Infernic

You can’t grow wheat in ℤ/6ℤ because it’s not a field.

This is the happiest day of my life

esta asignatura se está poniendo rara

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Algebra: These beautiful theorems prove that the universe is intrinsically good and life has a deeper meaning Analysis: Here is a counterexample

@KristapsBalodi3 @TonyTheLion2500 hmmm but isnt class field theory classifying the galois representations of degree one or something

@Infernic1 @TonyTheLion2500 You don't need cohomology nor do you need representation theory to start learning CFT.

You clearly haven't tried to learn class field theory. I wish I was just misunderstanding it 🥴

@TonyTheLion2500 @KristapsBalodi3 how can you even begin to understand cft without group cohomology, infinite galois theory, representation theory, and alg nt?? that has to be a waste or time

@KristapsBalodi3 Yeah I am a little chaotic, so I need CFT as motivation to learn those things. I know some Galois theory.

@eleusinianatlas @Unlearned_Hand @Draren_Thiralas @NLRG_it No, you misunderstand. You think i am handwaving and not rigorous, and you would be correct. But you are only correct because I am explaining it to a lay person like you over twitter, so it will never be completely rigorous. Consult a textbook instead, they will be truly rigorous

@Infernic1 @Unlearned_Hand @Draren_Thiralas @NLRG_it For me it's very simple - you guys have smuggled physics into math. You adopted the "for all practical purposes" approach. It's not mthematicallt rigorous.

scientific american, ladies and gentlemen

@eleusinianatlas @Unlearned_Hand @Draren_Thiralas @NLRG_it This doesnt make sense. All experts agree on this definition. Just because some (many) people do not understand it, does not mean it is not true. I do not understand general relativity, but that is not my domain, and i do not question it (i do not have the knowledge to do so)

@Infernic1 @Unlearned_Hand @Draren_Thiralas @NLRG_it They are declared to be understood in your bubble.

@eleusinianatlas @Unlearned_Hand @Draren_Thiralas @NLRG_it I sent you the wikipedia article where this is described earlier in a bit more detail. Its also covered at the start of most real analysis textbooks. This is old math, and is well understood.

@Infernic1 @Unlearned_Hand @Draren_Thiralas @NLRG_it I simply don't buy it. It's simply wrong. This definition is absurd.

@eleusinianatlas @Unlearned_Hand @Draren_Thiralas @NLRG_it I say = because in the real numbers, being = is defined formally as this idea of ‘approaching’ of cauchy sequences, roughly speaking (other conditions must be satisfied). This is made rigorous via the equivalence relations that i discussed earlier.

@Infernic1 @Unlearned_Hand @Draren_Thiralas @NLRG_it Then stop saying "=" instead of "approaching".

@eleusinianatlas @Unlearned_Hand @Draren_Thiralas @NLRG_it No, i do not say that. This does not have much to do with what we are even talking about. However, as an analogy, i am saying that the value of the line can be made equivalent to any cauchy sequence that converges to it. A graphs value converges to an asymptote.

@Infernic1 @Unlearned_Hand @Draren_Thiralas @NLRG_it You literally say this: an asympote crosses the line it approaches.

@eleusinianatlas @Unlearned_Hand @Draren_Thiralas @NLRG_it Well i dont question the centuries old results of real analysis, i simply put all my effort to understand them and why they are true, so that i can get to the cutting edge later (although not in analysis, because i prefer algebra)

@Infernic1 @Unlearned_Hand @Draren_Thiralas @NLRG_it Your course wasn't either, I know the curriculm of math departments.

@eleusinianatlas @Unlearned_Hand @Draren_Thiralas @NLRG_it Behold, the equivalence relation, an incredibly useful tool used everywhere in math. It redefines what it means to be equivalent. It turns out that if two cauchy sequences converge to the same number, you can define an equivalence relation called the real numbers:

@Infernic1 @Unlearned_Hand @Draren_Thiralas @NLRG_it I just totally reject connecting an algorithm with a simple number by using the "=" notion.

@eleusinianatlas @Unlearned_Hand @Draren_Thiralas @NLRG_it I guess the point of me saying this is that it is good to question results, but it would probably be more productive to question results at the cutting edge of mathematics where flaws in proofs are much more common. Your introductory real analysis course is not one of those areas

@eleusinianatlas @Unlearned_Hand @Draren_Thiralas @NLRG_it To prove a theory in physics wrong is (typically) to make an observation that undermines the theory, while in math to prove a theorem wrong is to find a flaw in its proof. But the proofs discussed here are 100s of years old, scrutinized by many people. Good luck finding a flaw.

@dezren39 @stikves @NLRG_it Z is a totally ordered set, R is not, so Z does not have this property that R has.

@stikves @NLRG_it ℤ there are exactly zero numbers between 0 and 1

@eleusinianatlas @Unlearned_Hand @Draren_Thiralas @NLRG_it No, i am simply a student studying graduate level mathematics. Although i am also more of an algebraist, so analysis is not really my thing. Regardless, this discussion is not really anything complicated in anysis so i am perfectly qualified to answer it.

@Infernic1 @Unlearned_Hand @Draren_Thiralas @NLRG_it Do you think you understand math better than Roger Penrose?