@BalarkaSen kinetics is k theory confirmed

@MaryStar $a_{n+1} = 3+(a_n-3)/10$

@MaryStar ja, das ist richtig

Ok, I should get some math done now

Great! Thanks!! @LeakyNun

keine Problem

Sheaf cohomology? @Balarka

That's on chapter 2; I'm still learning 1.

Sheaf Cohomology is in Chapter 3 of the only book that matters.

hah, what's that book?

That was a half-joke, but Hartshorne

lool

I never got past chapter 1 of Hartshorne

@MaryStar bist du sicher, dass es korrect ist?

Qing Liu for Alg Geo

@LeakyNun Glaub schon... Kann es nicht so sein?

@PVAL-inactive EGA/SGA or bust

@LeakyNun sup leaky

@MaryStar ich sehe kein offensichtliches Muster

Also as of today we're no longer gonna be in the same state

@KasmirKhaan god dag

buongiorno @AlessandroCodenotti

goddag :D

Hi

I got exercice on automorphism

I kinna need help with =p

@AlessandroCodenotti you should see this lol

@AlessandroCodenotti ih

@LeakyNun jesus, son.

godfather :o

I have never seen anything so beautifully complicated in my life.

@LeakyNun can you take a look at assigment 3 that i sent you , Question 2

@KasmirKhaan can you send again?

@LeakyNun ok ill send it now

@MaryStar Where's 4/5 in that list?

@MaryStar es soll 1/2,2/3,3/4,4/5,5/6,6/7,7/8,... sein, oder 1/2,3/4,5/6,7/8,... sein

i guess i don't know what the context is, though

@Semiclassical there is no context

I sorta doubt that.

@MaryStar anything else would have to rely on entirely guess work

@Semiclassical what if it's numberwang?

That has basically no context

Hello

@KasmirKhaan ok?

sure it does. it has the context of "say enough random s*** that it becomes bloody hilarious"

@LeakyNun sent =p

@KasmirKhaan received

all righty need to prove that tau_g is an automorphism

@Semiclassical there's no 6/7 either.

t_g (xy) = g'xyg = g'xg g'yg

= t_g(x) * t_g (y)

t_g(x) = t_g (y) implies x=y

since the t : G-->G , injective implies surjective

thus we have an automorphism

Fair

Let $F$ be a field of characteristic 0. Let V be a finite dimensional over F. Suppose that $ E_{1},...,E_{k}$ are projections of V and that $E_{1}+...+E_{k}=I$. Prove that $E_{i}E_{j} = 0$ for $ i \ne 0$. Please help

@LeakyNun .

this is wrong

yeah I was just thnking that...

hmm

why ?

any map that is injective from a set to another set with same order is also bijective

Is it possibly infinite?

No

or wait should i say that they are finite sets?

hmm

you said that any on-to-one functions is also onto.

Hey!!! I have a question... Why is a proper divisor of n, $\leq \frac{n-2}{2}$ ?

with same order

not any 1-1 fn

You need finite for that to work

The prime numbers have the same order as Q

hmm is Q countable?

@KasmirKhaan yes

Yup

SNIPED

that is odd

Rip

I thought only N and Z are

Why do I keep getting sniped? :'(

@Kasmir, there are many things about infinity, which you should not care about for now.

Focus on group theory.

okay

its not hard to show surjectivity i think

lets x in G

You have an injection from Q into N^2 by mapping each rational number to it's numerator and denominator in reduced form

and a bijection from N^2 to N by counting diagonals

@Evinda also,6 ist teilbar von 3 aber $3 \not\le \dfrac{3-2}2 = \dfrac12$

x= g'gxg'g

so t(gxg') = x

so t is surjective

but what to call that t_ ?

t subwhat

why do you need a new name?

Isn't there something about the axiom of choice giving you that any infinite set bijects to its "square"?

it is t_g.

@Daminark yes, there is

@LeakyNun Oh sorry, that was a typo. I meant every proper divisor of $\phi(n)$

oh yeah ><

'thought needed t_g'g

but that is not right

since we still conjugating by g

all righty then

@Evinda well, $\phi(n) \le n-1$

was that good leaky ?@LeakyNun

well your proof is all over the place

what does that mean

@LeakyNun Und wie folgt es dass jeder Teiler $\leq \frac{n-2}{2}$ ist?

@KasmirKhaan it means it's spread over the page in this chatroom

@LeakyNun oh let me put it in one line

t_g (x) = t_g(y) implies x=y

so this is an isomorphism

but the map was form G to itself, it is then an automorphism

@Abcd Kinetics and thermodynamics are kinda separate most of the time. Back in my undergrad, we are being taught thermodynamics before kinetics. It is more important to understand chemical equlibrium first before dealing with kinetics, as concepts like gibbs free energy is needed to make sense of kinetics

@Secret We weren't taught Gibbs free energy in equilibrium.

@Evinda weil der Divisor der am größten sein kann und ist nicht der Divisor selbst ist weniger als seine Hälfte

@Secret Anyway, okay. I'll deal with it. Thanks for replying.

damit ist jeder Teiler $\le \dfrac{\phi(n)}2 \le \dfrac{n-1}2$

@LeakyNun ill keep working on other parts and ill send you all at once

Where's semi when you need him :{

Let F be a field of characteristic 0. Let V be a finite dimensional vector space over F. Suppose that E1,E2,...,Ek are projections of V and that E1+E2+...+Ek = I (Identity operator). Prove that Ei . Ej = 0 for i not equal to j. Please help.

dodsy ill be your semi

z.B. wenn $n$ sieben ist, ist $\varphi(n)$ sechs, und damit ist der größte Teiler drei, wer weniger als $\dfrac{n-2}2=2.5$ nicht ist.

@Evinda

@KasmirKhaan I think i've figured it out. I have this silly physics assignment due tomorrow :P

I appreciate the offer though, friend.

Does Did always ignore follow-up questions?

haha that sounds good that you figured it out

Or is it just mine?

who is Did?

He's a probability guy. He's in here sometimes.

Hmm ask Ted and leakynun

they help you as much as needed :D

They do.

As long as you do not come across as combative.

@KasmirKhaan True that!!

@KasmirKhaan if we are finding the $f_{net}$ using the equation $F_{net}=ma$ and our mass is $2.75$kg and our acceleration is $4$ m/s. Do we write the $F_{net}$ as kg/ms?

well if you are learning something you should be asking to learn not to be stubborn

@Dodsy the part you dont get is the unit ?

@Dodsy newton is fine too.

at this point yes.

When you ask a follow-up question 2 hours ago, see that the guy has edited his answer with something that has nothing to do with your follow-up question 1 hour ago, and completely ignores you.

@Abcd oh good point

I can write it in Newtons.

Yes.

thanks friends.

@Dodsy in general units works just as noraml variables in equations

Apparently somebody has gone on a rampage of down voting his answers out of spite.

you had F=ma , kg * m/s

so then they get combined?

most of physic formulas are easy to derive if you know what the unit should turn out to be

I don't think that's the right thing to do, and I wouldn't do it, but I can understand that he frustrates people enough to make them want to do it.

@KasmirKhaan I wouldn't say it makes them easy to derive, but it makes it easy to see what they should more-or-less look like

Yes not allways make sense, and they youll find it to be called other thing=p like newton is general for force

@Dodsy yeah, and the combined unit is called newton.

Yes that what i meant

@Semiclassical makes it easy to verify the result?

you can see if you calculated right or wrong based on the unit in the result=p

eh. it makes it easier to detect a wrong result.

@Dodsy Your semi is here

yeah

Hello, can someone link me to non geometric proof of functions.wolfram.com/04.01.23.0006.01

And you know me - I'm an easy person to piss off.

@KasmirKhaan @Abcd You guys were very helpful, thank you.

Tried induction but got another sum equality i couldn't prove

Well, you are ALannister.

And I always pay my debts.

The drama here is too real.

This is nothing @Dodsy

Sometimes, it's like the Red Wedding in here.

@Semiclassical is acceleration written as $m/s$ ?

@Dodsy $m/s^2$

Thanks abcd :)

@Semiclassical looks like there's a new physics master in town.

Eisenstein devised a geometric proof in order to prove quadratic reciprocity. I want to see a non geometric proof. And not one thats mod 2 either. Sum[Floor[(q k)/p], {k, 1, (p - 1)/2}] + Sum[Floor[(p k)/q], {k, 1, (q - 1)/2}] == (1/4) (p - 1) (q - 1) /; Element[p, Integers] && Element[q, Integers] && p > 0 && q > 0 && GCD[p, q] == 1

lol

@Dodsy lol, this is high school level stuff so I could answer :P

position has units of length (meters), velocity is time derivative of position so has units of length/time

and acceleration is time derivative of velocity, so....

@Dodsy Kinematics? Which is the next chapter?

@abcd this is our review assignment :P but I'm also terrible at physics and the teacher is abysmal.

Oh, I see.

Ok, und haben wir strikt dass $\phi(n)<n-1$ und nicht $\phi(n) \leq n-1$ ? @LeakyNun

Elementary number theory anyone?

@Evinda seh meinen Beispiel

@Abcd first year uni, I really regret taking physics.

Ah ich verstehe.... Also gilt es dass der größte Teiler von $\phi(n)$ $\leq \frac{n-1}{2}$ ist und nicht von $\frac{n-2}{2}$, richtig] ? @LeakyNun

@Dodsy You don't like physics? Did you take chemistry too?

@Evinda wie sprichst du "$\phi$" aus?

@Dodsy You must have taken maths too. Is there no option of dropping physics?

@Evinda ja, das ist richtig

@abcd I am not taking chemistry, but the last day to swap a class was last friday :{

I mean, I can tough it out. But the labs are ridiculous.

@LeakyNun fi

Ok, danke :) @LeakyNun

kein Problem

@Abcd @Semiclassical how would you find the $F_{net}$ at 8.5 s? imgur.com/a/DtPzq

@Dodsy Chemistry is my favourite! I guess you will have to bear physics now :(. Maybe you will begin loving it soon....

perhaps. :)

imgur.com/a/DtPzq

forgot the image in my question to you guys.

@Dodsy given mass?

$F = ma = m \dot v$

@Dodsy find the slope at 8.5 s, that gives the acceleration. Multiply it by the given mass to get $F_net$

sniped :D

Yeah so I've been doing that

but for certain intervals.

like between 0 and 2.

$F_{net}$*

but I don't see how there is enough info on the graph.

given mass is 2.75 kg @LeakyNun

I'm sure you can find the slope from the graph

@Dodsy There's enough info. What is missing according to you?

okay so I can see that at 8.5 s the velocity is ~10 m/s.

@Dodsy slope

@Dodsy Slope from 6 to 10 s.

but for slope I need $m=\frac{y_2-y_1}{x_2-x_1}$ right?

oh doi.

it would have the same slope.

thanks guys.

Much appreciated.

let $F$ be a field of characteristic 0. Let $V$ be a finite dimensional vector space over $F$. Suppose $E_{1},E_{2},...,E_{k}$ are projections of V and that $E_{1}+E_{2}+..+E_{K}=I$. Prove that $E_{i}E_{j} = 0$ for $i \ne j$.Please help.

@Semiclassical is it a problem to say you have no idea how to calculate an ( I mean a certain integral) integral? I wouldn't have any if the case.

jaspa

Hiii

@Jasper Jasper

@Semiclassical @LeakyNun @TedShifrin help with the above please

Hi @Jasper

Jasper is the most popular person here.

He has exceeded ted's populatiry.

Sometimes, my anxiety causes me to poo 4 times a day.

@Dodsy By far the most popular user on MSE.

But I guess that's OK.

That's okay, I poop 4 times a day without anxiety.

not really needing discussion about bowel movements here

Sorry.

i will say, though, that the physical aspects of anxiety are a big deal

anxiety might originate in the mind, but the effects of an anxiety attack aren't so confined

Oh I agree.

I wasn't trying to trivialise Jasper's experience with anxiety.

Do you pronounce flour the same as flower?

(for me the most prominent instance of that is muscle twitches/spasms)

help please

@Jasper yes. Blumen, blumen.

@Jasper not quite, but very nearly

I tend to put a bit of emphasis on the w in flower

@Jasper yes

but I'm from HK, lol

have you seen my message?

@Semiclassical trying to think here. Giving the speed and weight of a bullet and how much it penetrated into a tree, to find it's stopping time how?

@LeakyNun Yes, the long proof right?

whereas with flour i tend to elide it

@Jasper yes

without giving too much away.

using just kinematics?

Yes.

@LeakyNun It seems you like logic a lot.

"the big 4"

:/

What assumptions are they giving you?

we are assuming a constant friction force.

@Semiclassical any hints please?

okay, so constant acceleration

that helps a lot

right, constant acceleration as well.

@Semiclassical hints on my question please

so you know what it's initial velocity is. how about its final velocity?

@Semiclassical I think I get stomach cramps and indigestion.

I feel like I used to have more of the indigestion

Only it's initial velocity is known.

@Jasper you only knew it now :P

not so much now though. maybe something to do with medication? I'm not sure

@Dodsy Tsk. You know more than that

@LeakyNun Who knows, maybe you will solve the P vs NP in future.

What is the final state of the bullet?

@Jasper lol

I remember at least the equation v=u+at, lol.

@Semiclassical in the tree.

bullet travelling at 350 m/s with a m of 1.80 g penetrates a tree with a depth of 0.130 m

Hi @Ted

Actually, we did quite a bit of mechanics in high school math.

Hi, @Balarka. Radius of convergence :P

@Jasper celestial ?

@Semiclassical find a girl. That might help with anxiety.

@Dodsy No, just the usual rectilinear motion, circular motion, etc. Nothing in the heavens.

@Waiting Do you still like Monica?

@Jasper I believe Spivak talks about celestial mechanics in Calculus, but I may be mistaken.

Hi @Ted

@TedShifrin let $F$ be a field of characteristic 0. Let $V$ be a finite dimensional vector space over $F$. Suppose $E_{1},E_{2},...,E_{k}$ are projections of V and that $E_{1}+E_{2}+..+E_{K}=I$. Prove that $E_{i}E_{j} = 0$ for $i \ne j$.Please help.

@Jasper Yeap, I think so. :-)

@Dodsy I think there is the Kepler problem.

@Waiting I still like Laura.

Hi, @NV. I saw your post. Can you do it when $k=2$? I don't quite see the general case.

@TedShifrin I don't understand that hint but all you wanted me to prove was that the etale space of the sheaf of holomorphic functions on $\Bbb C$ is Hausdorff, didn't you?

@Jasper When do you plan to get married?

Hi @Alessandro

That's just identity theorem.

No, @Balarka. I wanted you to see why it's not a covering space.

We already discussed Hausdorff (I thought).

@NV-US Multiplying $E_1$ and using the fact that projections are idempotent, you obtain $E_1 E_2 + \cdots + E_1 E_K = 0$. Repeat for other $E_i$ and you're done.

@Waiting I hate when people chalk up anxiety to not having a significant other in their lives. Such a joke.

yes i can

Right.

@TedShifrin Ah, gotcha.

@Waiting Haha, trying to be well first. If I don't get well, I will not even date. =D

Ok, let's think.

@NV: Well, I don't see it for $k>2$ yet, either. Feel better?

i am thinking what @LeakyNun said

@Dodsy Where is the joke? Do you believe that dating girls won't help anxiety? That would be the joke, such a belief.

What did Leaky say?

@Waiting What a strange and silly notion. But I won't continue this conversation.

@Leaky: I don't see how that works.

@Dodsy who cares?

@Jasper I encourage you to do it sooner! :-)

@Waiting Hehe, are things OK now for you over there?

@TedShifrin you obtain $E_1 E_2 + E_1 E_3=0$, $E_2 E_1 + E_2 E_3 = 0$, and $E_3 E_1 + E_3 E_2 = 0$, and you can flip all the products in every sum. Hmm, you're right, I can't make the orders match.

So I have this map $p : |\mathscr{O}(\Bbb C)| \to \Bbb C$. To prove it's not a covering space, suffices to show that for a point $z_0 \in \Bbb C$ there is no neighborhood $U$ around $z_0$ so that $p^{-1}(U)$ can be written as a disjoint union of open sets around the germs at $z_0$.

Plus you don't know they commute, @Leaky.

@TedShifrin right, that's what I'm thinking

Right, @Balarka. I'll settle for $z_0=0$.

Hm, hm, hm.

Right, let's just think about the origin.

@Jasper Things with me are simple, as before: working very hard, excepting now when I talk to you, that means I took some break (which I deserve I think).