Hey guys.

@Jasper Yo.

How are you

No. I am only active in Physics S.E.

Just wanted to look into other chats.

Feynman lectures ? Sometimes.

Why ?

They are.

Sorry, I dont know what that means.

You mean no ..? rather .?

Ah...okay.

So you realized that Im a foreigner.

;)

I dunno either.

Landau Lifshitz - mechanics

For deeper studies "Differential geometry, topology and Physics" by Nikahara

Of course they can. Its just classical mechanics.

Well, the following books are about QM.

No. I'm from germany. Why?

Really? Oh.

I used them.

That's it.

Well....yeah.

:D

Well, good luck. You'll be lucky if you get reborn after Merkel.

Oh. How do you mean that ?

Oh, I'm sorry for you. Do you feel good now ?

I hope you are gonna be better in the future. Don't give up.

I think my favourite scientist is Edward Witten. Because he did a lot for physics and for mathematics.

I like to read his papers.

I understand.

But I like a mixture of both: mathematical physics.

Thats my study area.

Yeah ;) The difference is not very big.

Not really. I read everything, if its good.

But I try to get the book "Differential geometry, topology and physics" in the not too-distant future.

Yeah, good night. And good luck for you, too ;)

o shit waddup

can someone tell me what exactly $\pi_1(M,x_0)$ means?

where $M$ is a manifold and $x_0$ is a point on it

I mean I know it's supposed to mean the fundamental group, but I'd like to know what the definition exactly is

*fundamental group consisting of loops starting and ending at $x_0$

It's the set of homotopy classes of loops starting and ending at $x_0$

Let $\Omega(x_0,x_0)$ be the loop space, i.e. the set of continuous maps of $S^1\to M$ that have $x_0$ in their image and let $\sim$ be an equivalence relation on $\Omega(x_0,x_0)$ where $\gamma_1\sim\gamma_2$ if they are homotopic

Then $\pi_1(M,x_0)=\Omega(x_0,x_0)/\sim$.

@SoumyoB

I see...

so what would $\pi_1(S^1)$ mean @Ocelo7 ?

Homotopy classes of loops that "go round" the circle

wouldn't that mean each equivalence class contains one element only?

no

go half-way around, then turn around

you can homotope that to a point, i.e. the trivial loop

oh riight

thanks @Ocelo7

what does $1$ as an element of $\pi_1(M,x_0)$ mean? I'm guessing the equivalence class of trivial loops?

aka the ones homotopic to a point?

No, it's an equivalence class of homotopic loops

it won't be null-homotopic loops in general

I think I read that a homotopy is like a slider control somehow

@Unknown123 if you really want it to have a name for some kind of peace of mind, I guess you could call it a dividend

yes, you know that 0 is 11 times an integer

and you know which integer

I assume you're on your phone and that's why your messages take up so much vertical space in that chatroom

Hi @Adeek.

Why does surface integral need double integration?

@ItachíUchiha I don't understand the question. Surface integral is defined to be a double integral.

umm..I am new to calculas.I want to ask what is surface integral (to a newbie)?

Do you know what a line integral is?

umm..If I plot y=f(x) and then draw a curve joining all points that fulfilling the criteria (x,f(x)) then the length of that curve is line integral??

That makes no sense, I am sorry.

You should understand what line integrals are before trying to understand surface integrals: the latter is a 2 dimensional generalization of the former.

If you want a one-line introduction to line integrals, then I'd say it's just the total work done by a vector field alone a path. Surface integrals are work done by a vector field along a surface.

But the description you gave tells me you don't really know the correct definition: knowing vague intuition before the definition is dangerous, so I'd recommend you to understand this. Maybe look in whatever textbook you're reading this up from.

Hi, Have a look at this number theory post - math.stackexchange.com/questions/1887036/… , Please, inform if you find anything inconsistent in the argument.

For a 1-d wave equation problem we have two initial conditions and two boundary conditions. If we transform the wave equation to the frequency domain with the Fourier transform we obtain the Helmholtz equation and we only have to satisfy the two boundary conditions...so what has happened to the two initial conditions? Its seems the constraint they have on the solutions to the problem 'disappears'...where has the constraint gone?

@Hippalectryon Salut, sais-tu où trouver le livre À la découverte des lois de l'univers de Roger Penrose ? (en pdf j'entends...) merci

@JeSuis Sans payer ? non

@Jasper You too.

hi

:(

hi :-)

@Hippalectryon hi

;(

Why the sad face ?

what is your profile pic ?

The main character of a Chinese light novel

overlordmaruyama.wikia.com/wiki/Overlord_Wiki

Let X and Y be uniformly random variables in [0,1)

What is the distribution of XY?

why don't you ask it in the main site ?

is asking here fine ?

of course it is ok to ask here

ok i will also ask one question

> Just ask; don't ask to ask.

i want map [3,5] to [0,3]

@A---B (x-3)*1.5

this was a unanswered question i found on the site some days ago

@LeakyNun wow how did you do it ?

@A---B x-3 is normalize to start at zero

1.5 is scaling factor

@LeakyNun I prefer (sin(x*10000)+1)*1.5

:P

@Hippalectryon i prefer 2, nobody said it has to be surjective xd

i was wandering all over coordinate systems and translation

@Hippalectryon how you got that ?

@A---B range of sin is [-1,1], +1 to normalize, *1.5 to scale

@LeakyNun i feel dumb

:(

My answer is correct but surely not one expected for the question >.> don't mind it

@Hippalectryon Thanks

i don't like probability, infinite series are better for me

:)

Infinite series ? Don't you simply mean series ?

@Hippalectryon there are finite series

O_o what are those ?

To me a series is an infinite sum

@Hippalectryon I've never heard of a serie

it's always a series

yeah my bad

Interesting, I always thought series can be finite

(I'm French and learn maths in French so I'm not sure about the English translations)

Just checked wiki

@Hippalectryon en francais on dit une serie :o

je ne l'ai jamais su

une série :-)

i thought series, when calculated till some finite number is called finite series

@A---B I call that a sum

odd distinction

'cause every finite series is also an infinite series (just add a bunch of zeroes)

@BalarkaSen To me there's conceptually a difference between summing infinitely many terms, eventually zero after some rank, and summing a finite number of terms

But maybe it's just me being picky

(i also call it sum rather than series, but regardless of finite or infiniteness)

i also

set A - set B, how do you say "-", difference or minus ?

minus

minus

Either "the difference of A and B" or "A minus B"

set A difference set B doesn't sound good

@Hippalectryon le premier c'est misleading

i also say "setminus"

@LeakyNun true

as in "A setminus B"

in programming we called it A with B filtered out

spelling out loud the latex code

to me, spoken maths statement never sound good

it feel so confusing

those symbols were never meant to be spoken out

completely agreed,

Can i find range of function $f(x) = |x-1| - |x-2| + |x-3| - |x-4| +... + |x-100|$ ?

just thought of it

The last one is a minus sign isn't it ?

If so the range is surely [-50,50]

@Hippalectryon oh yes

@Hippalectryon wow are you joking ?

No :-) think about it

For x>100, what's f(x) ?

99 - 98 + 97 - 96 + 95 - ... - 0

=?

0

Are you sure ?

no?

100

or 50

Why ?

don't guess

do it

99 - 98 = 1 + 97 = 98 - 96 = 2 + 95 = 97 - 94 = 3 + 93 = 96 ...

handwavey af

did it, ought to be 50

@LeakyNun have a better way ? please tell then ...

why?

(99-98)+(97-96)+...+(1-0)

how many pairs are there

50 ... :(

exactly

oh i thought the same thing but in a different way

like for every 2 number we increment sum by 1

yes

any way that is for x > 100 what about x < 100 ?

what is x

$f(x) = |x-1| - |x-2| + |x-3| - |x-4| +... + |x-100|$

@A---B That's my next question :P

@Hippalectryon ok :) , (49 - 48) + (47 - 46) ... (-49 + 50) = 50 ?

right ?

Why start at 49 ? The first term is 101 for x=-100

i took x = 50

Oooh mb

The question is "what about x<-100" ?

it would be same as x > 100

with a - sign

Why ?

The function isn't symmetrical with respect to the vertical axis x=0

(101 - 102) + (103 - 104) + ... + (199 - 200) = -50 ? :(

Alright

Now what happens hen you start at x=-100 and increase x slightly ?

if i increase by 1 every number increase by 1

so we still get -50

right ?

Why does every number increase by 1 ?

For instance |x-1| was 101 and becomes 100

|-101 - 1| = 102 ?

lol i got it

I said increase x. Increasing -100 by 1 gives -99

:P

yes you are right

ok i got how the range is [-50, 50]

Basically what I'm trying to make you show is that the function is increasing on [0,100]

And f(0)=-50,f(100)=50

yes

(for some reason I asked about f(-100) before but f(0) works too)

What's f(1) ?

(0 - 1) + (2 - 3) ... (98 - 99)

so, -50 again.

yes

Now let's increase x=1 by 1. What changes ?

every number increases by 1

still 50 :)

Really ? Every number ?

no wait

|2- 1| = 1 and then |2- 2| = 0, |2-3| = 1 ...

So indeed for |x-3|,|x-4|,...,|x-100| nothing changes

|2-3| = 1, |1-3| = 2

?

???

Well for x between 1 and 2, we have |x-1|-|x-2|=(x-1)-(2-x)=2x-1

Add |x-3|-|x-4|+... and we get f(1<x<2)=2x-50

So it's increasing between 1 and 2

You can do the exact same reasoning for x between 3 and 4, 5 and 6, etc

yes

All that's left is looking at the cases for x between 2 and 3, 4 and 5, ...

What happens in those cases ?

right ?

Look at x between 2 and 3, not x=2 and x=3

@Jasper Hey, laughing is healthy. :-)

@A---B Don't chose one x between 2 and 3. What I'm asking for is the simplified expression of f(x) for 2<x<3. For instance between 1 and 2 we had f(x)=2x-50

(slight mistake actually it should be f(x)=2(x-1)-50). But that's irrelevant.

2(x-1) - 49 blind guess

@Jasper give me more!!! :-) Post them here.

@Jasper dont lose hope somebody will watch them

:)

@A---B Don't use blind guesses >.> think

@A---B If you're stuck, look at the function and try to prove the result desmos.com/calculator/v9hacwjdwf

@Jasper I work every day. Well, these days I develop an important tool that is based upon an article that I suppose it is going to be published somewhere around the end of the year.

(if all is fine and I'm lucky enough)

@Hippalectryon it is 48 for 2.5, 2.6,2.7,2.8 ... 3.0 right ?

Yes

@Jasper I have many ideas to develop, and as I said before I would need a whole team to do that, for some years.

Well we just want to prove that our function is increasing, so all you have to do is to show that it's constant on [2,3],[4,5],...

ok done that

it is easy

@Jasper could you compose some music with Chris's sis and upload on youtube? :P

(maybe you have some cool ideas with that :D)

@Jasper LOL

@Jasper :D

@A---B Well then we're finished :-)

finally that was tedious

thanks for bearing me

@Hippalectryon but say i am getting 1 million $ for proving that, how would i do it ?

Exactly the way we've done it. Show that f(x>=100)=50, f(x<=1)=-50, that f(2n<=x<=2n+1) is constant and that f(2n+1<=x<=2n+2) is increasing

@Hippalectryon nice you are genius, :)

Haha not at all :D @user1618033 is

why ?

Because she keeps doing incredible stuff >.>

@Hippalectryon If I were a genius I would have probably had some diploma at Harvard, MIT, UCLA and so on ;)

Well I don't have any of those

:-)

Now srry but I'll be busy for 30 mins or so

@Jasper doesn't have to be mutually exclusive :-)

@Hippalectryon so did she do ?

@Hippalectryon The nice thing is to be a simple person, with a simple mind, that is able to do fascinating things. Doing fascinating things as a genius is not that fascinating, because after all you're a genius.

@A---B Nah she's a special case. No serious academic maths class whatsoever

away

@Hippalectryon but what she do with any serious academic maths class ?

@Jasper ok lol

@Hippalectryon then how is she genius

?

:(

@Jasper but ramanujan did many things, what did she do ?

Hi @Pedro

just some user

the world is a small palce

nope

(and since you're interested in English, "is it your other account" would imply I only have one other account)

only person I masqueraded as was robjohn for april fools day

meh

if one google searches e.g. "knapp basic algebra" the page with links comes up in the first page of results

so the people who want/need them will find them

yes