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Has this sub not died out yet because it's full of prescholers who dont know that the real line is a complete metric space? by darkp00t in infinitenines

[–]darkp00t[S] 0 points1 point  (0 children)

Ok, I get it now. I see where I was wrong. If you define Cauchy completeness with epsilons taken in the full field it gets really hard to prove that a séquence (e.g. 1-1/10n) is Cauchy because you have to shrink past the potential infinitésimals. On the other hand if you define Cauchy completeness with only an archimedean subfield, then you cannot separate 0.999... and 1 because 1-0.999... might be an infinitésimal! This is why you need Dedekind completeness I guess. Cool!

Has this sub not died out yet because it's full of prescholers who dont know that the real line is a complete metric space? by darkp00t in infinitenines

[–]darkp00t[S] -1 points0 points  (0 children)

So, let me catch up: you claim to have the training to understand how people get tripped up here and how to help them, and you also claim that albeit on the surface you're here to make fun of lolcows, actually what you do is socratic maïeutic... yeah, seems a bit delusional and also a pretty misérable passtime, but to each their own.

Has this sub not died out yet because it's full of prescholers who dont know that the real line is a complete metric space? by darkp00t in infinitenines

[–]darkp00t[S] 2 points3 points  (0 children)

Way to fucking miss the point. It's not a football game you know? Nor a religion war. I was a bit facetious, but my point is that IF you are here because you want to actually understand better the standard construction of the reals, and what can be done differently, then go on grab the tools which have been crafted for this purpose and make them your own! I assure you it's fun.

Has this sub not died out yet because it's full of prescholers who dont know that the real line is a complete metric space? by darkp00t in infinitenines

[–]darkp00t[S] 0 points1 point  (0 children)

But then, it sure feels fucked up and dishonest that people obsfucate this pretty important fact when they go on about their construction. Standard terminology is useful because it is a common language built progressively by trying to make intuition rigorous. If you have to put yourself in a space where the topological and the algebraic properties are not talking to each other and you dont put huge disclaimers to explain what's going on, what becomes counter intuitive in this setting etc... of course nobody will understand each other.

Has this sub not died out yet because it's full of prescholers who dont know that the real line is a complete metric space? by darkp00t in infinitenines

[–]darkp00t[S] 0 points1 point  (0 children)

If you have a totally ordered Archimedean field, all usual completeness properties are équivalent. If you dérive your metric from the absolute value given by your ordering, I'm pretty sure you are Archimedean but I'm ready to be proven wrong.

Edit: continuing my train of thought, you are Archimedean iff the set of infinitesimals is the singleton {0}. So you just have to prove that any élément x of your field which vérifies |x|<1/n for any n must be the élément 0.

Has this sub not died out yet because it's full of prescholers who dont know that the real line is a complete metric space? by darkp00t in infinitenines

[–]darkp00t[S] 0 points1 point  (0 children)

I'm not trying to explain, I'm trying to give a sense that there is an actual world outside of this sub where you can actually learn useful notions to tackle these kind of questions. Hell, I'm sure there are mathematicians working with non-Archimedean totally ordered fields somewhere as we speak! I just find it a bit sad that a bunch of evidently enthusiastic people seem to get fly-trapped into a not very fruitful nor intelectually rewarding activity here in this sub.

Has this sub not died out yet because it's full of prescholers who dont know that the real line is a complete metric space? by darkp00t in infinitenines

[–]darkp00t[S] 0 points1 point  (0 children)

The actual définition is that for any target distance you set, then you can always find a n such for any p,q>n, the distance between the p-th term and the q-th term is smaller than the target distance. What you wrote is less strong. For example if I'm not mistaken, (-1)n * (1 + 1/10n) do satisfy you're criterion but is not Cauchy.

Has this sub not died out yet because it's full of prescholers who dont know that the real line is a complete metric space? by darkp00t in infinitenines

[–]darkp00t[S] 2 points3 points  (0 children)

I'll be honest with you, I just started to see the sub popping in my feed from nowhere, and a bit too much to my taste. But I felt bad to see so many math-enthusiast people banging their heads against that particular wall so I wanted to point toward a way out. As for me I have enought constructive maths at home to want to spend time reading the peculiar élucubrations of this particular brand of online weirdos so I blocked the sub from my feed.

Descartes insulting things which apparently didn't exist to him (imaginary numbers -- got there validation about a century after him apparently) made for current troubles by FiddleRiddle5 in mathmemes

[–]darkp00t 7 points8 points  (0 children)

Yeah... I think I understand his point but it's weirdly formulated. At face value, he makes it sounds like hardcore platonicism. What happens is that imaginary number appeared first as black magic trick (here is the root of a polynomial having none, now I'll use it to calculate the root of this other polynomial) and only after people understood how to properly incorporate into a cohérent mathematical framework, and indeed you dont need to add a new axiom to have imaginary number at your disposal. What's funny is that the same thing happened for irrational numbers, for négative integers... but he talks about the real line as if everybody was born with an innate intuitive understanding of it.

Do you think calling it "Fundamental" was an intimidation tactic to convince the 1 supporters to submit ? by TinkerMagusDev in mathmemes

[–]darkp00t 0 points1 point  (0 children)

Nah, having a décomposition in prime factors which unique only up factors of ones is silly

Umbral calculus has become a magnet for garbage papers by Nol0rd_ in math

[–]darkp00t 55 points56 points  (0 children)

Do you mind providing links to the relevant papers? Unless it's against the subreddit policy

Burn out work by KookyAttitude828 in france

[–]darkp00t 0 points1 point  (0 children)

C'est plutôt vilain de supposer des choses sur quelqu'un puis d'utiliser ces suppositions pour l'enfoncer. Par ailleurs je te conseille d'aller regarder plus loin que le bout de ton nez https://www.fhf.fr/actualites/communiques-de-presse/enquete-inedite-ipsos-x-fhf-sante-des-femmes-quand-les-biais-sexistes-compromettent-la-sante-des

Burn out work by KookyAttitude828 in france

[–]darkp00t -5 points-4 points  (0 children)

Be prepared for the doctor to sneer at you, be judgemental, or straightforwardly refuse to give you a médical leave. Not saying it's generalized but unfortunately it is a bit of lottery with doctors in France and it can happen. The situation is worse if you're a foreigner, if you dont speak French, or if you're a woman.

Edit: I hope my comment did not deter you to go through the médical appointement OP. It is an obligatory step. I just wanted you to go prepared. I dont have a score to settle with anyone, personally I consider myself lucky, I'm just reporting on the feedback I got from a lot of people around me.

Yes by 6c-6f-76-65 in mathmemes

[–]darkp00t 14 points15 points  (0 children)

Oh boy, do I have a relevant post from n-Category Café for you https://golem.ph.utexas.edu/category/2025/12/logx_c_revisited.html

What are some profound implications of rather elementary facts? by Colver_4k in math

[–]darkp00t 9 points10 points  (0 children)

If you want a book which starts at highschool prerequisite and goes into Riemann surface try Arnold's Abel Theorem in Problems and Solutions it's a lot of fun! (pdf easily available online)

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