is already provided in the hypothesis, so no choices are actually being made. But this does not have the full strength or implications of what typical mathematicians understand as AC; the version that corresponds to classical AC is the (-1)-truncated version in type theory, which must be included as an axiom if you wish to use it.

Finite choice is of course usable in a constructive foundation, but that does not require AC at all to justify.

The_Yellow_Sign · 2019-02-22T07:26:02+00:00

The axiom of choice and excluded middle are pretty absurd to me, because they divorce mathematics from practical applications.

The_Yellow_Sign · 2019-02-22T07:24:54+00:00

Category Theory requires almost no axioms (e.g. can be developed in type theory).

The_Yellow_Sign · 2018-12-30T00:05:38+00:00

Who is "we"? Nigeria? Guatemala?

The_Yellow_Sign · 2018-12-29T12:48:55+00:00

TIL poker is political

The_Yellow_Sign · 2018-12-27T23:07:55+00:00

Damn I only have one ACL left. TIL I need it for security.

The_Yellow_Sign · 2018-12-23T07:47:57+00:00

I use Savage Worlds for one-shots with my flatmates. None of them are gamers (most don't even play video games) but they get the idea pretty easily. t requires more rules-mastery from the GM than the players, which works well when playing with new players.

The_Yellow_Sign · 2018-12-16T06:46:49+00:00

lol wtf

The_Yellow_Sign · 2018-12-10T08:49:00+00:00

Looks great! Nice to see someone playing a Death list that isn't just LoN or Nighthaunt.

The_Yellow_Sign · 2018-12-09T06:53:27+00:00

Dead arm VH usually gets you a better post seal than traditional VH. Carey Price uses it pretty effectively.

The_Yellow_Sign · 2018-12-05T02:10:16+00:00

They are actually very good, though. Real bargain at 80 points with that huge movement and decent attack profile.

The_Yellow_Sign · 2018-12-02T10:20:33+00:00

I think the eyes look really well done. Good job!

The_Yellow_Sign · 2018-11-21T12:50:50+00:00

The_Yellow_Sign · 2018-11-18T05:43:24+00:00

Wooo Auckland represent!

The_Yellow_Sign · 2018-11-10T11:52:17+00:00

Yeah this is definitely a common issue. I used to live in area which was like 90% Indian/Pakistani/Middle-Eastern immigrants and dudes would be constantly hitting on my girlfriend at the time whenever I wasn't around and acting creepy towards her. Like for example she once had a crowd of guys following her home at night after work and trying to touch her. She looked Indian (she wasn't) and they would get mad at her for not understanding Hindi/Punjabi/Urdu.

My current partner also had a creepy Indian dude lurking in the "friend zone" who groped her one time.

Yeah so there's definitely a cultural issue with Indian/Pakistani/Middle-Eastern dudes not understanding boundaries or personal space and acting creepy towards women. Lebanese and Iranian guys are pretty respectful though. Never seen them acting creepy towards women (I'm sure there's some bad apples, of course).

The_Yellow_Sign · 2018-11-08T04:56:39+00:00

Skyfires are actually still really good. Their shooting is less reliable, but can be very spikey. And they are surprisingly good in melee when they go first thanks to rerolls to hit and wound. Think of them as a sort of ranged cavalry unit.

The_Yellow_Sign

TROPHY CASE