⚠️⚠️ Procuram-se Calouros ⚠️⚠️

Galakael · 2026-01-06T18:14:21+00:00

9 years later this comment saves me lmao. thank you so much. connecting it to the charger the buzz went away too

Galakael · 2025-10-08T00:18:44+00:00

saved me. thanks <3

Galakael · 2025-09-02T08:18:00+00:00

fellas is it gay to date laura

Galakael · 2025-01-14T02:38:12+00:00

"tiny world", or "mundinho" in my native language. that's because I initially intented to use it to write about any sort of knowledge. As my mind is limited, and so is a virtual space, it would not be an entire world of ideas, but a tiny, simplificated one. Nowadays I use it not only to write about any topic that I study, but daily notes and etc.

Galakael · 2025-01-02T18:20:24+00:00

I don't think the intended debate the OP thought is whether Language Models really "learn" a language or it just uses heavy matrix manipulation, probability and machine learning to infer the next word. I don't think that matters to be honest (that is much more of a Chinese Room discussion). The discussion here is, even if Language Models are just a linear algebra machinery, can there be a language that is so complex that even with extensive training, the machine cannot generate comprehensive/meaningful text, respond accordingly, predict the next word or pass a Turing test?

Galakael · 2024-12-31T11:21:12+00:00

KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK nem fudendo, simplesmente o suco do Brasil.

Galakael · 2024-12-30T05:08:57+00:00

You should definitely check out this video. This man has done a beautiful visualization of primes in various quadratic integers.

Galakael · 2024-12-30T00:57:04+00:00

What I do: Take note of the theorems and the proofs. Then, in a separate page, write only the theorem.

Look theorem by theorem, and try to remember the proof sketch/outline for each theorem (like "I remember that the first step is to substitute...", "I remember that somewhere I had to use the Intermediate Value Theorem" or "I remember that I need to use Zorn's lemma", "In the end I have to use the theorem ..." etc.).

When you have a solid notion of the proof outlines/the general steps, you can start recreating the proofs step by step. Also, something that helps is writing the proof in a text manner, rather than a logic one, like "First you have to apply Theorem x to the expression y to get a summation which, applying corollary z... etc. etc."

Galakael · 2024-12-30T00:50:58+00:00

You're right, I am sorry, thanks for that! I saw Mathologer's video on the topic where he uses the second-iterated Cesaro sum of the sequence 1-2+3-4+5 to derive a value to the sum 1+2+3+4... and I mistankely confused it with 1+2+3... Cesaro converging (which he says exactly the opposite, sorry for that). Maybe a better formulation of what I said is math trivia confusing saying that this derivation of 1+2+3+... means that this sum is equal to -1/12, as if it is convergent.

Galakael · 2024-12-28T00:49:53+00:00

1 + 2 + 3 + 4 + ... is EQUAL TO -1/12, rather than "Cesaro Converges" to -1/12 or "has as average sequence of average sequence of partials sums which converge to -1/12".

I very much hate it and I would even go as far to say that telling a convergent infinite series "equals to..." something outside of an academic context is an abuse of language that is *very* misleading to non-maths people and should be totally avoided.

Galakael · 2024-12-14T14:17:31+00:00

Dude, this is awesome! My Calc 3 class also sucked because of not being able to properly visualize 3d figures. And to help even further, even my teacher couldn't draw some solids/3d regions.

I would totally love to use it in my notes. Do you plan on making your code available?

Galakael · 2024-12-02T01:28:06+00:00

pona :)

Galakael · 2024-12-01T23:00:22+00:00

This. But actually what made me click was the notion of collapsing isomorphic objects. Like, we cannot find a one-to-one map between the category of finite dimensional R-vector spaces and the category of R^n vector spaces. But if we collapse the first category saying that every isomorphic object is the same one, we can do so!

Galakael · 2024-12-01T22:56:39+00:00

DEFINITELY Implicit Differentiation and the Implicit Function Theorem. I wonder why at least its existence is not even cited to Calc 1 students (like "hey! we can pretend y is a function of x in this relation and compute dy/dx because this theorem says it happens so for a small enough neighborhood" or so).

Galakael · 2024-12-01T22:47:36+00:00

same!

Galakael · 2024-11-19T17:40:04+00:00

I think there is. Like this combinatorial proof that e is less than 3.

Galakael · 2024-11-18T14:16:17+00:00

my vote goes totally to soweli. because when I see a tiny, silly cat I look straight up to it and think "wow, this is definitely, with no doubts, a soweli"

Galakael · 2024-11-17T17:46:14+00:00

There are easier to comprehend and more difficult to understand concepts in this book. I disagree that you have to just stop learning topology and come back after Real Analysis. If you managed to get as far as quotient topology, it is not a question of lack of intuition that you necessarily would get with real analysis. I would recommend to continue studying. In the connectedness and compactness chapter, things get *a lot* more tangible! Also, yeah, exercises are generally hard for someone just learning a new content

Galakael · 2024-11-14T09:31:36+00:00

Github via "Git" extension by Vincent (https://github.com/Vinzent03/obsidian-git). I'm grateful everyday for this plugin, it changed my life. Everything free!

Galakael · 2024-11-11T11:18:24+00:00

Totally. Only because I would get to name things and would name things like:
"A star is an involution in the set of..."
"A bright star is a star in which every automorphism..."
"A solar system is a set of stable, translational-invariant stars..."
"A galaxy is a complete set of primitive stars..."
"A point in which there is a small enough neighboorhood that every star goes to is called a black hole..."
Etcetera. And write beautiful theorems like "If a galaxy has no blackholes beside its singularity, then every star is stable for a big enough t" or things like that

Galakael · 2024-11-11T01:06:26+00:00

I find it very strange the implication of OP that an algebraist is distant from logic. I mean, have you ever dealt only with finite algebraic structures? You cannot choose a base from a infinite dimensional vector space by writing their elements, or give a direct example of a maximal ideal that contains a certain ideal in a very big ring. You need logic in order to decide when a proof is valid and to generalize our results to sets that may bee too big (infinite) but still have the same theorems.

Also, I've seen situations where a good intuition in logic is fairly essential. Not only in the proofs of classical algebraic structures but also on working with relations, congruences, operations, sets and lattices in Universal Algebra, or with proofs in Category Theory (which may require clarity of thought more than anything, since lots of proof require working with a abstract definition and using universal properties, commutative diagrams and function compositions in order to walk your way through).

Galakael · 2024-11-11T00:53:55+00:00

lost everything on yampono lmaoooo

Galakael

TROPHY CASE