#math ask

[the-least-undefinable-ordinal]

6 and 9 and 56👀

6. Why do you learn math? (Copied from other answer)

Essentially, I enjoy it enough to think getting paid to do it full time seem like a great deal and learning more math, while enjoyable in its own right (to me), is pretty much a byproduct of trying to do new things with math.

Like, for my thesis sometimes I need to prove a statement X and that leads me to learn a bunch of other things; then I bring up some questions and comments to my advisor, we get talking and he just naturally starts telling me about all sorts of cool stuff.

9. Do you have any favourite theorems?

I cycle through them like I do with my favourite songs but some of the classics that have stuck with me are:

(i) [Cantor] Every set has strictly less cardinality than its power set, which in particular implies the naturals (and the rationals!) have strictly less cardinality than the reals.

(ii) [Cantor] Every unbounded dense and countable total ordering is order isomorphic to the rationals. This also implies every unbounded dense complete and separable (has a countable dense subset) total ordering is order isomorphic to the reals.

(iii) The independence of Suslin's problem from ZFC is pretty cool. To state Suslin's problem it's convenient to talk first about the countable chains condition (ccc). A total ordering is said to satisfy the ccc if all sets of pairwise disjoint open intervals is countable (or finite). All dense separable total orderings satisfy the ccc and I leave this as a fun exercise for interested readers.

Suslin's problem is the question "are the real numbers the only (modulo isomorphism) unbounded dense complete total ordering that satisfies the ccc?"

I just think it's neat how the ccc doesn't sound that much stronger as a condition than separability, but you switch separability for it and suddenly that corollary to Cantor's theorem is no longer solvable within ZFC!

56. Do you have a favorite sequence? Is it in the OEIS?

If it has to be an integer sequence, then the sequence of topologies on finite sets, it's pretty fucked up I think.

If it can be a sequence of anything, then any enumeration of all the rational numbers.

I think both must be in the OEIS but I haven't checked :/

[noodles-and-tea]

*its robin btw

[hawflake-folk]

brought jiaoqiu out to pull for them and the absolute speed at which they arrived...

[lady-starkiller]

going wild on a saturday night

*glass of bourbon*

*wikipedia page for 'photon'*

[more-mara]

This video is constantly on my mind

[stealingpotatoes]

Tbf she has, according to The Lore about Togruta headbands, killed a carnivorous giant predator that regularly decimates entire villages, at fourteen, as her coming of age hunt.

Granted, this is legends, but...

damn. or she found a loophole

(donation doodles! // tip jar)

[lilacgaby]

dunno if you take reqjests but

reader drawing on bakugos hand while theyre studying

PLAGUESMMY DREAMS BRO I WANNA SEE UR TAKE ON IT

katsuki had dragged you to his room to start studying for the practical exams. you groaned and whined the whole way, he was an academic, and so he was really big on being ‘focused’ and ‘committed’ to the work.

as he questioned you on quadratics and gave you a question to solve, as if you'd be able to solve it. you slammed your head against the table in frustration, as he continued solving the problem as if nothing was wrong. you pouted, you chin on the table as you watched him. one of his hands free as the others did all the work.

you were just so bored, your palms were already out of space from when you were doodling earlier so,

you started to draw on his hand, he was startled by the sudden feeling of a pen on his hand, jerking slightly. “don't move you're gonna ruin it!”

“fuck are ya’ doing anyways? we're supposed to be studying?”

“i'm bored. just do it yourself.”

his face scrunched up in annoyance as he finished up his work, doing his best not to move his hand.

you were actually really focused, or maybe you were just taking a long time because you wanted to hold his hand. who knows.

when you finished, clicking your pen again with a satisfied nod, he looked over his hand, eyebrows raised in surprise.

he actually really liked it. it looked like a mosaic almost, you drawing whatever had come to your mind, some of the things invoking his interests. small explosion doodles mixed in with flowers, chibi doodles of the two of you with heart in between, and a little skull reminiscent of his shirt.

he was so distracted by it, he didn't notice you copying down all of his answers.

almost.

he grabbed your face in his other hand, squishing your cheeks and forcing your lips into a pout. he silently looked over you for a second, pecking your lips briefly before resuming his original position.

“draw me some shit on a piece of paper next time, 'don't want it to get ruined.”

with another kiss to your lips, he handed a flustered you a piece of paper,

“but do your own work, baby.”

with a fastened heart and face dusted with pink, you'd never finished an assignment faster.

[cyfffff]

you’d think since dick was a mathlete hed b the number one guy to ask for help w math homework but actually he knows so much advanced math that the first time tim asked him for help with a simple geometry problem he pulled out his dusty ti-84 and started solving it in the most convoluted way that took an hour bc he was also just trying to relearn the math he hadn’t done in like 5 years. cue him screaming in frustration when he realized the actual way to do it would’ve taken him 2 minutes (tim asked him at the beginning if that way was right and he waved him off saying no) none of the batsibs can ask him for math help until they get to pre-calculus at least

[hotcinnamonsunset]

something something baby shark, right??🦈

[the-least-undefinable-ordinal]

I'm interested in your answers to questions 18&19 from the math ask meme :)

18. Can you share a good math problem you’ve solved recently?

I've solved so many cool ones but they're specific enough that they're very likely to identify me by name :(

I do have an old one that I think is pretty standard in the study of set theoretic trees, so there are these trees:

(that's an omega)

They have a partial ordering essentially given by the descendant relation, as partial orders it would be trivial to embed the binary tree in the infinitely branching one, the surprising result is that you can do it the other way around! Also giving an example of two trees that are pairwise embeddable but not isomorphic.

19. How did you solve it?

I had to endure a 2 hour lecture on a topic I knew nothing about by a guy speaking english (not my first language) in a heavy, borderline unintelligible, french accent. I took the path of least resistance tbh.

The idea for the solution is that since we're only interested in embedding the tree, we don't have to reach every node, so you don't have to map infinite levels to finite levels, which would of course be impossible.

By restricting ourselves to the subset of the binary tree with only sequences ending in 0 (plus the root node), we get back our infinitely branching structure. The set ends up looking something like this:

With the nodes boxed up being the subset we're considering, it's not immediately clear from this picture what this ordering looks like though, but the root and first levels of this new tree look something like this:

We can see how the first level of the new tree is now infinite! This is the case for all other levels but graphing those is much more annoying :/

Then comes the more technical part of actually proving this intuition is enough to construct an embedding, but the intuition is what I came up with during that lecture!

[becca-e-barnes]

Bucky pinning you down so you can’t squirm and he’s just sitting inside you while he tortures your clit feeling you clench around him. He makes you cum over and over until he finally cums.

Overstimulation + super soldier stamina = …

- 🍯

Dear God, I know I just don't have it in me to behave during cock-warming. When it comes down to it, I genuinely have no patience at all 😵‍💫

"You..." Bucky begins, pressing you down onto the bed before gripping your ankles and forcing you to flip over onto your front. "Have a problem with control."

With your face turned away from him, you can't help but smile to yourself. No one has ever said it out loud but you know he's right.

Being in control is where you're most comfortable. No hands are safer than your own. Except maybe his. You know he won't fuck this up.

"And you..." He continues, gathering your wrists behind your back, holding them tightly with one hand. "Need to learn how it feels to have control taken from you. Do you understand?"

As soon as you begin to nod your head, you feel him start to tape around your wrists, holding them together behind your back. Once he's content they're secure, he sits on the edge of the bed, facing the mirror before he pulls you onto his lap.

"Legs spread over the top of mine." He orders and you do as you're told, not because you have to but because you want to.

You notice the way your cunt is already glistening in the mirror and you're almost embarrassed because he hasn't even touched you yet.

"Fuck, you're made for this." He groans, lining his cock up to your slick entrance and you wonder if he's holding his breath too while he slides into you, as deep as your bodies will allow.

You're obsessed with the sight in front of you; your own naked body, with your legs spread so far apart you can see how your cunt is stuffed full of him.

Being shorter though, your feet can't touch the ground like this. There's no way you'll get enough leverage to fuck yourself on him but as soon as you start to tell him that, he silences you with two thick fingers between your lips.

"I'm not letting you fuck me." His free hand roams over your body, squeezing your breasts, pinching your nipples and then settling between your spread thighs.

"I'm going to play with you. I'm going to see how much you can take. I'm going to work out exactly how you like your clit stroked and I'm going to do that until your legs are shaking and your body won't let you cum any more. Maybe then I'll fuck you but sweetheart, that will be hours from now." His breath is hot against the side of your face, his fingers slipping from your mouth to your waist while he starts to flick gently against your clit.

"I'm going to start slowly. I'm going to do everything I can to drag this out as long as possible. I can feel every clench and flutter of this pretty little cunt and I'm going to enjoy it until you're dripping over my balls." At this rate, it won't be long until you're dripping onto the carpet, never mind over him. You dreamed he'd want to take control like this but you never imagined the way your body would respond.

"And then, when you've cum more times than you can handle, I'm going to tell you that I love you while I fuck you like I don't."

Update: Part 2

[oifaaa]

You know

You should add Cass and Steph's adopted (or bio) children in this au

What is it with you guys and the elderly anyway I'll think about it for now need to introduce someone more important the GREAT GRANDDAUGHTER of Dick Grayson

Fanny Grayson

[ask-the-pioneer]

According to all known laws of aviation, there is no way a squidcada should be able to fly. Its wings are too small to get its fat little body off the ground. The squidcada, of course, flies anyway

She tries to do some quick calculations in her head, but the numbers just aren't adding up...

[kenjakusbraincum]

Heey, I LOVE your writings on soft sukuna, you write so beautifully🩷 please can you do one where he is jealous (fluff)😭🩷

Thank you sm for the kind words!!! Here's my best attempt at doing your idea justice <3

Sukuna has no real reason to be jealous. He practically owns you, controls every aspect of your life, who or what could he possibly be jealous of? Every servant who dared approach you in an inappropriate way would be dealt with swiftly. And you're a good pet, who has eyes for no one other than your master. You really don't give him a reason.

But there's this one thing... Since you've been so good and obedient, Sukuna has allowed you many liberties. You're permitted to skip around the mansion, watch Uraume cook, even enjoy little hobbies. You've tried many before you found that crocheting particularly piqued your interest. Ever since you've learned the basics, you've been spending hours working on perfecting your skills. At first it was cute, watching you squint in concentration as you move the hook. But then the math became really simple - having this hobby to keep you busy meant you approached Sukuna out of boredom a lot less. And he noticed it. It irked him, but you're not technically doing anything wrong. You were still as happy to serve him as ever, he just had to ask. But why would he have to ask? You should be all over him on your own. He should have to push you away, not beg you to give him attention. He didn't like this disturbance in your master and pet balance that this little hobby of yours caused.

He stands at the door now. You're crocheting again. You and your favorite servant laugh at your failed creation so sweetly, you don't even notice he's waiting. He clicks his tongue to establish his presence, and your servant falls to her knees immediately. You however, are not held to that high of a standard anymore.

"Master!", you call him, and hop up to greet him with a deep bow. Before he can say anything, you've picked up the piece of fabric you've been working on and ran into his arms to show him.

He looks at the ugly form and scoffs. "This is what I'm sponsoring?", he says and pulls a loose piece of yarn, making your little creation fall apart. He always was a bully, but you note his bad mood.

"I'm only a beginner...", you sulk.

"That much is obvious.", he flicks the yarn away and it falls onto the floor. Before you can bend to pick it up, he seizes your wrist and pulls you back. "Aren't you a little young to waste time with hobbies for the elderly?", he asks. You look at him with your cutest, practiced doe eyes, but it doesn't work.

"Come, pet. I know an activity more suitable for your age.", he says when you don't respond, and steps out of the room. You hop after him, unaffected by his condescending comments. You know that they're just for show. If he really thought you were a hag, you would've been gone a long time ago.

"Sitting at your throne all day?", you tease innocently and join him at his side, sliding your arm underneath one of his. You hope your playfulness will distract him from whatever is bothering him. "Or in a bath?" His lower set of eyes peeks at you and smirks, noticing that you're feeling particularly daring today. He's not sure how he feels about that. "Or in your bed." He rolls his eyes gently and opens the door to his chambers.

"At least then you'd be serving your purpose and actually spending time with your master.", he comments and shuts the door. His comment catches you a bit off guard and you stop in front of his bed. He makes his way towards you, and you look up at him with an insulted expression.

"Master, are you jealous of a ball of yarn?", you ask playfully, and squeal when he suddenly pushes you down to sit on the bed. Now you're at eye level... with his crotch.

"You've got quite a big mouth today. Put it to good use for a change, will you?", he runs his hand from the crown of your head to the back of your neck. You seem to have struck a nerve, so it really is the ball of yarn. Is it possible that Sukuna is this clingy?

"Will you?", he repeats and tugs on your hair and narrows his eyes. You smile obediently and reach behind him to untie his obi.

"Yes Master."

-

You try your best to manage the time you spend crocheting from then on, working on productivity in the hours that you dedicate to developing this skill. And it helps that you have a specific goal in mind now: helping Sukuna realize that this hobby is a friend, not an enemy. He still catches you engaging in it sometimes, and gives you a dirty look, but you're as quick as ever to drop what you're doing and join him. That seems to satisfy him.

When you're finally happy with the result of your creation, you look for Sukuna around the mansion. It's not really that hard to find him, as he frequents three places most of all: the dining room, his bedroom and his throne room. This time, he's sitting on his throne, and a small line of people wait for their turn to be gifted his attention. You on the other hand, don't have to wait in line to get it. His lower set of eyes spots you the moment you enter the chamber. You're allowed to roam the mansion, but barging in unannounced is not standard even for you.

Still, Sukuna has learned that you usually only feel daring enough to cross boundaries when you're sure he'll like what you have in mind. So for now, he will let this slide. He's bored as hell anyways. The people are dismissed and you pass by them on your way to his throne, nestled on a pile of bones. You stop in front of it and greet him with a bow.

"Master, I come to you with a humble offering.", you say with your hands on your thighs and your eyes fixated on the ground.

"Show me.", he says simply, but you recognize entertainment in his voice. You climb up the bones and feel his stare scan you from head to toe, before you sit on his knee.

"May I ask you to close your eyes?", you ask and flutter your lashes. Oh the way you seduce him. Who else could ask Sukuna to do something as dangerous as close his eyes? Give his opponent valuable time to land an attack. Who else could dare? And who else would he ever listen to and really close his eyes? Really do as he's told? Oh how safe he feels with you.

You take one of his large hands into yours, and gently pry his long fingers away to open his palm. He has beautiful hands. The only ones you've ever known, but you're sure they're the most beautiful hands in the world. So dangerous, so elegant. You want to press a kiss to his palm, but you hope your gift will have the same, maybe even more profound effect.

Something soft touches his skin, and then you speak, as politely as before. "You may look.", in your softest voice. And when he opens his eyes, he finds himself looking at you first. You're an offering on your own.

Then he looks at his hand. Two crocheted plush figures resembling him and yourself lay flat on his palm, connected through their holding hands. At first glance, it looks like they're two separate creations. In a sense, they are, but... He tries to part them.

"We're sewn together.", you explain. He hums in amusement and inspects your gift more closely. His plush is bigger, recognizable by the pink hair and four buttons for eyes. It's even wearing his favorite kimono. Yours is smaller and less detailed. You look like any other human when placed next to him, insignificant. But in a sea of pets, entertainers and lovers he's had in the past, he would never fail to recognize it as you.

He's spent so long looking at it with that face of his that you just can't read. You're starting to grow restless in his lap, and he feels your eyes dwell into his soul. When he looks back at you with one pair of eyes, your brows are furrowed in worry and you're fiddling your hands in your lap. He pats you on the head and pulls you closer, so you have no choice but to lean on his frame.

"It's beautiful, darling.", his fingers run through your hair, scraping your scalp softly. "No loose threads either.", he looks at you with all four eyes now, and you feel so small in his arms. You're not used to receiving this many compliments from Sukuna at once. Not ones that weren't directed at your body or performance. Especially not when he's looking at you so tenderly, when every word sounds so loving and genuine. "You've improved so much.", his hand is on your face now, and you catch him glancing at your lips. You part them to start thanking him, but you already know how much he hates listening to that.

You stay quiet instead, and lean closer, letting him take you. And he kisses you so softly, fingertips light against your heated skin. You feel like you're floating, like a lily pad in a warm pond. The littlest gesture of his affection has you melting in his embrace. The power he has over you... and how wonderful it is to surrender yourself to it.

None of the liberties and privileges you've been awarded with compare to this. You know that many pets have walked these halls before you. Many warmed his bed and claimed the title of his favorite. But how many loved him like this? Enough to dedicate time of their day to making intricate gifts. How many could say Sukuna kissed them lovingly, for no other reason than to show gratitude and affection?

You're flushed completely red by the time his lips leave yours. You can't hold the intensity of his gaze, as he stares at you in adoration. "I'm happ.. I'm glad you l-like it...", you stumble through the words and win a giggle out of him. You are just so cute. Like a pet should be. He rubs your head again and pushes you away lightly.

"Go now, the people await me.", he says with a benevolent smile gracing his face. "I'll see you tonight."

You bow to him and leave.

And when you visit him that night, he is as gentle as he was when he kissed you earlier, still in a good mood after your gift. Caressing your hair, shoulders and back, as you lay comfortably with your head on his chest. Keeping you warm in his embrace. You're trying your best to follow the conversation, but sleep is slowly taking over you. Sukuna notices and plants a kiss to your forehead, wishing you goodnight. The last thing you see before your eyes close, is your handcrafted plushies sitting on his nightstand.

[kyri45]

ISAT: Sky cotl update when?

When I'm done with the 41 drawings i need to finish for work due to May 26th

[garbagechocolate]

What is the center and radius of the circle indicated by the equation?

(x−2)2+y2=36

-Cousin Throkmorton Anon