The h Bar

Sir Cumference

02:59

@Kenshin Something seems kind of fishy here

0celo7

03:53

hello?

OBE

hi

0celo7

Do you want an analysis problem?

OBE

nty. I'm not focusing on analysis specifically

i'm focusing on EVERYTHING

0celo7

...

Do you want an everything problem?

OBE

okay

0celo7

04:00

@OBE Let $M$ be a compact $3$-manifold (without boundary). If $\pi_1(M)=1$, show that $M\approx S^3$.

OBE

what is $\pi_1$?

some topology thing?

Slereah

homotopy group

OBE

right I heard of that before

0celo7

Oh, $M$ is assumed to be connected.

Slereah

I s'ppose

Otherwise u can just pick $S^3 \sqcup S^3$

OBE

04:07

is the homotopy group with $1$ label called the fundamental group?

0celo7

yes

Slereah

it just means every curve is contractible to a point

0celo7

Hmm

Am I banned?

OBE

I'm reading about it right now. then I'll try to solve the problem.

why?

0celo7

i.imgur.com/SHpXvXO.jpg?1

Does anyone know what that frak letter is?

OBE

04:09

it's because it ends in ?1

remove that part

0celo7

It might be E but that doesn't make sense

@OBE I had to edit the image in Imgur

OBE

oh

0celo7

@Slereah Wait, what's smooth in French?

OBE

does that squiggle mean isomorphic

0celo7

It means homeomorphic.

OBE

04:11

$\cong$ is isomorphic?

0celo7

Yes.

What's the motivation for calling a sigma algebra $\mathscr B$

After Borel I guess

Slereah

@0celo7 lisse

0celo7

@Slereah that's what you'd call $C^\infty$?

Slereah

$\mathfrak{ABCDEFGHIJKLMNOPQRSTUVXYZ}$

Looks like E yeah

Classe de régularité

En mathématiques et en analyse, les classes de régularité des fonctions numériques constituent un catalogue fragmentaire appuyé sur l’existence et la continuité des dérivées itérées, sans se préoccuper de la forme ou de l’allure de la fonction (monotonie, convexité, zéros, etc). Toutefois, les classes de régularité ne reflètent en aucun cas un type exhaustif des fonctions : en particulier, les critères portent sur la globalité du domaine de définition. == Domaine en dimension n = 1 == Si J {\displaystyle J} est un intervalle de ...

Fonctions lisses ou régulières

OBE

weird @0celo7 every book I'm looking at uses $\approx$ for isomorphic and ~ for homeomorphic

they are physics books btw

0celo7

04:17

$\sim$ is homotopic or homotopy equivalent

or is that $\simeq$

OBE

idk

0celo7

Just accept that I mean homeomorphic. What is the issue?

Who gives a shit?

OBE

nothing.

just wanted to know which is used more.

0celo7

depends

OBE

okay I'm still reading

i need to finish this chap on homotopy and also manifolds after.

Sir Cumference

04:20

Howdy

Secret

[Me in the maths chat] Attempting to derive some super high valued iterated integral formulae

OBE

@SirCumference hey

Secret

i.e. things of the form $\int ^{(m)}=\int \cdots \int$

Sir Cumference

What language should I learn?

0celo7

Kikongo

@OBE What book?

OBE

04:23

icelandic is pretty cool but I dropped it

Sir Cumference

@0celo7 ...uh, why?

0celo7

So the vocal cord parasites take you out

Sir Cumference

So far I've got English and (mostly) Spanish under my belt

@0celo7 thanks

tho seriously, I'm considering Russian or German

0celo7

I can help you with German

OBE

@0celo7

worldscientific.com/worldscibooks/10.1142/10202

Sir Cumference

04:24

@0celo7 teach me a word

or saying

OBE

I really like this book because it tells you why all the concepts are relevant to physics immediately after describing them.

0celo7

where do you even find these books

@SirCumference Ich bin nicht ein Idiot.

Sir Cumference

@0celo7 I somehow don't trust that...

OBE

books.google.com searching key words that I want to learn about

Sir Cumference

Just a feeling

0celo7

04:26

google translate dude

OBE

it shows you all the books that have all those words on the same page

Sir Cumference

OK, lemme try from memory

Ich bein nein Idiot

I'm way off...

OBE

that's like bad grammar isn't it?

kind of

0celo7

it's bad.

Physics Meta

0

Q: Change accepted answer if a better one appears

The title pretty much sums it up. Should I change the accepted answer if someone answers the question "better" or more extensively ? Even though the accepted answer is right ?

Sir Cumference

04:29

By tomorrow I'll read the papers Einstein wrote in German

OBE

you'll be like a purist JD.

0celo7

oh no

@OBE do you think you can solve this problem?

Sir Cumference

@ODE I'd be JD^2

OBE

@0celo7 the one you gave me?

0celo7

yes

OBE

04:32

I'm readdddddddding

give me a few days

Sir Cumference

@OBE So...why's your name capitalized now?

0celo7

It was unsolved for 100 years, you need to read more

OBE

wow you spoiled it

Sir Cumference

Does it stand for ordinary...bifferential equation?

0celo7

what

OBE

04:33

dude how come every problem you give me is some super duper problem you can't solve yourself. (70% of the time)

Slereah

why do you take problems from him

are you his mommy

OBE

wut

0celo7

When's the last time I gave you a problem I couldn't solve?

Sir Cumference

what

0celo7

Do you want a problem I have solved?

OBE

04:34

not right now.

0celo7

I don't know of any cross-disciplinary problems that are reasonable

OBE

wait up I need to learn more stuff first.

I'm trying my best

well I'm trying to try my best at least

Slereah

here is a problem

OBE

omg

Slereah

The largest number and cDonalds Theorem - Look Around You

►

OBE

04:37

@0celo7 LOOK I found it

a formula for what I wanted

0celo7

What?

Sir Cumference

@OBE That makes one of us... ;-;

OBE

$\delta(\mathrm d^4x) = \partial_\mu(\delta x^\mu)\mathrm d^4x$

what's the proof for that

0celo7

Jesus christ

what the hell is that

that's even worse than what I was doing earlier

OBE

variation of spacetime measure

0celo7

04:39

with respect to what?

what are you on about

OBE

what do you mean wrt. to what?

the fields?

0celo7

???

what are you trying to do, boy?

OBE

when deriving the euler-lagrange equations for field theory

you vary the action right?

but don't you also need to technically vary the measure?

also

0celo7

Nope.

Why should you?

OBE

so you just vary the lagrangian only?

idk

0celo7

04:41

correct

OBE

then what's this

my derivation of E-L for field theory was much simpler

0celo7

Wrong? I don't know what you want me to say.

OBE

what's this book trying to do

oh

why's it varying the lagrangian and the measure?

0celo7

Beats me.

OBE

@Slereah any idea?

0celo7

04:43

I don't have the book.

OBE

I'm pretty sure this is wrong

the e-l equations it derives at the end don't look like what I'm familiar with

0celo7

wat

OBE

oh well better scrap this book

¯_(ツ)_/¯

0celo7

Pic

OBE

0celo7

04:46

Lol

What does that delta thingie mean

OBE

functional derivative

wait no

it's some new notation

one sec

it's the "lagrange derivative"

0celo7

@Slereah Aha, the only distributions that have support = one point are delta functions or derivatives

@OBE better throw this book away

OBE

and the lagrange derivative of that lagrangian is the e-l equations

0celo7

hope you didn't spend money on it

OBE

if that's non standard then yea

i didn't

Slereah

04:49

@0celo7 even worse they are SINGULAR SUPPORTS

dun dun duuun

OBE

@0celo7 what has to be satisfied to have a chain rule for functional derivatives?

since you can't compose functionals

0celo7

beats me

be more specific

OBE

you can't compose functionals but you can compose a functional with an operator that has functional components

therefore you can make a chain rule

you do that by taking the $n \to \infty$ limit of a multivariable function to turn it into a functional and doing the same for an $R^m$ function you compose it with which will look like a function with functional components.

i think...

this is for field theory btw

0celo7

can you give an example?

did you check wiki?

OBE

yeah

I read about this in greiner's field quantization book

but some of it I made up myself but it should work (he didn't explain all the details so I had to figure it out myself)

@0celo7 i don't have a real life example though because Idk of any kind of application for this

0celo7

05:00

Details of what? I'm still confused by what you want to do

Composing functionals won't work well, so idk what chain rule you want

OBE

I don't know. apparently it's used in condensed matter (functional chain rule) but I don't have any examples right now.

what I wanted to do was construct a general one

0celo7

Think some more and ask a better question

I'm off to bed, cheerio

OBE

same

night

i'll think a bit more

John Rennie

06:10

@AccidentalFourierTransform I don't like rabbit. We used to eat it a lot when I was a child because the local countryside was overrun with rabbits and my brother and I used to hunt them for the pot. However I find rabbit meat rather soft and textureless and generally unpleasant.

user228700

06:32

@JohnR: Morning :-)

John Rennie

Morning :-)

I take it you got an answer to your maths question?

user228700

@JohnRennie Yep :-) How did u know about that? You weren't around when I deleted my messages...

John Rennie

I'm a room owner so I see deleted messages.

Along with the mods.

user228700

Oh wow, I didn't know about that.

John Rennie

YOU CAN RUN BUT YOU CAN'T HIDE!! :-)

user228700

06:35

Geez :-|

user228700

Say, dyou happen to know anything about the monotonicity of functions?

John Rennie

Err ... that depends. What did you want to know?

user228700

I'm trying to understand a problem to check the monotonicity of some functions about a given point.

John Rennie

Monotonicity of $f$ just means $f' \ne 0$ doesn't it?

user228700

Erm, not exactly.

John Rennie

06:39

Ah, OK, it could have a point of inflection

user228700

Yes. In fact, it could have several points of inflection, as long as these points aren't contained in an interval (which has infinite points, essentially)

John Rennie

OK it means $f'$ doesn't change sign

user228700

Yep.

user228700

The graphs for all functions have been given and you'd think that this would make it ridiculously easy for me to comment on their monotonicity but these functions aren't exactly continous about the given point.

John Rennie

Link?

user228700

06:41

Image. Let me take a photo...

user228700

I am to ascertain the monotonicity of these functions about the point $x=a$

2017

The second one is monotonic....

The first one is not

John Rennie

Monotonicity means that if $x \le y$ then $f(x) \le f(y)$

user228700

...and I find myself a bit confused because of the discontinuity of the graph about $a$

2017

06:45

@JohnRennie Not really, it could be decreasing also...

user228700

^

user228700

@2017 Right. Why not? Like I said before, all this discontinuity is a bit confusing...

John Rennie

In the first graph it is possible to find values of $x$ and $y$ for which $x \lt y$ but $f(x) \gt f(y)$.

@2017 no, what I've said is correct.

2017

@Kaumudi.H For (i), just before a, the function is increasing while just after it is decreasing...

John Rennie

Monotonicity means the function preserves order

2017

06:47

@JohnRennie What you said is correct only if the function is an increasing function....

For a decreasing function if x<y then f(x)>f(y)

user228700

@JohnR: Even monotonically decreasing functions are termed "monotonic". Lookie here:

user228700

John Rennie

Oh OK, just tack on a and vice versa to my statement.

2017

@JohnRennie :)

@Kaumudi.H So did you get it now?

user228700

@2017 Riight. And how to address the discontinuity about $a$?

2017

06:49

@Kaumudi.H What do you mean by address?

John Rennie

@Kaumudi.H: take the left part of the first graph. It's obvous that for this part if $x \le y$ then $f(x) \le f(y)$

2017

It doesn't even matter

if there is a discontinuity or not

the definition remains same

John Rennie

Now take $x = a - \epsilon$ and $y =$ the extreme right of the graph

user228700

Riight.

John Rennie

$x \lt y$ but $f(x) \gt f(y)$

Which contradicts our earlier conclusion. So the function is not monotonic.

user228700

06:50

@JohnR: I was having trouble with the fact that the function is discontinuous at $a$. I understand it now :-) Thanks, guys.

John Rennie

Whee, I got a maths question right! :-)

user228700

:-)

2017

07:52

@Kaumudi.H Are you appearing for BITSAT?

user228700

Yep.

2017

@Kaumudi.H So which date slot are you selecting, after advanced or before advanced?

user228700

Before. Why dyou ask?

2017

@Kaumudi.H I'm confused because I haven't prepared for the english test

in bitsat

so I think i need one extra week for that

is the level of test same on all dates ?

or are the later tests tougher?

user228700

Ohh, I see. Well, I've been chatting with you for a few weeks now and it seems that u are fluent in English; I don't see why you'd need another week. Besides, IIRC, there are only a few slots left after advanced; certainly not one more week and all.

user228700

07:58

Also, this "level of tests" is debatable; some have told that the test gets easier toward the end and some others have told that it's easiest in the first few days; it's entirely unpredictable.

2017

@Kaumudi.H Ah, thanks for the suggestion. I will talk to my parents about this. BTW the slot booking begins on 20th march, right?

user228700

Sure. Yep, 20th March.

2017

Okay, thanks :)

user228700

I have another quick question about monotonicity; if, for a given point, the derivative changes from positive to zero, why isn't it monotonic about that point?

2017

@Kaumudi.H Who said it is not monotonic about that point? In such a situation it can be called monotonic (non-decreasing function). However, it cannot be called "strictly increasing".

user228700

08:07

> Who said

user228700

My textbook .__.

2017

As wikipedia frames it "In calculus, a function {\displaystyle f} f defined on a subset of the real numbers with real values is called monotonic if and only if it is either entirely non-(increasing or decreasing). That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease."

Monotonic function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. == Monotonicity in calculus and analysis == In calculus, a function f {\displaystyle f} defined on a subset of the real numbers with real values is called monotonic if and only if it is either entirely non-(increasing or decreasing). That is, as per Fig. 1, a function that increases monotonically does ...

user228700

I'm well aware of the definition; I'm confused because my crappy textbook disagrees :-/

2017

You know your textbook is crappy :-P

user228700

Uhhhhh.

user228700

08:09

Thanks anyway :-) I'm going to try to figure out if I've made a mistake.

user228700

Is it possible to comment on the monotonicity of a function at a point that is not in its range? (End-point)

John Rennie

Is the function defined for points not in its range?

I would have thought not, so it's impossible to comment on its monotonicity or otherwise.

user228700

Uh, no, it's not. And yet, this problem...

user228700

Alright, so the function is given by-

user228700

1) $x$ ; $0\le x\le1$

user228700

08:15

2) $[x]$ ; $1\le x\le 2$

user228700

Where $[x]$ represents the Greatest Integer Function (given by the greatest integer less than or equal to a given element in the domain)

Slereah

Infinity is the greatest integer

user228700

Ohhhhhhh. Dang it, I missed that the value of the function at 2 is 1.

user228700

Alright nope, I'm a bigger idiot than I was before; the value of the function at 2 is 2, not 1.

user228700

In any case, the graph would look something like this, no? :

Koolman

08:21

@2017 thanks

user228700

2017

@Kaumudi.H So what is the question?

user228700

Does that look OK? If my textbook is correct, then nope, it would turn out that I've made a mistake...

2017

The graph seems ok

user228700

Right. Well, now u see what I was talking about; my textbook says that the function is non- monotonic at 1.

2017

08:26

How does your textbook define monotonicity ?

user228700

In the proper way; the same way u defined it a few messages ago.

2017

Hmm, the function is definitely monotonic at x=1 according to the definition...

user228700

Would u say that it's monotonically increasing or decreasing at 1? The former, yes?

2017

monotonically non-decreasing

user228700

Any by "non-decreasing", u mean to highlight the fact that it's not strictly increasing, yeah?

2017

08:30

@Kaumudi.H right

Koolman

@2017 why we cannot say , it is monotonically increasing

2017

@Koolman mathworld.wolfram.com/MonotoneIncreasing.html

Koolman

sorry , monotonically non increasing

2017

It is just a semantics problem...

Different books have different conventions...

Koolman

what we will write in exam

user228700

08:33

Heh. Well, my book says "It's neither M.I, nor M.D"

Koolman

board and jee

2017

@Kaumudi.H That's right

It is neither

Koolman

i think both answers are correct

2017

@Koolman They won't ask such stupid questions in exam :P

And if they ask both of them should be correct

Koolman

oh yes

user228700

08:35

How is it neither? It's certainly monotonically increasing, just that it's not strictly increasing.

user228700

The way they've defined this about given points is kinda vague...

2017

@Kaumudi.H Monotonically Increasing=Strictly Increasing (according to what I learnt)

user228700

And this is what I've learned:

user228700

2

A: Difference between Increasing and Monotone increasing function

I'm used to the following: $f$ is increasing iff $x\le y \Rightarrow f(x)\le f(y)$ strictly increasing iff $x< y \Rightarrow f(x)< f(y)$ decreasing and strictly decreasing: similar, with the inequalities for $f$ reversed. Monotonic: either increasing or decreasing strictly monotonic: either...

user228700

Anyway, I'm glad to know that it just comes down to the semantics.

2017

08:36

@Kaumudi.H I told you that it is a semantics problem :P

user228700

In any case, @BalarkaSen I could use ur help with this :-P

2017

"(In general there is always some freedom when it comes to definitions, this is why I wrote 'I'm used to'. In case you are reading a textbook on analyisis the author should define these terms and then stick to them)."

user228700

And clearly, my textbook hasn't stuck with the definitions they introduced before.

2017

just move on

Secret

[What is not art] For me, it is anything that makes me treat them as daily life items and the notion of art never came to mind

For example, with no thinking, I literally almost sat down on the middle column thinking they are just stone benches

MartianCactus

09:34

anyone mind reading this para?

i think its really weird to consider that all the stars were once touching each other..

is this fact true?

Slereah

stars did not exist back in that era

MartianCactus

this guys is saying that when the universe was still pretty small compared to today's size

and stars were there

wait

lemme put it again in a different way

2017

@MartianCactus That would be a child's perspective :) In reality things are far more complicated.

MartianCactus

he is saying that when stars were formed, universe as still pretty small and stars were touching each other

yes thats why

i think he is wrong here , right?

2017

"Stars were touching" doesn't make much sense.

@MartianCactus As I said, the author is explaining the facts in a child's perspective. If you want to get into the technicalities then start with the Wiki page (en.wikipedia.org/wiki/Big_Bang).

MartianCactus

09:41

oh

so what he means is they were closer together than today right?

2017

@MartianCactus First go and read the Wiki page. Otherwise whatever I say won't make sense.

This is a really good answer :) physics.stackexchange.com/a/136861/102705

232

A: Did the Big Bang happen at a point?

The simple answer is that no, the Big Bang did not happen at a point. Instead it happened everywhere in the universe at the same time. Consequences of this include: The universe doesn't have a centre: the Big Bang didn't happen at a point so there is no central point in the inverse that it is e...

Key Point: The universe didn't shrink down to a point at the Big Bang, it's just that the spacing between any two randomly selected spacetime points shrank down to zero.

MartianCactus

oh!!

but isn't that

the same thing?

ohh

2017

@MartianCactus What makes you think that "stars" were touching?

MartianCactus

so the space between the galaxies is expanding

2017

Did you read what Slereah said ?

MartianCactus

09:50

not the galaxies moving away from each other!

i will in a second once I finish what I am currently reading :D

and about the star touching stuff

i knew it was wrong

it would be too unstable

but the article was saying it

so i came here to verify

Transcript for