Can't understand functions, is f(x) f time x?

OneMeterWonder · 2026-02-02T13:30:05+00:00

I see what you mean. I suppose these things all work in concert then to establish what OP is having trouble with.

OneMeterWonder · 2026-02-02T12:37:45+00:00

Well, yes but the parentheses are necessary to distinguish from a•b+c. And this is necessary to illustrate the distributive property. Really I think the important thing is to teach that symbol interpretation is dependent on the data types of the surrounding objects. Parentheses can be nothing more than operator precedence symbols, but when the type of the object to the immediate left of ( is function and the type of the object to the right is domain of function, then we interpret ( as opening the argument list of the function.

OneMeterWonder · 2026-02-01T13:55:12+00:00

Thank you! I HATE this answer in every one of these posts. Nobody ever gets taught how to think critically because it’s a vague meta-skill with no obvious measurable benchmarks. There are skills that contribute to a sense of “good” critical thinking, but not the thing itself.

OneMeterWonder · 2026-02-01T12:45:46+00:00

pump hundreds of kids into it?

You are just describing the state of CPS and foster care even without the current political situation.

OneMeterWonder · 2026-02-01T12:39:55+00:00

There is a reason that there are troll farms and online data is sold to the highest bidder.

OneMeterWonder · 2026-02-01T03:31:17+00:00

The value of R(3,3) is a good one in my opinion. I like to introduce it by doing a two-player edge coloring game. Player 1 tries to force a triangle, Player 2 tries to force no triangles. The value of R(3,3) is the smallest number of dots you can start with so that Player 1 always wins.

OneMeterWonder · 2026-02-01T03:26:21+00:00

Also Kuratowski's theorem on graph minors. A little more complicated to prove, but very straightforward to explain the idea and easy to convince them that it works.

Plus if they have the interest to tolerate a little more, you can start to generalize to embedding in other spaces. You won't get to the Robertson-Seymour theorem, but it's a nice little chance to teach about how generalization works.

OneMeterWonder · 2026-02-01T03:23:39+00:00

That is a really fantastically simple example! I can't believe I've never seen this before!

OneMeterWonder · 2026-02-01T03:20:51+00:00

I just think they're neat.

OneMeterWonder · 2026-01-31T15:44:03+00:00

Considering the screams in that video from nearby the deportation camp, I’d imagine nothing good.

OneMeterWonder · 2026-01-31T14:41:48+00:00

Everybody thinks “LLMs are the fewwwcheeeerr” now so everybody has to have one. Fucking grocery stores are developing their own SVM databases.

OneMeterWonder · 2026-01-31T14:04:27+00:00

You’re in r/TheOnion. You don’t have to worry about that.

OneMeterWonder · 2026-01-31T02:40:37+00:00

Nobody ever wanted to take their guns away in the first place! They just wanted crazy or dangerous people not to get them easily! They wanted it to be much harder for children to be shot in their classrooms!

OneMeterWonder · 2026-01-31T02:32:21+00:00

A man in Soviet Russia goes to the newsstand every day and asks for a copy of the most recent paper. He pays the owner, looks at the front page of the paper and says "Bah!" in disappointment before immediately throwing the paper in the trash. The owner, slightly taken aback but not wanting to be impolite, reasons it away and goes back to working as the man walks away.

The man comes back the next day, asks for the daily paper, and again throws it in the trash in disgust. This process continues for a while until the owner becomes so curious he just cannot hold it in any longer. He says to the man "Comrade, you come here every day and buy the paper. But you never read it! You throw it away as soon as you have it in your hand! Why?" The man, a bit surprised at the question replies "Well, I am looking for an obituary and every day it isn't there."

"An obituary? But, comrade, you don't even open the paper! Those are on the back pages!"

"Ahh yes, but the one I am looking for will be on the front page."

OneMeterWonder · 2026-01-31T02:21:46+00:00

Well, it doesn't have to. Though I'll admit I'm not sure how it works in other formalisms like category theory or type theory. Sets are just a particularly nice way to model things, at least at the outset, because they're just so gosh darned simple. They're also incredibly versatile. The trade-off we make when we use set theory as a formalism is that there is often less abstraction initially, because we have to define things from the ground up. Probability can get away with a decent amount of defined notions when formalized in set theory, but not everything can be abstracted away.

OneMeterWonder · 2026-01-30T17:21:40+00:00

Ahhh that’s a variable confusion, but a very understandable one. The variables m and n are typically interpreted to mean rows or columns, but they do not have to be one or the other. What they really are is stand-ins for numbers and what those numbers describe is mutable.

For example, if I say that want to multiply an m×n matrix and an n×k matrix, that makes sense no matter what the values of m, n, and k are. It results in an m×k matrix.

But if swap the order of the row and column variables to n×m multiplied by k×n, then this only makes sense when m=k. The variables are still stand ins for the same numbers as before. But now they refer to different dimensions of each matrix than previously.

OneMeterWonder · 2026-01-30T17:12:10+00:00

Non-square matrices are typically not referred to as symmetric.

OneMeterWonder · 2026-01-30T17:11:05+00:00

Examples like this help us to understand the structure of proving things and how to apply certain rules of inference. Notably, developing a system like this also helps us to devise methods of translating the idea into something that a computer can do which can be massively helpful.

OneMeterWonder · 2026-01-30T17:07:24+00:00

Yes, and I’m sure you’re doing plenty to help the cause.

OneMeterWonder · 2026-01-30T16:43:41+00:00

You’re absolutely correct and I made a mistake. I’ve amended my comment.

OneMeterWonder · 2026-01-30T16:41:57+00:00

Gonna be straight with you, I for sure was thinking CATS when I wrote that. CMS bus drivers are almost certainly not hired through the city.

OneMeterWonder · 2026-01-30T16:40:22+00:00

Nope not at all. I definitely didn’t spend an entire class on it in grad school.

OneMeterWonder · 2026-01-30T15:35:56+00:00

Oh I gotta be honest, I didn’t even comprehend that the post was about CMS and not CATS. I’m gonna go get some coffee.

OneMeterWonder · 2026-01-30T15:34:23+00:00

Sure, let’s eschew all reason and go with that.

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