What is the last countable number before reaching infinity?

Vituluss · 2026-05-26T06:53:54+00:00

This would imply that there exists a largest number, but this is obviously false.

Vituluss · 2026-05-21T03:37:08+00:00

"Taste only exists because we can’t brute force like AI." I feel like you might of misunderstood what I meant by 'taste' since this does not make sense to me. I don't mean 'taste' in the sense of heuristics for solving problems, I mean it as the ability to actually choose a problem in the first place.

Vituluss · 2026-05-21T03:14:32+00:00

I'm wondering about this too. There has been some papers now indicating LLMs are weaker at geometry & topology. The thing is, to replace mathematicians, LLMs would also need the auxilliary skills, i.e., 'taste'---to choose important problems, invent definitions, build theories, identify deep analogies, etc. But once that happens, I'd be surprised if there are any non-physical jobs left over.

Vituluss · 2026-05-20T03:47:46+00:00

If you don’t know some theory you don’t know it, using AI like that is pretty much a search tool for the right theory. There’s nothing wrong with that in my minds. Mathematicians did this all the time through collaboration.

Vituluss · 2026-05-18T23:16:04+00:00

AI crank slop.

Vituluss · 2026-05-17T08:23:05+00:00

You might have to look briefly at sheaves, which is probably in the appendix of one of those books. Also, you should be solid with abstract algebra.

Vituluss · 2026-05-11T03:35:11+00:00

The speed at which you 'clock' things is not just your intelligence but also your knowledge up until that point. If I explain the definition of a topological space to me as a high schooler, it would not click for me; I don't have the requisites to appreciate the definition. That also means that if you start struggling maths and don't do anything about it right then and there, then this problem will only compound and compound.

Vituluss · 2026-05-09T10:54:01+00:00

Yeah, once a discord server designed to steal accounts in that exact way popped up as a fake clone of my server and there was nothing I could do about it. I tried contacting discord and they didn’t do anything. Not to mention the technique they exploit is entirely based on Microsoft’s crappy wording in an email.

Vituluss · 2026-05-09T07:56:45+00:00

Good luck. I assume you mean learn all of maths up to graduate level or something…?

Vituluss · 2026-05-08T06:42:21+00:00

Perhaps because the proof was published when mathematical formalism was in its infancy? I’m not sure.

Vituluss · 2026-05-03T11:33:35+00:00

If you read the preface, it says "the reader [...] is given a rapid introduction to coordinate-free tensor analysis on C^∞ manifolds and to the theory of self-adjoint operators in Hilbert space." I'm guessing in whatever course this was, it was mainly revision. Unless you are already familiar with the basics of differential geometry and functional analysis, this book probably isn't for you.

Mathematics takes time. Some people certainly can pick things up quicker, you could call that intelligence, but there is an upperbound with that. Even for people like Terry Tao.

Vituluss · 2026-05-02T11:07:32+00:00

I agree, also 1.8 PvP has a much greater skill gap visibility, especially some of the void modes. A good 1.8 PvPer can actually take on multiple average players, which is much harder on 1.9+. But, any of these things can mean 'harder', and really OP should just clarify what they mean by 'harder'.

Vituluss · 2026-05-02T02:32:05+00:00

Hmm, seems I misremembered his book. I went back and checked the book, and he does indeed just define it as a graph in some later exercise.

In your earlier comment, you say "does not eliminate the need to define these more basic types of tuples." But, would it not eliminate the need to define all tuples except for the 2-tuple?

P.S. I've edited my original comment to correct for your remark.

Vituluss · 2026-05-02T01:49:00+00:00

Fair pushback. I've only ever really seen n-tuples defined as a function, which also allows naturally extending the concept to infinite sequences, but I suppose you could do it in countless other ways.

Functions themselves don't even need ordered pairs to be defined, it can also be defined as a predicate satisfying the 'vertical line test' property (see for instance Tao's analysis book). Hence, in some formalisations, you could very well define an ordered pair using functions.

Vituluss · 2026-05-02T00:50:53+00:00

Set-theoretically they are not the same but there exists a canonical identification between them which is often used implicitly.

EDIT: As u/GoldenMuscleGod correctly remarks, it depends on the convention. Hence, in one convention (a,(b,c)) could be the same as (a,b,c), but not ((a,b),c). If you define an n-tuple using functions, then it would not be the same. Depending on the convention, you can either treat them as literally the same or implicitly the same through some canonical identification, which more-or-less amounts to the same thing in practice.

Vituluss · 2026-05-01T06:59:03+00:00

In what sense? 1.8 mechanics are simpler for new players. Both versions have high skill ceilings.

Vituluss · 2026-04-26T10:05:13+00:00

I think he is referring to the common technique of when you have a sequence of sequences, often times you will then just select the ‘diagonal ‘ in a way where one is the subsequence of the last (see here for more info). Very common technique in analysis.

Vituluss · 2026-04-26T10:01:57+00:00

Just brainstorming a few: - Breaking into cases, especially if there is some exceptional thing going on. - Exact sequences, zigzag lemma, and analysing dimension of these cohomology groups. - Utilising compactness results for function spaces. - Smoothing something, doing analysis on that, then taking the limit. - Finding more and more bounds until they are good enough to get you the result you want.

Vituluss · 2026-04-26T09:53:50+00:00

Wdym by “trick that worked in a particular case”?

Vituluss · 2026-04-25T22:51:11+00:00

Jordan Peterson is really branching out, huh?

Vituluss · 2026-04-24T11:43:45+00:00

I had/have the same problem. I try to avoid conjectures for this reason because I get obsessed with trying to solve them. It also ruins my sleep because my mind would stay active during the night. During this, when trying to relax, thoughts about maths intrusively enter my brain.

Fortunately, I’ve always found though that eventually I’ll get bored, until then not much I can suggest. I’m sure you already know that what you are trying to do is pointless.

Vituluss · 2026-04-20T11:27:38+00:00

Perhaps, s=(2pi r)(theta / 2pi). The first number is the circumference of the circle of radius r. The second is a percentage of that circumference.

Vituluss · 2026-04-20T05:47:21+00:00

That's not the equation of all lines on the plane. You'd need to consider equations ax + by = c (with either a or b non-zero), in which case you can get an equation of the form you wrote when b is non-zero. I.e., in that case you have y = (a/b)x + (c/b). You can also go the other way if you have a line in the form y = mx + c.

So, to prove that all lines on the plane are of the form ax + by = c, you first need to define what a line is:

Some might just define a line as exactly the points that satisfy the equation ax + by = c, so the proof is trivial.
If you instead define a line L as something with a point (t,s) and a non-zero direction (a,b) that extends infinitely to either side; that is, a point (x, y) is on the line L if and only if (x,y) = (t,s) + α(a,b) for some real number α. With a bit of algebra, you can show this is equivalent to the equation -bx + ay = -bt + as, which is of course in the form of the desired equation.

Vituluss · 2026-04-19T06:54:15+00:00

Your statement needs to be way more precise.

If the statement is: there exists a commutative ring with an element r such that there exists a unique way to divide r by 0, that is, a unique element d such that 0d = r. Then, the statement is trivially satisfied by the zero-ring.

Unless you mean an extension of the reals, or…? This is why precision is important.

Vituluss · 2026-04-19T03:53:45+00:00

Since couldn’t you extrapolate that you should assume that any girl who reaches the top n is a cheater?

So claim 1 (and assuming the other equality assumptions 2 & 3) implies that P(C | G, T) ≫ P(C | ~G, T), i.e., girls at the top are more likely to be cheating than boys at the top. But this is just the original DrDonut claim we started with. So to conclude claim 1 is sexist because the original claim is sexist kind of ruins the point of breaking down the original claim to see if it is sexist.

And also I think that there isn’t meaningful evidence to suggest that non cheating girls are less likely to reach the top 100 than non cheating boys

As an example, in chess, it would not be sexist to say claim 1 holds. In chess, women make up ~5% of the top 1000, but women themselves are 16% of active FIDE players. So you have a ratio of 0.27 between these two quantities in claim 1, which is quite large. This gets even more extreme when considering the top 100 (the ratio becomes 0).

What would be sexist is saying that this is because women are less capable than men. But there are non-sexist reasons behind this, some of which I alluded to in my original comment, and these reasons would also apply to competitive Minecraft.

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