#real analysis

[lipshits-continuous]

#I saw a meme in this format and instantly had this idea #I did this on my phone so it's a little messy but yeah #maths posting #maths memes #lipshits posts #lipshits memes #analysis #real analysis #undescribed

[drowninginthedarya]

“suppose for a contradiction”

bro suppose i contract my own life and just die on the spot how’s that

#real analysis #math #mathblr #math memes #fuck real analysis #epsilon delta proof more like prove you can get bitches #my exam is in 22 and a half hours #yikes

[leaderoftheduckresistance]

As time progresses, the distance between my math classes that mention Cauchy is getting progressively shorter

#math #real analysis #cauchy #Cauchy convergence #nerd #newton #Einstein rolling in his grave #leibniz #is quaking #France wins once again

[demonicseries]

let epsilon be greater than the number of bitches you get

#this will be funny to like 3 people on here #math #mathematics #math jokes #math humor #humor #calculus #real analysis

[speronyx]

does anyone know how much of measure theory (and from where) I should study so I can learn more set theory? I'm aiming to learn logic and forcing as soon as I can, and I've covered some of the very basics like the convergence theorems and the decomposition theorem, but idk where to go from there, and my only source of reference is a stat student who's learnt it for studying more probability

#math #measure theory #nyx asks #mathblr #set theory #real analysis

[bubbloquacious]

Rearranging conditionally convergent series

Okay so the alternating harmonic series converges to the natural logarithm of 2, right. Moreover, it is a conditionally convergent series because the regular harmonic series diverges to infinity. By the Riemann rearrangement theorem, there are rearrangements of the terms of the series that make its value equal whatever real number we want. It's also relatively easy to rearrange them in such a way as to make the series evaluate to positive or negative infinity. Given a specific series, consider the set of rearrangements that leave the series convergent to some finite value.

There 'rearrangements', concretely, are elements of the symmetric group on the natural numbers. Let's call a rearrangement σ finitary w.r.t. a series (a[n]) if the rearranged series (a[σ(n)]) converges to a finite value. For which series is the set of finitary rearrangements a subgroup of the symmetric group?

The identity rearrangement, which leaves everything the same, would need to be finitary. This is simply the statement that our original series (aₙ) is convergent. A more interesting question is whether the composition of two finitary rearrangements is itself finitary. It is not obvious to me that that would always be the case! If it is, does it also hold that the inverses of finitary rearrangements are finitary? I think these two questions probably have the same answer.

Clearly the answer is yes to both if the series is absolutely convergent; the set of finitary rearrangements is simply the entire symmetric group. Certainly it will also hold that all finite permutations, which only swap finitely many elements around, are finitary, as they leave the value of the series unchanged (note that these together do form a group!).

This idea could lead to a way of comparing the relative 'conditionality' of various series' convergence. We could say that (aₙ) is more conditionally convergent than (bₙ) if the former's set of finitary rearrangements is contained in the latter's.

Any additions welcome! :)

#math #real analysis

[caffeine-integral-studies]

|| 01.24.2023 ||

The Spring 2023 semester started this week. ☀️ It’s been lovely to have clear skies and sunshine, in contrast to the prior two weeks of rain. ✨

Here’s some of my notes from my first Real Analysis lecture. I was concerned when I first saw the syllabus, but felt better once the instructor explained it further.

The countdown to graduation can officially begin! 117 days. 👩🏼‍🎓

#stemstudying #mathblr #real analysis #studyblr #college #apple ipad

[mjlol52]

the proof of the completeness of the real number line is nice and cool and i like it and i feel confident i could explain it but if anyone asks me abt Fourier Analysis it will trigger my ptsd and i will have a stroke

#real analysis #fourier analysis #math #proofs

[ambrosiagourmet]

I want to talk about why I think this is the one of the most important Falin panels:

So, Falin is really nice, right? It's one of the first things we really learn about her. She's kind even to the monsters of the dungeon - choosing to ward the party rather than fight spirits and cause them needless harm.

In the above early flashback in chapter 11, we see Marcille fawning over Falin's kindness, calling her an angel. Namari calls her soft-hearted. We see Falin choose not to fight even when a zombie attacks - instead she resolves the confrontation with a hug. After the flashback, the first thing Senshi says is that Falin "sounds like quite the person," which Marcille strongly affirms.

At this point in the story, all we have seen of Falin are these impressions; she is a healer, an angel, a caretaker with an infinite well of kindness towards everyone she meets - both friend and foe.

And honestly, that remains most of what we have to go by to understand her. The only times we get to see Falin on the page, alive and just herself, are in the opening and closing pages of the story and in the brief period of time after she is resurrected.

Nonetheless, we do have some more details to work with. For one, there is the scene that The Panel is from - a short memory in chapter 75, when Marcille flashes back to while she's dying. In that scene, Falin prepares to teleport them all out, and says that she's sorry "if there is a person at [their] destination." And that's when we get The Panel.

If you teleport someone or something into another person, the person teleported into is likely to be, at minimum, severely injured. They could die.

We can see a lovely little horrifying example of exactly why in one of the Daydream Hour doodles:

So, hmm. That's not... that's not SUPER nice. Certainly not displaying the same "kindness to all, friend and foe included" we saw represented earlier. On a basic level, this adds some nuance to Falin's kindness. We see it break a little, when pushed to the limit. We see her chose to protect the people she loves above all else.

Which makes sense! As Laios says when the Winged Lion accuses him of similarly being motivated more by his friends' safety than everyone else in the dungeon, "...most people, aside from virtuous do-gooders, would feel the same way."

So, we can take The Panel as simply showing a moment of weakness for Falin. A time when she was pushed to her limits, and that "most people" selfish side of her shone through.

However... I think there's a little more going on with Falin than just her being an angel 99% of the time, except just that once. I love The Panel because I think it helps us understand that Falin isn't just motivated by kindness - she also has a desire to avoid seeing people in pain.

Isn't that the same thing?

No, no it very much is not.

Let's look at a short comic from the Falin section of the Adventurer's Bible, because I think it illustrates this point perfectly. The group is complaining about how much Marcille's healing hurts, and comparing it to Falin's, which "doesn't hurt a bit." Marcille retorts with the following:

Now, the punchline of this comic is that, despite Marcille's sentimental assertion that she's "thinking of [them]" by letting her healing magic hurt, they all still prefer to be healed by Falin.

But hey, this wouldn't be the first time that Dungeon Meshi hides a very real character beat or insight in a gag, so let's think about this somewhat seriously.

If Marcille is right (and she knows a fair bit about magic, so we can assume that she has at least somewhat of a point), then what Falin is doing isn't kind. I suppose if someone specifically requested to not feel the pain, it could be kind, but that's not really what happened here. She is the one who felt badly about the others being in pain, and she is the one who decided, without telling them or giving them a choice in the matter, to take away that pain.

Both Marcille and Falin are healing the party, but Marcille is doing it in a way that accomplishes the task in the most straight forward way, without any additional interference. Falin is going out of her way to perform the healing in a way she is more comfortable with. A way that avoids pain.

Going back the The Panel, I don't think its a coincidence that the only time we see Falin (well, non-chimera Falin) willing to do something that could hurt someone is when any potential pain will be far away from her. If she got someone hurt or killed by teleporting the party to the surface? Not only would it be far out of her sight, but she'd be dead before she had to deal with any consequences of that action.

Falin is not a confrontational person. She doesn't push when Marcille won't tell her the truth about the resurrection, and she comforts Laios about her own death - both of those things happening in the only full chapter she is alive and conscious in the whole story.

We also know that she considered accepting Shuro's proposal, despite not having any special feelings towards him, and that Falin never explained to Marcille that she wanted them to share a meal together. When she brought Marcille various foods at the academy, she just accepted Marcille's confused rejection and gave up.

And lastly, we know that she is still in contact with her parents, despite the neglect and abuse she suffered at their hands. Although the way someone chooses to handle contact with abusive or bad family is a complicated topic, which I don't want to overly simplify, I do I think this fact gets at the heart of how she handles conflict.

So many people that Falin loves have hurt her. There are understandable hurts, like Laios leaving the village, or Marcille not understanding the food. And there are bigger, far less justifiable hurts - like her parents neglecting her throughout her childhood, and sending her away to be alone at the magic academy.

It doesn't seem like Falin has ever confronted any of it directly.

And the unhealthy aspects of this kind of avoidance of pain and confrontation is one of the things that the story of Dungeon Meshi is all about. We see Laios grapple with it before he goes to kill Falin, and we see Marcille acknowledge it at the end of the story, when she tells Laios that she has come to terms with Falin's death:

Eating is a part of life. Consuming other living things is a part of life. It isn't really possible to avoid that pain - you can only hide from the truth of it. You have to be selfish everyday. You have to eat - to choose to live. To choose to take up space.

And this is something Falin embraces, too. She comes back to life, after all.

We see her choose to come back to life.

And how does she make that choice? She eats. She consumes, and then she is asked a question by the manifestation of hunger itself:

Do you want to eat more?

There is a double meaning in the Winged Lion's final words on the next page.

When I first read this, I took it as him saying: life is cruel. You will suffer. You will feel more pain.

But perhaps, especially for Falin, this also means: you are choosing a path where you must cause pain. Where you must consume. Where you must take, and must be selfish. Because eating is the special privilege of the living, and it is their burden, too. In order to stay alive, she will need to keep eating.

And she chooses that. Chooses to be selfish. It's why her resurrection scene is so important, and it's why The Panel is so important. Because Falin coming back isn't the ultimate reward for all of the party's hard work.

It's her choice. Just like it was her choice that started everything in the first place. But this time, she doesn't choose to accept causing pain for the sake of Marcille and Laios. She does it for her own sake.

#dungeon meshi #delicious in dungeon #falin touden #dunmeshi analysis #I love it when dungeon meshi says. the trauma was real and it changed you #and the way you are because of it isn’t anything to be ashamed of #but you have to keep living. you have to chose to keep living. #and you can #dungeon meshi spoilers

[lipshits-continuous]

Analysis proofs be like:

#analysis #real analysis #complex analysis #maths #mathematics #maths memes #math memes #mathblr #undescribed #lipshits posts #maths posting

[17matboy]

Examples of the Direct Comparison Test and Limit Comparison Test for the convergence series

#direct comparison test #limit comparison test #ratio test #geometric series test #test for divergence #series #real analysis

[krpublications]

𝗖𝗦𝗜𝗥 𝗡𝗘𝗧 𝗪𝗶𝘁𝗵 𝗚𝗔𝗧𝗘 𝗦𝘁𝘂𝗱𝘆 𝗠𝗮𝘁𝗲𝗿𝗶𝗮𝗹 at the Lowest Price.

This Study Material also includes tips and tricks to help students with exams.

✅ 𝘼𝙡𝙡 𝘾𝙤𝙢𝙥𝙡𝙚𝙩𝙚 𝙥𝙖𝙘𝙠𝙖𝙜𝙚 𝙤𝙛 𝗡𝗘𝗧 𝗪𝗶𝘁𝗵 𝗚𝗔𝗧𝗘 𝙎𝙩𝙪𝙙𝙮 𝙈𝙖𝙩𝙚𝙧𝙞𝙖𝙡

👉 Real Analysis. 👉 Linear Algebra. 👉 Complex Analysis. 👉 Ordinary Differential Equation (ODEs). 👉 Partial Differential Equation (PDEs). 👉 Group Theory. 👉 Topology. 👉 Statistics. 👉 Ring Theory. 👉 General Aptitude. 👉 Vector Calculus. 👉 Integral Equation calculus of Variation Operation Research.

Have any query? ☎️ [phone]

Prepared by famous Mathematics author Mr. Rajendra Dubey Sir

#csirnet #netwithgate #study material #topicwise #real analysis

[tilde-tilde-at-hash-pound]

just found out about the Volterra function which is everywhere differentiable, with a bounded derivative, but its derivative isn’t integrable????? what in the fuck how do they keep getting away with this shit???

#math #maths #calculus #real analysis #fractals

[artist-issues]

Look I know Rapunzel paints and Tiana cooks, but if you guys don't think Mulan is the Most Creative Disney Princess, you're wrong.

She's literally introduced in this perfect scene that highlights her whole character, flaws and strengths:

The first time you see her she's:

Cheating, which is totally the opposite of what honor-code General Shang would do.

Undisciplined, which is what going to the army fixes.

Problem-solving—by writing the recitation she can't remember on her wrist—

BUT LISTEN. That last one is the first hint you have that she's the Most Creative Disney Princess. Because guess what? She's not the first young woman to cheat at the matchmaker test. The Matchmaker specifically checks to see if she's cheating when the test begins. But the rest of them wrote their cheat sheet on their fans.

The Matchmaker was prepared for the usual kind of tricks. But Mulan's full of her own ideas, not everyone else's.

You guys know the rest. She dresses up like a soldier—nobody suspects her because the idea that someone would do that never occurs to everyone else. She climbs the pole by tying the medallions around each other when none of the other recruits can figure it out. She lights the cannon by grabbing Mushu instead of searching for flints. She creates an avalanche instead of just taking Shan Yu out. She tricks the Huns by dressing her friends up as concubines. She defeats Shan Yu with his own sword and a bunch of fireworks.

But even beyond problem-solving, Mulan never does things like other people do. She doesn't even do things like other women do.

She doesn't just walk across a bridge, she jumps from pillar to pillar. She doesn't just bring her father tea, she puts a spare teacup in her sleeve because she knows she's clumsy.

Mulan is creative. But you know what that moment proves? That she's not just a representation of all women-versus-men. Mulan is representative of a human, who sees where she has strengths, and sees where she has weaknesses. She uses her strengths to her advantage and works to improve or make up for her weaknesses. She doesn't try to be exactly like a man. She just tries to use what she's got to do the right thing. And finding ways to use what you've got, even if it's not like what everyone else has, is creativity.

#Mulan #Mulan meta #hua Mulan #fa Mulan #General Shang #Shang #china #Disney #real Disney #Tom Bancroft #Disney's Mulan #animated Mulan #mulan 1998 #meta #character analysis #Rapunzel #Tiana #Disney Princess #Disney princesses

[gallusrostromegalus]

Kenpachi Realizes Nobody Else Actually Read The Employee Handbook And Decides To Get Inventive, A Story In A Ranking Chart

Yamamoto Thought He Was Punishing Everyone Including Zaraki By Making Him Actually Fill Out That Report, Was Not Ready For Zaraki To Deliver A Twelve Hundred Slide Powerpoint Category Seven Autism Infodump About It A Week Later, A Sequel

#Bleach #Bleach Fanfic #AEIWAM #An Elephant Is Warm And Mushy #kenpachi zaraki #the key difference between Canon Zaraki and AEIWAM Zaraki is about 500 Menial Labor Jobs worth of practical skills and skepticism #For real though if yamamoto made Zaraki fill out a Report on everyone fighting ability the lad would go hog fucking wild #Yamamoto has never seen analysis like this #Yamamoto would prefer not to see analysis like this #but he DID ask and Zaraki is having so much fun he feels bad interrupting

[caffeine-integral-studies]

Hey, mathblr! Drop your best resources for a real analysis course (one semester, undergraduate). Thanks! 👩🏼‍🏫📚

#stemstudying #mathblr #real analysis #resources #collegestudent