Mathematics - 2018-03-31 (page 1 of 2)

@Perturbative you're welcome

Semiclassical

12:55 AM

@XanderHenderson and that I'm secretly some intelligent swirl of gas

1:32 AM

are you gonna join the revolution? @0celo7 :P

(in the hbar)

Jean-François Savard

2:07 AM

Anyone here have time to chat about proof theory? I'm currently struggling with a proof but I don't feel it deserve a question..

come on

why u using my precious spacse

3:01 AM

Nice comment @XanderHenderson :-)

+1

Semiclassical

The Beatles - Revolution

►

user131753

3:31 AM

@Jean-FrançoisSavard You may go to the Logic room to ask @user21820 about this.

yup @Semiclassical, "...and you know it's gonna be alright..." :-)

3:57 AM

hi @TedShifrin

hi Karim

math is hard :(

so many open problems I cannot solve

very depressing

That's mostly why they're open :) I didn't exactly solve everything I tried to. :)

Hey Forever, Adeek, and Ted!

Ted: hopefully the move went well?

Hey Demonark.

I had more drama than I needed (elevator remodel shrank the height about 6", so my sofa, which had fit in fine for move in, couldn't move out). But I was able to hire professionals who got it expertly down and up staircases. But pretty much settled now, so much happier. You back for spring quarter?

4:13 AM

Yup, I am. Just got through first week of class

sup dudes

Yo

Oh, already! I guess the same is true for Mr. Eric.

indeed

You guys settle on your overloads for this quarter?

4:14 AM

Yup, finally decided after quite a lot of bouncing around

i think im happy with my schedule but it's a nightmare

No one listens to my advice ... shrug :P

Yeah same situation here. Like I'm set up to die but it's gonna be so much fun

Ted: Masochism, I guess? (I presume here you're talking about not taking 4 math/cs classes)

Among other advice(s) I've given, yes.

to be fair im not doing that cause half my classes are humanities

4:18 AM

Well, that's cool :)

im only taking 1 math this quarter :P

Wow ... which one did you settle on?

complex

I think it's a smart thing to take a slight break before you burn yourself out. And you can always play with Bryant, etc., if you miss geometry.

hi @Daminark

4:21 AM

Yo

next year i plan on taking $\leq 1$ per quarter

I don't think I ever got that low, but I tried to do just 2.

@TedShifrin I have some slight issue my previous supervisor whenever he sees me he glares and stares at me

so weird

this is the first time ive done less than 2 since my first quarter in my first year lol

You can either confront him about it or else just ignore him.

4:22 AM

Yeah, I will ignore him. He seems crazy.

Well, Eric, you can keep us posted.

I guess in academia your bound to run into crazy people.

@Adeek is your bound upper or lower?

@Daminark hahaha

@TedShifrin i do plan on doing more physics tho

4:24 AM

I am not good with confrontation as well. I am here to learn.

Okay I probably shouldn't do that, that's one of those mistakes that you can internally autocorrect

hey @TedShifrin do you want to discuss a cool geometric thing ?

@Eric is it just that you don't have that many classes left you want to do? Or is it that you're toning it down after having taken as much as you did for a while?

I don't have much brain at the moment.

@Daminark a little bit of column a, a little bit of column b

4:26 AM

I opt for column c.

Don’t do physics , that’s just guess work

Some of us aren't so interested in your opinions, Zee.

I know , but am interested in your opinion of my opinion

oh okay

@Daminark would you like to hear cool geometric intuition of something

I think Ted's comment tells you his opinion of yours

@Adeek sure

4:29 AM

Am being a little annoying but I speak the truth , do math and then when you get really good at it physics would be much easier

so you know you can classify all vector bundles over paracompact space X as the space of homotopy class [X,Gn]

you know that ?

Physics gave us nuclear weapons and the internet , math gave us Grothendieck , which one do you think is more valuable?

I like the weapons bit

@Adeek is Gn like, the Grassmannian?

infinite Grassmannian

4:33 AM

I've heard of this, yeah

man

If $X$ is a continuum (compact connected metric space), $p\in X$, and every two points of $X\setminus \{p\}$ are contained in a nowhere dense subcontinuum of $X$, then is there a nowhere dense subcontinuum $N$ with $p\in N$ and $|N|>1$?

That problem is UNSOLVED. LOL so simple and nobody knows the answer.

I tried finding an example but so hard.

Lol

don't you love that?

I can't stop thinking about it.

like 5 days straight it's all I've done

It sounds an interesting question, but I need to wrap my head around what the nowhere dense continuum look like first

well in $[0,1]^2$ you could think of arcs (homeomorphic copy of $[0,1]$)

those are nowhere dense subcontinua

4:40 AM

okay do you want to know the intuition of this @Daminark ?

It will require some deep thought. Very deep. A famous mathematician has asked it.

Do tell

okay so essentially a vector bundle is built locally from X. So essentially it is just a twisted version of X.

so picking a vector bundle is the same as picking a family of twisting.

okay @Daminark ?

One thing I don't quite understand though: is it for every two points in X\p they are contained in the same nowhere dense subcontinuum, or there are more than one disjoint nowhere dense subcontinua that points in X\p belong to?

good question. what I mean is, for every two points $x,y\in X\setminus \{p\}$, there is a nowhere dense subcontinuum $M$ with $\{x,y\}\subseteq M$. There will not be a single $M$ for all pairs.

4:45 AM

Uh, that I'm not sure about

Like, I think of a vector bundle as a bunch of vector spaces continuously parametrized by $X$, the idea of "twisting" doesn't quite come to mind

@Daminark locally it it trivial product

@Daminark that if we look deep enough it is trivial product

Ah, in that case it will be a lot harder, since there are many possible Ms to choose from. Hmm...

Yeah, that I know

It's the vectors spaces that are twisting. I don't know what your $X$ means, Karim.

yeah so the vector spaces are twisted

4:48 AM

Oh, okay yeah that works

@Daminark think mobius band vs cylinder

I'm guessing $X$ is the base space

so imagine now we stalk family of such twisting on top of each other

like some kinda of pancake

okay ?

this problem is absolutely insane. how can we not know such a simple thing? How could it be overlooked?

to me this is the most beautiful open problem in math

@Daminark okay?

4:50 AM

You're not making much sense, even to me, Karim.

I'm still trying to process

In my mind I don't really have much of a notion of stacking vector bundles on top of each other

You shouldn't be trying to do that.

There are many open problems in general topology of that nature , see recent progress in topology III

(Is that what you meant by the above? If not, sorry)

there is a volume III? WHAT???

@Zee

4:51 AM

I am thinking of stacking twisting family of twisting on top of each other @TedShifrin @Daminark

I have no idea what you're talking about.

And I'm not in a very patient mood. So I think I'll just leave.

Lol

Formally, what object are you trying to describe by that process?

@Zee dont you mean II?

I am trying to imagine how [X,Gn] works visually.

i.e I am trying to imagine how we can think of that

4:53 AM

books.google.com/…

When III comes out, my name will be in it, cause I solved one of the problems in II :) :) :) :) :) :)

:(

oh wait, that's different

I like general topology but it’s a dead field , I would avoid it

So, just the fact that a vector bundle is a continuous map from a space to the infinity Grassmannian really registers in my mind as, we're putting a topology on the space of rank n vector spaces, so now if this is a way where you can continuously assign a vector space to each point

Like, when you think of the tangent bundle of a manifold, you're gluing a vector space at each point which is tangent, and nearby points have tangent spaces which are "close" to each other

@Zee I was talking about this book by Elsevier carma.newcastle.edu.au/jon/Preprints/Books/…

Now, what I'm not sure about here is why we're modding out by homotopy

4:55 AM

General topology is dead?

Pretty much

Where is Balarka

Still studying?

Or more like it got absorbed into other areas

I have some point set topology to tell him about

ask me instead

I am expert in general topology

4:57 AM

they're not questions, they're things for him to think about

related to axiomatic geometry

very boring stuff unless presented by a madman professor

@Daminark I see

Let me ask you this forever Mozart’s , this isn’t an open question though , show that a hausdorrf paracompact topological space with homeomorphic transition maps is a topological manifold

what are heomeormorphic transition maps

How you have smooth charts for smooth manifolds except here they are homeomorphisims

??

5:00 AM

manifolds are not general enough for me

??? I thought you were a diff geometer

I work mostly with non-locally connected spaces.

that should be a sin

I learned only enough differential geometry to understand Relativity

beyond that, I'm inept

It’s funny how people pick their level of generality , I mean where do you stop? ZFC ?

Or philosophical logic ?

5:03 AM

$\Bbb R^n$ is bad enough for me

I thought you were a diff geometer...

lol

I don't know why people think that

oh Idk , maybe it has to do that you wrote a 70 page thesis in diff geo ?

158 pages

5:05 AM

Oh am sorry , that makes more sense now

lol?

Yes

@Zee if it takes that level of abstraction to understand infinity, I will go all the way to there, lol

I would give a finger to solve that problem. It is going to kill me.

And I generally like pathological stuff

5:07 AM

@Secret we are kindred spirits then

Chemistry is applied physics , physics is applied math , math is applied logic , logic is applied philosophy, philosophy is applied bullshit

pathological is all I do. testing the boundaries of what exists.

I use pathological structures to test how well I understood some theorems

And the Cthulhu like mindset they introduced allow me to work easier with nice things

having said that since I am mostly a chemist, it will take me some time to be completely solid, though I am optimistic I will make my topology foundation solid since Balarka and Leaky taught me the intuitions

@Zee bullshit is the application of bulls

I need a wizard to help me.

5:13 AM

@Zee philosophy is indeed a subset of bullshit that is not nonsense generally

next week I will see such a person. maybe we can answer that problem, but he doesn't like me very much.

He is famous though

you're famous for just trying :-)

no I feel like an idiot

That, my friend, is an important feeling.

How do you know he don’t like you ?

5:19 AM

we've been around here for a few years, pal

I hve no idea what your saying and I also don’t remember seeing you here a few years ago buddy

lol

Ok , good job , you was here before anybody else , you get a prize of 0 dollers with a bonus of zero shits given by me

>8(

::puts zee on ignore::

Still have no shits to give you , sorry

5:25 AM

I don't know if Skull is a mathematician or just likes to mess with us

are those mutually exclusive ;-)

I had hope for the latter but he gave up quick

@ForeverMozart you should look into Grothendieck work in functional analysis

for now I can't stop thinking about my problem

If you have the luxury of time then go ahead but make sure you got your priorities straight

yes my priorities are out of whack for sure

but eventually I'll sort it out. mathematics research takes its toll

5:32 AM

Then put them in order , solving problems is thrilling specially if they are open problems , but if you suffer academically and/or don’t pick up enough breadth , you may not have the chance to be doing math for much longer

I will try :(

I just really want to solve problem :(

Even if you solve an open problem in general topology , most schools don’t even have people who work in general topology , so they can’t even supervise your PhD

Not trying to be mean just letting you aware of the bitter reality

:( but i love

Then make sure you pick up some mainstream stuff that is near by , functional analysis for example

@ForeverMozart I'll solve your problem if you solve mine

5:40 AM

is it easy to describe?

Very hard

Well, one of them

the other is deceptively easy

can't tell you here because @EricSilva might see and get famous off the solution

can you locally isometricly embedd a surface into R3 ?

That’s a fields medal question

I have some fields medal questions in mind. But they're probably completely hopeless

7:12 AM

[Explosion]

in The h Bar, 2 hours ago, by vzn

in theory salon, 2 days ago, by vzn

A Math Whiz Has Become a Crucial Political Figure in France (Cedric Villani + AI) / bloomberg

/end explosion

Sierpiński space

In mathematics, the Sierpiński space (or the connected two-point set) is a finite topological space with two points, only one of which is closed. It is the smallest example of a topological space which is neither trivial nor discrete. It is named after Wacław Sierpiński. The Sierpiński space has important relations to the theory of computation and semantics, because it is the classifying space for open sets in the Scott topology. == Definition and fundamental properties == Explicitly, the Sierpiński space is a topological space S whose underlying point set is {0,1} and whose open sets are ...

hmm.. can we make a non hausedoff space hausedoff by union copies of it together in some way?

7:48 AM

in The h Bar, 20 secs ago, by Secret

I am not sure what pro-mathematics policy will do though, other than the obvious AI and data science stuff

Unraveling DNA with Rational Tangles | Infinite Series

8:02 AM

►

Q: Prove that unit circle is a Lie group

8:16 AM

I wonder if we can prove $e+\pi$ is irrational by looking at them in the context of irrational tangles (a sequence of rational tangles)

but then I only just learnt what tangles are so I cannot do anything yet

YOUSEFY

9:35 AM

I'm trying to find definition of 'bounded treewidth'.. for example here 'http://wwwmayr.in.tum.de/konferenzen/Jass08/courses/1/holzer/Holzer_Talk.pdf' there is no definition of this. Does he mean that treewidth with fixed number?

Niing

10:04 AM

Oh why the rubber duck disappear? I just mis-clicked 'I hate this duck'...

Noooooooo

BAYMAX

Hmm.. still doesnot have an answer :'( -

0

I want to prove that unit cricle is a Lie grouop. $i.e$, want to show that the multiplication and inverse function is smooth. The multiplication and inverse is given by \begin{align} &m(e^{i\theta}, e^{i\phi}) = e^{i(\theta+\phi)} \\ &i(e^{i\theta}) = e^{-i\theta} \end{align} i tried to find...

Niing

Where is the duck?

I need it

1

Q: What is Quack Overflow?

It's in the lower right corner of some of my pages:

support

en.wikipedia.org/wiki/Rubber_duck_debugging]

Rubber duck debugging

In software engineering, rubber duck debugging or rubber ducking is a method of debugging code. The name is a reference to a story in the book The Pragmatic Programmer in which a programmer would carry around a rubber duck and debug their code by forcing themselves to explain it, line-by-line, to the duck. Many other terms exist for this technique, often involving different inanimate objects. Many programmers have had the experience of explaining a problem to someone else, possibly even to someone who knows nothing about programming, and then hitting upon the solution in the process of explaining...

sounds like thinking out loud

10:48 AM

it does

11:09 AM

[Random]

Consider the following topology:

Let the space of all knowledge be a set. Then for each point p, let the open sets be "Given p, there exists some q such that it is unknown if there exists some f such that f(q)=p "

Then clearly, this space is non hausedoff

A perhaps interesting question concerning about this topology is the following: For every p, is q also inside an open set

English translation of the above random:

Basically, the above is an attempt to abstract the following observation concerning the frontier of knowledge:

> X is an open question and little is known about it, let alone whether if X is converted to Y, it is reversible

We are interested to know whether it applies for all X

PVAL-inactive

12:07 PM

There was already way too many quacks on this website.

Hello everyone I have one question to ask. Please help me. Find the annual interest percent on 17% debentures of the face value rs.100 each and available at rs.85 each.

12:32 PM

how would you call the functor 1 -> C that sends pt to a given x in C?

1:01 PM

When should I plug in value, when I want to differentiate a function? It seems to me that this route is harmless: First compute 'derivative function' and then plug in value at which i want derivative (e.g., derivative of $x^2$ at $x=1$ is $2x|_{x=1}=2$, but if i had plugged $1$ in $x^2$, i would get 'derivative' $0$), but here things work, even if I plug in value first, and then differentiate.

@LeakyNun

so the initial object is the limit of the full diagram and the terminal object is the limit of the empty diagram?

@Silent where did they plug in value first?

@LeakyNun $P(\alpha) = f(\alpha)0^0$, and noticing $0^0=1$, he concludes $f^{(k)}(\alpha) = P^{(k)}(\alpha),\quad k=0,1,\dots$

that doesn't mean he differentiated it

he didn't directly differentiate the expression $P(\alpha)=f(\alpha)$ to conclude $f^{(k)}(\alpha) = P^{(k)}(\alpha)$

Oh! thank you :)

1:19 PM

@Astyx hello

Hi

I solved that population question.

@Astyx need your help in another question. How much should a person invest in 5% debentures at rupees 104 in order to secure an annual income of rs.152 after paying an income tax of 5 paise per rupee.

I don't understand the question

@Astyx I never solved any debentures questions before and also find nothing online. I explain. Suppose you invest 104 rupees per item. And 5% debenture means you have income 5 rupees on 104 rupees. And overall income of you should be rupees 152 after paying tax of 5% on each rupee.

what does the duck do

1:30 PM

@Astyx understood now?

Ylvis - The Fox (What Does The Fox Say?) [Official music video HD]

►

Oh stfu

rages

@KanwaljitSingh gimme a sec

anyway I see it's an SE-based rubberduck

what a troll

I have no idea what you're on about bsen

1:35 PM

Open up a stackexchange site

See the duck on the lower-right corner

@Astyx I solved it. Leave it now.

@KanwaljitSingh cool, good job

Thank you

If you click on it it asks your question for you @BalarkaSen

hi @Balarka how is it going with exams?

1:37 PM

@LeakyNun, This is Taylor's Theorem and its proof as given in Rudin.

I love that duck

@Astyx Nice try. @Alessandro Not bad, but I fucked up 6 marks on my statistics exam today

And the duck does say quack

A little sour about it

1:38 PM

I think is is not guaranteed that $g'$ is continuous (or perhaps not even defined) at $\alpha$, if $\alpha=a$ or $b$, so how can we use Mean value theorem to deduce that there is $x_2$ between $\alpha$ and $x_1$ such that $g''(x_2)=0$ ? Shall we restrict $\alpha\in(a,b)$? Can $\beta =a$ or $b$?

@LeakyNun

Ylvis predicted it all

@Astyx I lost my duck, by clicking on it. How to regain

??

You have to baleet some cookies apparently

Reload the page maybe ?

Q: Stack Exchange has been taken over by a rubber duck!

18

I couldn't miss this now, on all SE sites: What are the duck powers? Was anyone able to make it do or say anything other than "Quack"?

discussion fun april-fools quack-overflow

1:41 PM

@Astyx yep, worked! thanks

Glad to help

@Astyx pls help me with this. A man charges at the rate of 10% percent payable in advance. What effective rate of interest does he charges per annum?

annum ?

Annually

I don't know how advance payment works here.

hello folks

1:47 PM

I have no clue

do you guys think people can get points out of talking in chat rooms?

Can or should ?

@Astyx you are my last hope. But you also don't know. Ok.

@Astyx You have failed us

YOU WERE THE CHOSEN ONE

1:49 PM

We trusted in you, that you were the only one

You were supposed to destroy the dark side, not join it

[in a dramatic Batman voice] I had to

can, q's about stack exchange. I mean do you get points for hanging out in chat rooms

@hungryWolf no lol

sorry for the silly question

1:51 PM

@BalarkaSen can you help me with that question?

this is a black hole of procrastination in itself. you don't want SE to give you serotonin boosts everytime to procrastinate a little more

@BalarkaSen, will you please look at this? It may seem a big theorem, but my question is little: how can we use MVT on g'?

14 mins ago, by Silent

@LeakyNun, This is Taylor's Theorem and its proof as given in Rudin.

@KanwaljitSingh @Silent Sorry, I really don't have the time to look right now

Otherwise Balarka would be the one with the most points in MSE

np

1:52 PM

More than all the others combined

@BalarkaSen meaningless internet points for wasting time? I think we have a business model here!

@BalarkaSen when you have time then try that question please.

@Silent It's defined because f is differentiable, P is a polynomial so it's differentiable and same for the last term

And even though all derivatives are not continuous, they all satisfy the IVT

@Astyx I missed '$f^{(n-1)}$ continuous on $[a,b]$' in hypothesis! thanks for pointing out.

@LeakyNun, got that, never mind.

Mary Star

Hello!!

The five employees of a small business get the following raises (in%):
$3 \ \ \ \ \ 6 \ \ \ \ \ 7 \ \ \ \ \ 3.5 \ \ \ \ \ 5.2 $

I want to caluclate the mode. The mode of a sample is the element that occurs most often in the collection. In this case every number is once in the list. So, are all these numbers modes?

2:10 PM

statisticshowto.com/mode

If all numbers are equally likely, there is no mode

(That is new to me, in the past I used to treat all of them as modes)

What is with this rubber duck, it asks me whether I have a microphone which I say I do not, it tells me to speak! What does it mean?

Q: Stack Exchange has been taken over by a rubber duck!

19

I couldn't miss this now, on all SE sites: What are the duck powers? Was anyone able to make it do or say anything other than "Quack"?

discussion fun april-fools quack-overflow

The rubber duck in right corner

Short answer: April fools joke

@Secret yeah

Oh its hardly 1st today

2:14 PM

It's 1st somewhere

rschwieb

@KingTut When I saw it, I hoped it was a new feature that helped people solve their questions by talking to the duck, as in rubber duck debugging: en.wikipedia.org/wiki/Rubber_duck_debugging

Consider $A = [0,1] \cup [2,3]$ and $f: A \to \Bbb{R}$ which is defined as $f(x) = x^2, x \in [0,1]$ and $f(x) = x^3, x \in [2,3]$. Is $f$ continuous on A

Mary Star

@Secret Ah ok! Thank you!!

@rschwieb i got fooled by it.

@Secret Its still 31st in my country of south east asia

Ok who leads in terms of time, according to time conventions

@Albas check the preimages of these two functions, and see if they are a closed subset of $A$

2:21 PM

@Secret isnt it directly continuous as it is on the two intervals

But the preimage of $x^3$ for $x \in [2,3]$ is $[{}^3\sqrt{2},{}^3\sqrt{3}]$ which does not lie in $A$

o wait

Why we need preimage and what is it

@Secret

I know that using topology I can say a continuous function maps closed sets to closed sets

So I do think it is continuous

I have to prove this using sequences definition of a continuous function

yeah I mixed up the set which to act the preimage on, thus under the usual topology of the reals, both of these functions are inded continuous. As for proving continuity using sequence definition, I am still not terribly good at those proofs.

This duck is annoying, how to remove it from my sight :\

2:28 PM

@Secret Yes

no let me think (my mind is a bit messed up because I am in the middle of copying some notes)

I guess one way to approach it is to justify the following limit interchanging:

@Albas That's false, not all continuous maps are closed

@AlessandroCodenotti But if a map takes closed sets to closed sets isnt it continuous

I mean the reverse is not true

@Albas no, every map with a discrete space as codomain maps closed sets into closed sets, but not all of them are continuous

$$f(\lim_{n \in \Bbb{N}} x_n) = \lim_{n \in \Bbb{N}} f(x_n)$$ but I don't know the theorem that can do that, other than for the domain in question, the $f$ are monotonically increasing

2:34 PM

For example the identity from $\Bbb R$ with the usual topology into $\Bbb R$ with the discrete topology is both an open and closed map but it's not continuous

@AlessandroCodenotti Yea true

Its inverse is continuous but it's neither closed nor open

Okay, so how do I argue in this case, if given that I give the standard topology

If we have to use sequences cant I argue using the fact that a convergent sequence inside a bounded set should converge to a point inside it

So if we have $x \in A$ and $p_n$ which converges to $x$. Say $x \in [0,1]$ then there exists an $N$ such that for all $n> N$, $p_n$ lies in $[0,1]$

But how do I proceed after that