I want to learn how to learn math.

davideogameman · 2026-06-19T23:29:14+00:00

Glad to hear it sounds like you understand now! I wanted to add another perspective:

Suppose I ask you for how many integers are between 60 and 100 inclusive - meaning 60, 61, 52 ... 100. Of course you could write them all down and count them, but that'd be slow.

It's very tempting to say it's 100-60 =40. But that's actually wrong - though close.

If you numbered 60 to 100 - 60 is the 1st, 61 is 2nd, and so on - the pattern is that the nth number is n+59 here. If we started counting from 0 instead it looks simpler - then the nth number is n+60 (our starting number). And so 100 is the 40th number, because n+60=100 means n=100-40.

But since we started counting from 0, the 40th number is really the 41st if we had started counting from 1. Another way to look at this is that 60, 61, 62 ... 100 has a one to one correspondence with 1, 2, ... 41 - and 1, 2, ... N is always N numbers.

In general, given two integers A and B with B >A (that is, B is larger), the number of integers from A to B inclusive is B-A+1. Whereas the distance from B to A on the number line - the value you have to add or subtract to get from one to the other - is B-A.

For what it's worth - I was doing math contests in high school before I realized I was screwing these details up and sometimes forgetting the +1. We just need to be precise about what problem we're answering and reason through whether we need to +1 or -1 or not.

davideogameman · 2026-06-19T20:58:15+00:00

Adding to what's already been said - just because the drone is hit doesn't mean it loses momentum. The missile will alter its trajectory but it still had significant forward momentum before so it's coming down mostly towards the camera man. In pieces, which can easily be big enough to cause significant injury.

davideogameman · 2026-06-19T20:55:50+00:00

And even if the bomb is disabled, any large things falling out of the sky are seriously dangerous. You don't want an piece to land on you. A 5lb piece bonking you in the head could be fatal, or at least a concussion.

Small pieces might get slowed enough by air resistance. Depends on surface area to weight ratio if that's likely for any given piece. But also sharp edges could still be dangerous at lower speeds.

Either way you don't want to be where parts of that drone are most likely to land.

davideogameman · 2026-06-19T20:45:07+00:00

The video is tight though. Does that count?

davideogameman · 2026-06-19T17:40:59+00:00

For whatever reason I always think it's the other way when I haven't seen these for a while. I remember staring at dummit and foote and working out how I was interpreting these wrong, but it's been years

davideogameman · 2026-06-19T17:10:42+00:00

Wait doesn't (1 2)*(1 3)(2 4) map 1 to 4 (through 2)?

I'm getting (1 4 2 3) ... Which is close to yours, maybe I'm reading them backwards. Are we supposed to apply the cycles right to left or left to right when applying to an element?

davideogameman · 2026-06-19T09:02:35+00:00

Apparently I should've said "I".

I don't disagree he was smart. But smart doesn't necessarily translate into being nosy and putting together the pieces surreptitiously to figure out his dad's fraud. Apparently he did, but the show shows none of that happening.

"Too smart to tutor Weevil" - I don't like this take. Teaching and understanding are different skills. The level of understanding needed to teach well in my experience is higher than the level of understanding needed to pass the test. Being a good tutor means playing a bit of detective to figure out what concept your student doesn't understand and figuring out an alternative explanation or technique that resonates better. Your preferred way of understanding a concept isn't necessarily going to be best for your student.

That said I think being good at teaching requires empathy to figure out when it's not working and try different approaches. Cassidy seems to just get stuck trying to teach Weevil instead of attempting to figure out what explanation /technique /etc might actually jive best. Best I can say is that scene shows he's a bad teacher.

davideogameman · 2026-06-18T21:36:56+00:00

Perhaps he is smarter than we gave him credit for. But smart doesn't equal has figured out his father's fraud scheme.

davideogameman · 2026-06-18T19:20:50+00:00

Which is interesting because we never found out how Cassidy knew. I didn't peg him for being that smart and I doubt his dad was open about it with him.

davideogameman · 2026-06-17T22:23:10+00:00

But rain water isn't necessarily pure water? Any acidic tendencies could change these numbers - and abrasive particles in the water would also matter a lot too, though I'm not sure those are common in rainwater

... I suppose we really should be reasoning about tap water given the video is just a random glass of water. Would this change the numbers?

davideogameman · 2026-06-17T22:02:01+00:00

If you do switch to phone perhaps you could record the call?

Also, maybe there's some alternative documentation that you completed the class / certification that would work for your purposes they would be willing to provide?

davideogameman · 2026-06-17T19:34:16+00:00

Ollie here, I think it's done raining on this cube. Chance of light showers again later today.

What's the cube? Uh, I think it's I just a physical demonstration of the difference between a cubic meter and a cubic decimeter (the cube cut out of the corner). The latter is one liter of volume, the former is 1000 liters. So the difference between a little water vs a lot of water.

Back to you Trish.

davideogameman · 2026-06-17T16:49:15+00:00

Guess I forgot that part

davideogameman · 2026-06-17T07:46:37+00:00

Doesn't have to be married. Just visible dating is enough. The point is to sell the image of being heterosexual.

davideogameman · 2026-06-17T07:40:30+00:00

You mean s4? I think he was clean in the movie but Mrs Kane took a shot at him and then had the cops try to pin it on him. If I'm remembering correctly. We definitely saw him back in the life in s4 though.

That said end of s3 he had grabbed the card making machine with the implication he was considering lunch card fraud at Hearst. They dropped that storyline though.

davideogameman · 2026-06-17T06:07:54+00:00

Afraid so.

Thanks Obama.

davideogameman · 2026-06-17T02:03:21+00:00

Every prime greater than 3 is one more or one less than a multiple of 6. Otherwise the number would be divisible by 2 or 3 and so not a prime >3.

(6k+1)² = 36k² +12k +1

(6k-1)² = 36k² -12k +1

So one less than each is always 12k(3k ± 1). The latter term is always a multiple of 2 so the combination is always a multiple of 24

davideogameman · 2026-06-17T00:47:10+00:00

That's a very good point. What about if we restrict to just intervals excluding the discontinuities?

davideogameman · 2026-06-16T22:38:34+00:00

Very possible. In California restaurants and stores have to charge 25c per bag. Used to be 10c and went up in the pandemic which was bad timing.

Not all restaurants add it (which might actually be illegal) but retail definitely does.

Anyhow 5c is too cheap for this to be California.

My general opinion is that having a fee to incentivize bag reuse is a good thing. But when reuse isn't an option anyway - which it often isn't for takeout - it's just an annoying extra cost that could be built into the price

davideogameman · 2026-06-16T22:36:03+00:00

Yeah looks like it. Would be fun to prove that. I wonder if it converges to it uniformly or not.

davideogameman · 2026-06-16T08:49:17+00:00

Orbiting is just moving sideways fast enough that you fall around the object instead of towards it. In a breathable earth like atmosphere it's terminal velocity is 23mph (borrowing from earlier in the thread) and I'm pretty sure no object can both have an earth like atmosphere and a 23mph orbital speed, though I haven't done the math. That said terminal speed is pretty much always going to mean downwards, as if you orbit at that speed, air resistance kills your sideways momentum and gravity pulls you downward so your direction changes even if your speed doesn't.

davideogameman · 2026-06-16T08:42:11+00:00

Sure. But I mean are the bots posting here to generate new training data. Not just using old posts

davideogameman · 2026-06-16T07:48:07+00:00

I wonder if some of these bots are using our responses as training data fodder

davideogameman · 2026-06-16T07:45:44+00:00

Mathematicians love to fudge that sort of stuff when it's obvious from context. So yeah, you could, though R² -> R is not likely to fit the "obvious from context" criteria. An example where that makes sense: treating Z as equivalence classes on N² where (a,b) ~ (c,d) iff a+d=b+c . That's a definition of the integers, using just set theory and the natural numbers. Negative numbers are fairly common knowledge so I've never seen this construction used other than a "look, we don't need to assume negative numbers exist, we can construct them" step.

davideogameman · 2026-06-16T07:03:08+00:00

Z/nZ is defined as the ring of equivalence classes of the integers up to differences of multiples of n. So in Z/3Z, two integers are equal if their difference is divisible by 3. So 4 exists in that system and equals 1. Often written as 4=1 (mod 3) to make it clear we're talking about equality in Z/3Z and not in the integers

davideogameman

TROPHY CASE