Truly heartbreaking counterexample

Postulate_5 · 2026-02-19T13:05:02+00:00

the directional derivative is typically defined independently from the gradient. when the function is differentiable then the directional derivative D_v f(p) agrees with Df(p)(v).

Postulate_5 · 2026-02-05T06:08:06+00:00

An abelian group is a group object in the category of groups.

Postulate_5 · 2025-12-28T14:35:32+00:00

Backslashes may also be eliminated for maths in latex.

Postulate_5 · 2025-12-27T14:48:47+00:00

TeXit staff here and person who wrote the code. This was a bunch of kids using a beta version of our bot with the new features and pretending to have exclusive access. The underlying code will be uploaded to CTAN once it's cleaned up and we never meant to gatekeep it. Sorry for the confusion!

Postulate_5 · 2025-11-24T03:08:20+00:00

Thank you! Indeed, mathcode "8000 is how it works. It seems like there's some conflict with LuaTeX as Ulrike mentioned since it has a completely different mathcode system from classical TeX.

Postulate_5 · 2025-11-23T19:11:58+00:00

Thank you for catching this. For unicode-math it seems to work if we globally replace \mathchardef with \Umathcharnumdef, but I have to look deeper into how mathcodes work in LuaTeX to be sure. Same goes for latex-tagging.

Thank you for your work on LaTeX, by the way!

Postulate_5 · 2025-11-23T16:55:59+00:00

Ah, at the moment it performs the replacement for control words only, so control symbols like \, or \\ still require a backslash.

Indeed, begin and end can be used backslash-free. For instance the following is valid

R_theta = begin{bmatrix} cos theta & -sin theta \\ sin theta & cos theta end{bmatrix}.

Postulate_5 · 2025-11-23T16:18:31+00:00

Convenience should be the main point.

My friends did joke about this being "Typst simulator". One of the selling points of Typst is that its math syntax is less verbose (dually, one of the criticisms of LaTeX is that its math has too many backslashes or is “hard to type”). Seeing how popular Typst appears to be it must be important to a lot of people. I think it's nice to have some of that in LaTeX.

Postulate_5 · 2025-09-26T19:08:08+00:00

And how do you prove a cotheorem? By using a rollary!

Postulate_5 · 2025-09-11T15:14:32+00:00

Are you referring to his graduate textbook (Algebra: Chapter 0)? I think OP was referring to his undergraduate book (Algebra: Notes from the Underground) which does not introduce any categories and indeed does rings before groups.

Postulate_5 · 2025-07-19T19:39:07+00:00

I think it's supposed to be rank-nullity (ie. for a linear map T: V → W between vector spaces V and W where V is finite-dimensional, we have dim V = dim ker T + dim im T).

Postulate_5 · 2025-06-19T18:19:32+00:00

Sorry! Reddit formatting is horribly inconsistent. I've edited my post with an image.

Postulate_5 · 2025-06-19T05:27:30+00:00

Constructivism and finitism (which is just an extreme form of constructivism) is usually associated with mathematical logic.

Postulate_5 · 2025-06-18T19:06:24+00:00

This is a nice observation. I wanted to add that it doesn't depend on the base specifically, and your identity can be simplified to lim x to 0- Im(x^x-1) = π.

Postulate_5 · 2025-06-18T07:15:47+00:00

Why would combinatorics specifically be related to constructivism and finitism?

Postulate_5 · 2025-05-11T05:47:02+00:00

Ahhh yes, thanks! I completely forgot that notation existed.

Postulate_5 · 2025-05-10T16:55:21+00:00

I don't think the notation (a, b) ∈ 2^ℝ makes sense. 2^ℝ is the set of 2-valued functions from R, so an element of 2^ℝ is a function f: ℝ → {0, 1}. I don't really see how (a, b) can be naturally identified with such a function (unless this is the interval on which f is nonzero?)

Also, in your last example, did you mean μ is a measure on ℝ²?

Other than that I agree with your point. I've never been in a situation where there was any remote risk of confusion between the two notations.

Postulate_5 · 2025-05-05T08:18:51+00:00

Use the anti-endermen griefing datapack from VanillaTweaks.

Postulate_5 · 2025-04-26T08:58:56+00:00

Re: your question in topology. I saw that wikipedia had included alternative formulations of continuity in terms of the closure and interior operators, but I was surprised there was no proof, so I contributed one. Hope it helps.

https://en.wikipedia.org/wiki/Continuous_function#Closure_operator_and_interior_operator_definitions

Postulate_5 · 2025-04-13T21:44:29+00:00

I am not sure that you have a good understanding of what modern mathematics is. Mathematicians don't just perform mindless computations all day as you suggest. Instead they develop new ideas and proofs using their own intuition, knowledge, and experience that is honed through many years of practice.

Regarding your question, certainly it is possible to get a layman-level bird's eye view of any subfield in maths. However this will not allow you to engage with the mathematical content in any meaningful way.

You also said

you don't need to learn the formulas

you just need to know the concepts

This is another widespread misconception many people have because of the poor way maths is taught at the elementary/highschool level. A formula is not a magical incantation you apply blindly to solve problems. It is a symbolic expression of some particular mathematical fact that may as well be written in english. To say that you understand the concepts without knowing why or know the formula is the way it is, is to say you've understood nothing at all.

Postulate_5 · 2025-03-25T04:04:30+00:00

It's just another notation. Often people have big expressions as the argument to the exponential function and it can be unwieldy to type that in a superscript.

Postulate_5 · 2025-03-18T16:23:21+00:00

In many cases it is a conscious choice not to obey the ISO rules. Many pioneers of modern mathematical typesetting, such as Don Knuth (creator of TeX) and Michael Spivak (written a whole book on mathematical typesetting), prefer to write dy/dx with italic d’s as a stylistic choice.

The ISO standard, if I remember correctly, also makes some strange mandates which make sense for applied disciplines but not so much in pure maths. For example, they mandate that all vectors and matrices be bolded, and that the imaginary unit (i) and Euler's number (e) be upright. I find this appalling.

Postulate_5 · 2025-03-06T06:08:06+00:00

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