My Favourite Fucked Up Math Fact™ Is The Sharkovskii Theorem:

My favourite fucked up math fact™ is the Sharkovskii theorem:

For any continuous function f: [a,b] -> [a,b], if there exists a periodic point of order 3 (i.e. f(f(f(x))) = x for some x in [a,b] and not f(x) = x or f²(x) = x), then there exists a periodic point of ANY order n.¹

Yes you read that right. If you can find a point of order 3 then you can be sure that there is a point of order 4, 5, or even 142857 in your interval. The assumption is so innocent but I cannot understate how ridiculous the result is.²

For a (relatively) self-contained proof, see this document (this downloads a pdf).

(footnotes under read more)

¹ The interval does not have to be closed, but it should be connected. (a,b), (a,b] and [a,b) all work.

² Technically the result is even stronger! The natural numbers admit a certain ordering called the Sharkovskii ordering which starts with the odd primes 3 > 5 > 7 > ... , then doubles of primes, then quadruples of primes and so forth until you get no more primes left, ending the ordering in 2³ > 2² > 2. Sharkovskii's theorem actually says that if you have a periodic point of order k, then you have periodic points of any order less than k in the Sharkovskii ordering. It is frankly ridiculous how somehow prime numbers make their way into this mess.

More Posts from Bsdndprplplld and Others

2 years ago
Lagrange Markipliers Or Something Idk I Forgot All My Multivariable Calc.

Lagrange Markipliers or something idk I forgot all my multivariable calc.

2 years ago

but how is this related to adhd? I'd say my ability to have fun is diminished because of the dopamine deficiency, I'm basically constantly bored, and afaik adhd increases the risk of substance abuse disorders, so I don't see the point of bringing up adhd in this context

Me: I don't take alcohol, smoke weed or do any other substances.

Everyone: Omg!! then how do you have fun??

Me: I have ADHD.

3 years ago

i've been working on it with my boyfriend for a while now and–

our first video is up!

i hope you enjoy it and subscribe to our channel

https://youtu.be/-X2BBtRI1Xw


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2 years ago

lmao wtf people seriously say shit like "math is homophobic"? because queer people can't do math… a priori?? isn't it inherently homophobic to claim that homosexuality implies being bad at math? this is the most unhinged thing I've seen this week

It's so funny to me when people reblog math posts on this site and say shit like "this is homophobic" "this is an attack on queer people" like hello this is tumblr. OP is queer. Like we've got a HANDFUL of cishets here on mathblr but most of us are queer. Because it's tumblr. And everyone is queer on tumblr. If you see math on this site, a queer person probably put it there. Stfu about "gays can't do math" if it's on tumblr, gays can do it, that's why it's on tumblr.

And of course there is also a large and brilliant and beloved queer math community off of tumblr but I just think it's extra funny when people don't notice it ON TUMBLR.

Alan Turing didn't kick the Nazis' collective ass laying foundations for the field of computing and then go on to also lay foundations for the field of biomathematics, Leonardo Da Vinci didn't give us fundamental physical and mathematical diagrams used in engineering well beyond his time, Moon Duchin doesn't study the math of fair redistricting, Chad Topaz and Jude Higdon don't analyze criminal sentencing disparities, et cetera et cetera, for y'all to call math homophobic and an attack on the queer community.

1 year ago

hairy ball theorem, stokes theorem, poincaré duality, nullstellensatz, idk too much to choose one

What is your favourite mathematical theorem? I'm personally torn between the compactness theorem for first-order logic, and the fundamental theorem of Galois theory.

1 year ago

i am! obsessed! with this book from the late ming dynasty about scams to watch out for (esp. if you are a traveling merchant). this guy is like, there ARE immortals who can survive without food but you WILL NOT encounter them because they live alone in the mountains and don't talk to anyone. if a monk comes to your house and claims to not need to eat, it's probably because he's secretly eating human fetuses, or something. eunuchs are invariably corrupt and the court system is useless. however, do NOT try to bribe anyone for a better SAT result for your idiot failson; this never works. nuns WILL try to seduce your wife into cheating on you. if your idiot failson does really badly on the SAT, make sure to have his father's remains buried somewhere with A+ fengshui; this is Guaranteed to work (unless your wife is cheating on you).

2 years ago

Very funny when mathematicians call weird edge cases "pathological".

Mathematician looking at a function that's continuous everywhere but differentiable nowhere: yeah that function has something wrong with it.

3 years ago

ok i get it now, most people need plans and structures so then they can study what they're really into in the future

btw today i'm doing operations on topo spaces, i love that already

i gotta say i don't buy all them planning strategies and tips that require more effort than just sitting and doing the work

i mean that might help some people but i find that when i am doing something important to me i need no plans nor do i need motivation, i also don't procrastinate, everything falls into its right place

and if achieving something takes so much effort in preparation, is this even supposed to be a thing? idk, maybe that's the reason why i have no external proof of my work lol

1 year ago

I'm glad I never encoutered anyone with such serious mindset while I was studying programming because now I wouldn't have as much fun writing branchless things in python, which is completely useless in highlevel languages but I just can't resist

I Feel Like Some People Are Too Serious With Learning How To Program. “I Gotta Be The Best In This
I Feel Like Some People Are Too Serious With Learning How To Program. “I Gotta Be The Best In This

I feel like some people are too serious with learning how to program. “I gotta be the best in this and that and build this and that to impress this employer” blah blah, that kills the fun out of programming. I see a lot of people (bashing people on Twitter again and actually a few people on here too, oops) making programming such a serious topic and you can’t have fun in it. Besides the proper syntax, documentation, best practises whatever, people in the tech community have putting up “rules” about how you should program and what to learn and if you fall out of that, you get ridiculed for it. Literally making it less fun.

Someone said that there’s no point in learning jQuery because JavaScript alone can do all that jQuery can and more.

So? I’m still going to learn it for fun? I’m having a blast with SCSS and jQuery, I don’t care 🤷🏾‍♀️ and I’ll learn the other frameworks and libraries that suits me because I want to. I don’t care if the entire tech community stops using a technology - if it interests me, I’m still going to learn it~!

Also no hate or anything to that person who said that to me - I completely understand your POV on jQuery! 💗✨ When I first read comment, I was a bit down like “oh what’s the point then…” but slapped myself and was like “I’m not learning for them or anyone. This library is cool and I like it so I’m still gonna use it”

Moral of the story: just do you. Do what makes you happy, code what you happy. Don’t be so serious all the time and make stupid dumb programs or games or websites whatever. Have fun in such a hard subject!!!

2 years ago

"Wow you're so naturally talented!" "You truly are gif-" biting you biting you biting you biting you die die die die I didn't work for thousands of hours to get called naturally talented fuck you fuck you fuck you I wasn't a particularly gifted beginner I just didn't stop doing it aaaaaaaaaaaaaaaaaaa

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bsdndprplplld - you can't comb a hairy ball
you can't comb a hairy ball

⁕ pure math undergrad ⁕ in love with anything algebraic ⁕

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