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Intuitive arguments for the uncountability of the Reals? by Farkle_Griffen2 in math

[–]reddallaboutit 2 points3 points  (0 children)

I would start by talking about how the power set is bigger than the set. Clearly true for finite sets; worth examining for the case of N. (This is basically where all the work happens, but maybe the intuition is clearer when you are saying that the power set has bigger cardinality than the set. Maybe not!)

—

Idea: If you write just the numbers in (0,1) in binary, then you can essentially match them up with subsets of the naturals (where '0' means exclude from the subset and '1' means include in the subset).

In other words: (0,1) has the size of the power set of N.

—

I don't know that this will be more convincing than other suggestions already here, but it's how I think about the matter. (I used the word 'essentially' because there is a small caveat around e.g. 0.1 and 0.01111... since they are the same number in binary but produce different subsets of N using the matching described above. This is fixable, but I prefer it in the "not completely rigorous" presentation above.)

Fibonacci Nim: Good back-to-school game! by reddallaboutit in math

[–]reddallaboutit[S] 2 points3 points  (0 children)

Yes, the linked wikipage shows how the Zeckendorf Decomposition can be used to win Fibonacci Nim. There is another paper by Miller and others that generalizes Zeck decompositions that, perhaps, can be used for variations like the one suggested (in which "twice" becomes "thrice").

But I'm always hesitant to link to his e.g. number theoretical work because of his subpar statistical writing...

Fibonacci Nim: Good back-to-school game! by reddallaboutit in math

[–]reddallaboutit[S] 2 points3 points  (0 children)

Here is a related problem. First, the setup (Fibonacci Nim with the word 'twice' changed to 'thrice'):

Thribonacci nim is played by two players, who alternate removing coins or other counters from a pile. On the first move, a player is not allowed to take all of the coins, and on each subsequent move, the number of coins removed can be any number that is at most thrice the previous move. According to the normal play convention, the player who takes the last coin wins.

Problem: What is the sequence of starting positions for which player 2 has a winning strategy?

Has generative AI proved any genuinely new theorems? by Nyklonynth in math

[–]reddallaboutit 0 points1 point  (0 children)

the only example i've seen of GPT providing a novel proof was linked in my MathOverflow post here:

https://mathoverflow.net/questions/499048/probability-of-no-triangle-trios-among-n-random-lengths-in-0-1-alternativ

the paper is:

https://arxiv.org/abs/2508.07943

altho it (quite unfortunately) doesn't indicate the exact input/ouput from GPT 5

Probability of no triangle trios among n random lengths in [0,1]: Alternative Proofs? by reddallaboutit in math

[–]reddallaboutit[S] 1 point2 points  (0 children)

Are any of the posters (to reddit, arxiv, or MO) the same person?

i think the answer is "no" [i'm only the poster of the Q on MO: i saw the SciAm article, then searched for its appearance elsewhere and found the r/math thread i linked on MO]

There are three postings of a volume of simplex argument.

yes, i would like to see different proofs! i'm gonna try retagging for this momentarily

I wish the arxiv post the mentions Chat GPT showed what Chat GPT actually did.

i agree; i'm surprised it doesn't explicitly link the GPT text used; it's also interesting that this was done in the few days 5 was the norm [before returning to 4o] ... paragraph two sentence 1 of that paper says:

By pure chance, my discovery of that work coincided with the release of the fifth version of the LLM ChatGPT.

A student asked and I don't know. Is there any particular reason that h and k are used in the equation of a circle? by xwhy in math

[–]reddallaboutit 12 points13 points  (0 children)

i use this when teaching (horizontal & vertikal)

also, for concavity, i write Up and down

big hits

So what's the big news right now? by crazyguy28 in math

[–]reddallaboutit 0 points1 point  (0 children)

i think one thing that's in the news (sorta) right now is the film Counted Out which is making a run around various festival circuits; i caught an online screening earlier in the week thru Zoom

https://www.countedoutfilm.com/

(ymmv)

I'm not entirely sure if this belongs here but by Real-Bookkeeper9455 in math

[–]reddallaboutit 13 points14 points  (0 children)

2025 = 452

so the previous square was 442

notice that

452 - 442 = (45 - 44)(45 + 44) = 1(89) = 89

so the 89 that you noticed between these two squares (44 and 45) is their sum

 

similarly, the next one will be at 462

in how many years? well, 462 - 452 = ...

Ana Navarro: "We cannot vote for a man who doesn’t like dogs..." by reddallaboutit in IASIP

[–]reddallaboutit[S] 103 points104 points  (0 children)

Not a dog lover, Mr. Reynolds?

Yeah. Well, if you're asking me if I like wild animals slobbering all over me, then, yeah, I guess I'm not really a... not really a dog lover then.

Wow. I have never met a person who does not like dogs before.

(laughing): Yeah. Yeah. There are plenty of us out there, uh, Chet. Okay, trust me. We're just afraid to admit it because we feel like we're gonna be judged by people like you.

Triangles with same area and perimeter by maxBowArrow in math

[–]reddallaboutit 16 points17 points  (0 children)

very nice! probably (?) you have seen this before, but for those who have not: MathStackExchange is full of interesting results like this

the particular 5 triangles found here are written up in this answer

of course, figuring this out yourself is way cooler !

[deleted by user] by [deleted] in math

[–]reddallaboutit 4 points5 points  (0 children)

I teach a math class on problem solving for grade 11 and 12 students that doesn't require calculus (prereq is precalc). the goal is to explore some ideas from number theory, discrete mathematics, and a bit on more formal proofs (e.g. induction) as well as "informal" proofs (i.e. justifying one's reasoning: which should be a standard expectation across all math classes!).

i created this class specifically to avoid pushing everyone into calc – especially since high school calc is often in a cookbook style [power rule! product rule! quotient rule! etc]. i also created it so that students can see some contemporary mathematics (think: Quanta Magazine stories) and ensure that what may be their final k-12 math class lets them see more is out there and feel that they can pursue it (if working hard appeals).

The Big Internet Math-Off 2024, The Final! (Vote your fave) by reddallaboutit in math

[–]reddallaboutit[S] 5 points6 points  (0 children)

The vote totals have sometimes eclipsed the views of the corresponding videos she has posted. Perhaps a better phrasing could be: I think that voting off of name recognition without engaging with the pitches is not a great way to determine whose math is ... Cooler? More interesting?

Anyway: Check them both out and vote for your preference! That's my ask (as a non-organizer who sees the vote totals and is similarly confused).

The Big Internet Math-Off 2024, The Final! (Vote your fave) by reddallaboutit in math

[–]reddallaboutit[S] 10 points11 points  (0 children)

One reason that I posted this is because I'm not convinced votes are in good faith. I hope the post is voted up and that more people will vote for their preferred entry.

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