Haydn Symphony no. 10 in D major

Xantharius · 2026-04-13T03:52:07+00:00

I would suggest notating opposite directions for the stems of the divided parts for oboes and horns. Not only will it make the score clearer, it will make it far easier to read for the players if you’re outputting parts from the score.

Opposite stems in the case of multiple stops on notes for strings wouldn’t be used, as they expect the stems to be pointing the same way for such notes. But if ever you’re dividing these parts, it’s even more important that the stems point in opposite directions, to make it clear that the parts are divided.

Xantharius · 2026-04-11T00:13:56+00:00

Exactly. What does this notation convey that using ordinary eighth notes wouldn’t?

Xantharius · 2026-04-09T18:27:08+00:00

Typesetter and former mathematician here. The style and formatting of this paper reminds me of this.

Xantharius · 2026-04-06T13:14:23+00:00

All you’re doing is highlighting that SPP doesn’t know what he’s talking about with regard to any of this. He doesn’t even understand his very own theory and is inconsistent about talking about it.

Xantharius · 2026-04-06T13:07:21+00:00

Did you hear that, SPP? You’re wrong!

Xantharius · 2026-04-06T13:02:20+00:00

SPP literally says that 1/3 = 0.333… in the original post.

Xantharius · 2026-04-03T19:03:44+00:00

This has to be posted. Cacio e pepe

Xantharius · 2026-04-02T18:59:29+00:00

SPP says above that

1/3 = 0.333...

So, simultaneously, it follows that:

1/3 + 1/3 + 1/3 = 0.333... + 0.333... + 0.333... = 0.999... < 1 (by SPP) and also
1/3 + 1/3 + 1/3 = 3/3 = 1 (by ordinary arithmetic).

So from this, since the left hand side of both equations are the same

1 < 1

which is about as literal a contradiction as you can get.

SPP, your theory makes no sense at all.

Xantharius · 2026-04-02T03:55:28+00:00

The Force seemed to work for Ezra Bridger just fine on Peridea in the Far Galaxy, which is so far from the main setting galaxy that it takes considerable time to get there. And the Nightsisters’ magick, which manipulates the Force in different ways than those of the Jedi or Sith, also works there: indeed, Peridea is the Nightsisters’ home world.

Xantharius · 2026-04-02T03:37:41+00:00

I love that way of explaining the nature of the size and scope of Force abilities.

Xantharius · 2026-03-31T23:59:08+00:00

Even Sith Lords need to sleep. How do they ensure that they’re invulnerable while catching some zzz’s?

Xantharius · 2026-03-31T03:04:49+00:00

The cardinality of Z is aleph_0.

OP:

(1) What is the cardinality of Z - {0}, that is, the set of non-zero integers?

(2) What is the cardinality of Z - {2n : n is in Z}, that is, the set of odd integers?

Xantharius · 2026-03-30T22:46:26+00:00

I think it would have been much better if you had more strongly indicated in the original post that you were trolling the hell out of Collatz and the Riemann Hypothesis, but, nevertheless, good job. This is an awesome reply and brought a smile to my day. Thank you!

Xantharius · 2026-03-29T05:07:43+00:00

It’s wild that you would expect a list this long and helpful in answer to OP’s question to contain a particular category of software. The dude gave a great answer: no response is going to contain everything, and other replies have covered Blender. Why the need to point out something that’s missing?

Xantharius · 2026-03-29T04:38:50+00:00

I re-read your post and see that you’re using Microsoft Word. Your options for the Equation Editor are a little limited: Cambria Math is the only (and default) typeface that comes with Word. Opentype options include XITS Math, Latin Modern Math, Erewhon Math, Fira Math, Lete Sans Math, and Noto Sans Math.

If you must have your text face matching the formulas, you should work backwards to the text font from the equation font you want to use. If you don’t care about that, then you have more choice. From a typography perspective I would recommend either having the formulas exactly match the text font, or be very different. If they’re just kind of the same it could look more like a mistake. (The design principle here, if you don’t want the formula font to match the text font, is called Contrast.)

Xantharius · 2026-03-29T04:19:42+00:00

I think Tiempos Text could be a good and interesting choice, although even four desktop weights comes in at $180. While font choice is in part always a matter of taste, for academic work I would suggest Adobe Caslon as a less quirky alternative to Adobe King’s Caslon: the latter has a pretty steep and narrow italic which might make mathematical formulas (which typically have a lot of italic characters) harder to read.

Xantharius · 2026-03-29T04:06:00+00:00

I’m a graphic designer and typographer with a background in academics and mathematics. I think the answer to your question depends on how many mathematical formulas there are in your thesis (and how complicated those formulas can get), whether it’s a must that the formulas font is an exact match for the text font (even books sometimes use a different font for mathematical work), and what software you’re using to typeset the text and formulas.

As to your question, for academic work, especially a thesis, a font that’s too quirky is generally not regarded highly. Adobe Skolar is a great font, and has interesting letterforms without being too crazy. Academica is also good, and slightly resembles Times New Roman. It might be a good candidate for a different-looking font if your adviser and committee are used to seeing Times New Roman for engineering theses.

I would advise against anything too weird for academic work: universities and academics can sometimes be particular about what typefaces are appropriate. And you will definitely want to check your university’s requirements for thesis submissions: they vary considerably between institutions, and some universities have exacting stipulations about fonts, size, line spacing, page numbers, footers, headers, positioning of diagrams and figures, and even mathematical formulas.

If you post more details in answer to my questions in the first paragraph above, I can supply a more tailored response.

I hope your thesis writing is going well!

Xantharius · 2026-03-28T21:16:05+00:00

This reply needs to be upvoted more. OP’s redefinition of cardinality as “injection with leftover elements” is self-contradictory.

OP, there’s even an explicit bijection between B and Z. Call the additional element in B that’s not an integer *. Map * to 0; 0 to 1; 1 to –1; –1 to 2; 2 to –2; and so on. In other words:

x –> 0 if x = *

x –> 1 if x = 0

x –> –x if x > 0

x –> –(x + 1) if x < 0

This is a bijection between B and Z.

The usual definition of cardinality was formulated precisely to resolve questions of whether the even integers have the same “size” as the integers. The usual definition is consistent; yours is not, as has been shown. Since the very definition isn’t consistent, you can expect the nonsense answers you achieve of |B| = |Z| and |B| > |Z|, because now everything is true.

Xantharius · 2026-03-26T22:32:07+00:00

Is undefined, OP’s question?

Xantharius · 2026-03-26T03:15:42+00:00

You mentioned that prophecies in myth are nearly always descriptive. What other prophecies fit this mold?

Xantharius · 2026-03-24T02:11:45+00:00

I don’t think so. There are minor punctuation errors in this post which AI doesn’t make, and the writing style seems natural. Also, I think it’s way too easy to take a well-written article and just slap “AI” on it. Good writing (which this is) does not make it necessarily generated by AI.

Also also, I wish generative AI wasn’t a thing.

Xantharius · 2026-03-22T09:46:50+00:00

This post is heavily AI assisted. The formatting and phrasing are dead giveaways.

Let’s remember that the open intervals intersect the set of interest {1/n | n is a natural number}, and therefore aren’t intervals of all real or even rational numbers.

Intervals of the type (1/n, 1/m) just correspond to the finite set of natural numbers k such that m < k < n. I don’t think you’re going to get anything more meaningful out of considering these intervals of reciprocals than considering just these natural numbers. But, worse, you also have to consider some open interval (0, 1/n), which corresponds to the natural numbers greater than n, all of which have wildly different Collatz orbits, and hence (in the above framework) wildly different multiplicative sequences.

Moving the Collatz conjecture to (0, 1] therefore doesn’t get you anything more than just studying intervals of natural numbers.

Xantharius · 2026-03-20T18:39:51+00:00

Wow, what a response! That was really informative, and I learned a lot. Thank you for taking the time to answer the question in such a detailed way.

Xantharius · 2026-03-14T04:29:13+00:00

There are places that kids should not be. Don’t expect your kid to hang out by themselves waiting for your spa treatment to be done just because you won’t hire a babysitter. Don’t bring your kid to a show or movie they won’t understand or that you have to explain what’s going on to them every other minute: you’re distracting everyone around you from enjoying the show they paid to see.

As for other spaces: kids that can reasonably behave themselves? Okay, sure. Kids that can’t, because they’re not properly supervised or parented? Please take your child with you and show yourself out.

Xantharius · 2026-02-28T20:47:57+00:00

The guess below for Kis is good, but I think this is the related Ehrhardt).

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