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12:00 PM
what does $$\sum_{n-k}$$ mean?
 
Oh! That is binomial! so $$\sum_{n-k=0}^s$$
@BalarkaSen, is that now ok?
Please help@BalarkaSen
 
@Sush yes. that's better.
so the sum runs through $n$, right?
I am not even sure why you are trying to prove umbral binomial theorem this way. there are much better and cleaner proofs out there.
OK, I guess I need to bubyes now.
 
12:22 PM
@Chris'ssis this one is definitely for you math.stackexchange.com/questions/829105/a-frightening-sum
 
@G.T.R, will you please let me know how $\displaystyle \sum_k \binom r k x^k \sum_{n-k} \binom s {n - k} x^{n - k}=\displaystyle \sum_n \left({\sum_k \binom r k \binom s {n-k} }\right) x^n$?
 
@Sush the second sum in the LHS makes no sense to me
 
@DanielFischer, please!
@G.T.R, OK! I asked from this
 
@G.T.R Comment ça ? C'est pas juste la somme avec $n-k$ pour $k$ variant ?
 
Ok, I think this is clearer.
 
12:32 PM
@Hippalectryon je sais pas, si tu penses ça dis le à Sush
 
@Hippalectryon, I translated.
 
@Sush Utterly screwed up notation. It's $$\left(\sum_{k=0}^\infty \binom{r}{k}x^k\right)\left(\sum_{m=0}^\infty \binom{s}{m}x^m\right) = \sum_{n=0}^\infty \left(\sum_{k=0}^n \binom{r}{k}x^k\binom{s}{n-k}x^{n-k}\right),$$ the usual Cauchy-product of series.
 
@Sush Basically the one you wrote in the chat and the one you linked are the same
@Sush It's just a matter of notations ($i$ for $k$ and $j$ for $n-k$)
@G.T.R Such rain outside for you too ?
 
@DanielFischer, Thank you! I didn't know that it is called Cauchy-product of series.
 
@Hippalectryon yeah, utter shitty weather
 
@BalarkaSen, you are right.
(Though I couldn't understand that :P)
@HI! @skullpatrol
 
@Sush Hi pal :D
 
12:51 PM
Good Morning Mr
 
I'm really confused. Since I logged in last time my reputation seems to have increased by about 500.
 
congrats
 
But I cannot view anything of that on my reputation tab on my profile.
@robjohn Are you there?
@robjohn Something very funny is going on here.
 
@MattN. what's up?
 
@robjohn About 3 days ago my reputation was around 17090. Today it appears to have changed to 17510 but I cannot see any rep change on my reputation tab.
 
1:03 PM
he's complaining about a gift horse :-)
 
@MattN. read this
 
@robjohn Oh, I see. That helps, thank you!
@robjohn It doesn't say why the reputation was restored though. That's not normal, right?
Normally the votes get deleted I thought.
 
@MattN. You're lucky, I only got 230
 
@G.T.R Ton exercice vient d'un oral de l'ENS ?
 
oui
 
1:06 PM
never look a gift horse in the mouth
 
posé l'an dernier
 
@robjohn : )
@robjohn But tell me: if someone deletes their account it usually deletes the votes, right? This one here is special or perhaps a new policy.
 
La personne a du croire à une farce..
 
@Nico je sais même pas comment le calcul pouvait tenir au tableau
 
@robjohn They should have waited for christmas with the recalculation.
 
1:10 PM
@G.T.R Moi non plus, les exos de l'ENS pour certains sont vraiment sadique..
Et le pire c'est que les gens ici ont toujours l'expression que tu mens quand tu dis que ça vient d'un oral..
 
@MattN. This is usually taken care of before a user who has voted a lot leaves, but perhaps a community mod took care of the removal who did not know the usual procedure, so they had to take care of it afterwards.
@MattN. ah, I was looking in the wrong place. I only got 90 :-(
 
@robjohn I had no idea. Interesting that it's different for users with lots of votes.
@robjohn [>:( ] (impression of an angry square)
Anyway. Thanks and I'll see you later!
 
@Nico pour eux un oral c'est ça math.berkeley.edu/~cawong/files/qualtranscript.pdf
 
@G.T.R lol ?
 
@G.T.R Lol ?(moi aussi). Après de toute façon c'est pour entretenir le mythe des prepas françaises.
 
1:21 PM
au moins y'a des questions de cours :D @Hippalectryon @Nico
 
pour moi ça c'est un oral. Surtout que Qiaochu Yuan est certainement beaucoup plus """"fort"""" qu'un mec de Ulm :p
 
@G.T.R En théorie sans ton cours tu ne passe pas les écrits lol
 
@Hippalectryon D'ailleurs ojd c'est les résultats des mines non ?
 
@Nico ojd ?
 
oui à 18h
 
1:25 PM
@Hippalectryon Language sms mal fait, aujourd'hui*
 
@Nico Ooh aucune idée je suis en sup moi :) (PCSI)
 
@G.T.R Merci, @Hippalectryon ah d'accord tu as encore le temps..
 
Eh oui :)
'What is your favorite space?' <- cette question ^^
 
@Hippalectryon Avec ce forum c'est l'X que tu dois viser :-P
 
@Nico Bah je tenterais tout :D - mais il faut que je m'améliore en physique :C
 
1:28 PM
@Nico j'espère ne pas être éliminé à cause de la chimie :P
 
La chimie c'est simple :P
Quoique la chimie des MP cette année aux mines elle était assez calculatoire
 
@Hippalectryon Pour ça faut apprendre son cours et ne pas négliger la sup, cette année en PSI (apparemment) beaucoup de sUP en physique.
 
pour les chimistes
 
Des réacteurs bizarres
 
@G.T.R haha Pareil. J'ai pas fait grand chose sur ce sujet..
 
1:30 PM
Le pire (en coefficient) c'était la physique de Centrale avec l'optique
 
et ne surtout pas négliger les applications numériques, des points faciles à prendre. Pour nous (enfin je suppose que tu es en MP) ? @G.T.R
 
De toute façon moi je prend PC pas PSI (aaah la SI fuyons)
 
@Nico oui en MP info (le sudoku :D)
 
oui bha PC t'as effectivement intérêt à aimer la chimie lol
 
@G.T.R ugly
 
1:34 PM
@G.T.R haha! Par contre c'était les mines maths avec dunford encore c'était cool..
 
@Nico ah ouais j'ai pas trop aimé ça. Je préfère la deuxième épreuve sur la topologie
 
@robjohn I want to make a poster with that series, also some wallpaper for my desktop ... :-)
 
Salut @GTR, @Hippa, @Nico ... C'est toujours la salle française :)
 
@Ted Salut, yes, we're taking over
 
@TedShifrin J'avais prévenu qu'on s'emparerait du chat :P
@TedShifrin Dans quelque jours on vous reprochera de parler anglais ;)
Majority rule WINS
 
1:38 PM
Ça m'étonnerait un peu :P
 
@G.T.R Pas faux! @TedShifrin Salut ted, what's up ?
 
Not much, Nico ... Just came to see if there was any interesting math ... or gossip :D
Et maintenant il n'y a rien ...
 
Haha, gossip on MSE ? Never had such echoes :p
 
@Nico you need to go to META.MSE
 
@G.T.R this is the dark side there
@TedShifrin interesting math, here we go : Soit $\lim x(n)=0$
et $\lim \frac{ln(x(n))}{s(n)}=a<0$ avec
$s(n)=x(1)+...+x(n)$
Montrer que $\lim \frac{ln(x(n))}{ln(n)}=-1$
tout les $x(n)) sont $>0$
 
1:46 PM
@Nico BTW, tu l'as trouvé où le truc $f'''+f'$ ?
 
@G.T.R BTW ?? Dans un RMS.
 
@Nico btw = by the way
 
et by the by ≠ bye bye
 
@Hippalectryon Ah d'accord merci!
 
1:50 PM
@GTR: BTW, je suis ravi de voir que tu ne t'es pas noyé :)
 
Bon je dois y aller. Bonne journée à vous. et GTR : j'espère voir GTR sur la liste des admissibles ;).
 
@++ alors :)
 
à bientôt, Nico
 
@Nico haha j'espère que tu y seras aussi. A+
@Ted My mom freaks out whenever there's a storm now
 
She'll get over it :)
 
1:53 PM
Over the storm ? =D (lame pun duh)
 
Maybe that makes a pun in French ? :)
 
@Hippalectryon @DanielFischer durch den Monsun ?
 
@G.T.R ??
 
@Hippalectryon Mines-Ponts website is down :O. It's a song
 
Hello, Professor.
 
2:02 PM
@G.T.R trop de demandes de connection ?
 
Keine Ahnung @Hippalectryon
 
@G.T.R I don't speak German :o
 
Anyone can help me in sieves?
 
@Hippalectryon wie erkennst du Deutsch, wenn du es nicht kennst ?
 
@G.T.R 我不该死说德语 !!!
 
2:08 PM
@Hippa কি?
Hah! Take that.
 
@BalarkaSen 你别指望我说孟加拉语,是吗?
 
You all are nuts!
 
Nope i'm a hazelnut :3
 
A hazelnut is a nut, QED.
 
Uh i'm a magical hazelnut. Hence my hair is a hazelnut. Your argument is invalid =D
 
2:11 PM
@Hippalectryon We can play this game whole day, but no point.
 
@BalarkaSen do you really speak Bengali ?
 
Yeah, my native language.
 
@Hippalectryon Captain Obvious is in da place
 
@G.T.R Captain Obvious?
 
2:13 PM
@G.T.R Through the monsoon. And don't expect German song texts to make sense.
 
Yeah, seen that.
 
@DanielFischer so you know which song I'm talking about ?
 
But I am thinking of a different captain obvious.
 
2:14 PM
@G.T.R Do I need to? It's a German song, so it doesn't make sense by definition.
> Is this proof legal?
 
I guess so
Support :D
 
@DanielFischer nah, it's better if you have never heard of it
 
@G.T.R So bad?
 
@DanielFischer see/hear for yourself youtube.com/watch?v=S_Sy5-sOodA
 
Aaaaaah not that AAAAH
 
2:17 PM
@G.T.R You won't get me rick-rolled.
 
@DanielFischer I assure you I won't
 
@DanielFischer I PROMISE it's not a rickroll bringvictory.com (Oh and i've never ever lied in my life and i'm a cow)
 
@DanielFischer don't click that, it's pure evil
 
@G.T.R @Hippalectryon This
 
2:20 PM
@G.T.R Google says Tokio Hotel. That's even worse than rick-rolling.
 
@DanielFischer omg, you know about them :D
 
They should have an "ignore" on main just like in chat. There is someone I cannot stand.
 
Math has no ignore.
If he did the math incorrectly, point him out.
 
Hehe, it's that same person @BalarkaSen
 
2:22 PM
@JasperLoy I know, but it's silly if you can't stand correct answers.
 
Tell us who :3
 
@BalarkaSen Yeah, we used to be friends, until he did some things that made me see his true colours, lol.
@Hippalectryon It's top secret, lol.
 
:o did he divide by 0 ? OOOOOO i see now :D
 
And I guessed the top secret.
 
Well, some people here know as well, Pedro, Charlie, etc.
 
2:26 PM
Anyone who's good at set theory?
 
2:47 PM
This chat is dead.
 
So I figure.
 
Hey all.
 
@IlanAizelmanWS Hi there.
 
Is this chat active?
 
3:04 PM
A chat can't be alive, @AnubianNoob. It's acorporial.
 
k then
 
@IlanAizelmanWS Hello, and not really. Well either nobody is good at set theory, or chat is dead. I'm guessing the latter is true
 
set theory let's go
 
@NikolajKyed the first should also be... how advanced is your stuff ?
 
@AlexanderGruber Well, this ain't your first rodeo.
 
3:13 PM
@G.T.R Well we have two axioms. 1. To each $a \epsilon S such that $a \noteq z \exists a' \epsilon S such that $a * a' = a' * a = e$. 2. If $a * b = z$ then $a = z or b = z$ or both. Basically it's to prove that if any ring fulfills 1. then 2. will also hold.
I've tried to work through it, but I've run into a problem.
 
@AlexanderGruber Acorporial? A corporeal patronus?
 
Okay ready for training.
 
@NikolajKyed The formatting isn't working... I
I'm new to Math SE, I hang out in SO.
 
@AnubianNoob I don't know what SE and SO means. I'm probably from a different country than you
 
@BalarkaSen acorporial, like calistra flockheart 10 years ago.
 
3:15 PM
@NikolajKyed what is $z$ in 1. ?
 
@AnubianNoob look over on the sidebar for "$\LaTeX$ in chat"
 
@G.T.R I'm assuming that it means a can't be a value z outside of the set S. I worded 1. and 2. exactly as it was written.
 
if you're seeing dollars signs and whatnot, there's a link you need to bookmark and click on to have things render
 
In short, it's what we call chatjax.
 
@G.T.R Essentially 1. explains that the product of a value $a$ and it's inverse $a'$ is commutative and the product is a constant
 
3:18 PM
anybody seen any good problems lately?
 
@AlexanderGruber yes.
 
@BalarkaSen whatchya got
 
@G.T.R give @AlexanderGruber the sum from the orals
 
@AlexanderGruber open wide
 
@AlexanderGruber $F/\Bbb C(z)$ and $F'/\Bbb C(z)$ be galois extensions. if $\text{Gal}(F/\Bbb C(z)) \cong \text{Gal}(F'/\Bbb C(z))$ then prove that $F \cong F'$
I have been able to do this (well, not completely, but have an idea sketched) using galois theory of coverings, looking for a classical GT proof.
 
3:20 PM
I can make sense of 1. being true, a slight problem occurs when proving that 2. automatically holds because the end result might be different.
 
@BalarkaSen I think that is a problem in Isaacs algebra
 
@AlexanderGruber Oh?
I got to see it.
 
@NikolajKyed $z$ and $e$ are anonymous elements if I got you right ?
 
@G.T.R Correct, and like I said. I can make sense of 1. I however have a problem with 2. since something just doesn't seem right.
 
I made it up, by the way, it comes from one of my sketches of understanding of parametrizing quinitic riemann surfaces using automorphic forms. @alexander
 
3:24 PM
@BalarkaSen I'll check if it's really in there or not when I go to my office in a couple hours.
It sounds real familiar but I'm not sure if it's just similar.
 
@AlexanderGruber OK. Meanwhile I'll try to download Isaacs up (though I don't trust my connection)
 
just woke up
time to go back to sleep because i can.
 
Interesting fact : Isaac Asimov got a book named 'realms of algebra". Any idea what's it about?
go back to where you came from, @mike.
@AlexanderGruber it sure is weird, that stuff, isn't it? feels like it shouldn't be true, but you can't find any counterexamples.
 
@BalarkaSen it's a great book.
@BalarkaSen no, i'm not sure
 
@Balarka is it about Algebra?!
 
3:30 PM
Is it possible to have a ring where $a * b = 0$ while $a,b \noteq 0$?
 
@Studentmath i dunno.
 
@Balarka yeah it is, it's a really great book. Haven't been published since 1900 or something like that.
 
:16008144 Sorry, not entirely used latex typography
 
@Studentmath you mean asimov?
 
Yes @Balarka
 
3:31 PM
@Studentmath you read it?
 
Heard about it
Have a copy of it in my uni's library as well
How you are, @Balarka?
 
Got Isaacs, @alex.
@Studentmath Fine me is.
 
@BalarkaSen You should get his book Finite Group Theory too, if you can find it
best book I ever read
 
best book i ever read was "JR", by william gaddis
 
yeah, you referred it to me, i recall that.
so i guess it's in transcendental extension chapter, @alexander?
 
3:34 PM
@BalarkaSen i'm not sure.
my copy is in my office
 
i guess fiction doesn't count for this chat, though.
then the best nonfiction book i ever read was "reflections on the way to the gallows". fascinating stuff.
 
c c
@Hippalectryon @G.T.R "[...] dans cette discipline dont j'aimerais dédier mes futures années" dont est correct à cet endroit? ou il vaut mieux "pour laquelle"?
 
@Alexander I have my Graph Theory test on the $30^{th}$, don't have any tests out there though. Any suggestions on exercises I can go over, preferbly with solutions?
 
@cc à laquelle
 
c c
@Hippalectryon thanks, ok, I got neither right :)
 
3:37 PM
@cc It's 'dédier qqchose à qqun' :)
 
c c
yep
 
the problem with books like isaacs (or, Lang!) is that it contains older perspectives.
 
@Studentmath Actually I don't know of any good sources for that
 
@Hippalectryon admissible avec 17 en français et 18 en anglais wtf
 
I always had trouble getting graph theory solutions
 
3:39 PM
@AlexanderGruber heya Alex
 
@G.T.R :D :D :D CONGRATS
 
books like Artin on the other hand has very modern way to think of stuffs.
 
Hi @N3buchadnezzar.
@BalarkaSen nah that ain't no problem
 
like, it introduces algebraic geometry in the course through ring theory and explains modules loads after representation theory.
 
not with isaacs anyhow
 
3:40 PM
I should start making a brand of product called iTried or iTried&Failed
 
@Alexander thanks anyhow, guess I will dig out good problems from the course's standard book.. They have a solution manual online, better than nothing
 
@Studentmath I was thinking about making a solutions manual wiki for a graph theory book
 
$$
I_n = \int_0^\pi \prod_{k=1}^n \sin(kx)\,\mathrm{d}x
$$
 
simply due to the lack of a source for examples of good graph theory proofs
 
Dividing it into four parts, mod 4 and mod 3 is zero. Could not find a transparent pattern for the two latter cases.
 
3:43 PM
@N3buchadnezzar prod sin(kx) has a standard formula.
 
@G.T.R et dans les autres matières ?
 
Mathématiques 1 12
Physique 1 10.75
Langue vivante écrite Anglais 18
Mathématiques 2 12.5
Info/S.I Informatique 5
Français 17
Physique 2 13.5
Chimie 5.25
@Hippalectryon
 
@AlexanderGruber i trust you but not trust pedro in giving references.
 
@G.T.R :O CHIMIE
 
Yeah, for the infinite case. Note however the limits here are finite
 
3:44 PM
stuffs like mendelson are decades old!
 
@G.T.R et SI :c
 
@Hippalectryon LOLOLOLOLO
 
@Alexander did you write your seminar paper in Graph Theory or something else?
 
I remember when I had french. like 8 years ago or something
 
@G.T.R what LO?
 
3:48 PM
 
Lolno ^
 
if you go to my website, I've got my paper up there.
 
Obviously how physics work.
 
it's a combination of graph theory and finite group theory.
 
Sounds interesting, will check it out!
 
3:52 PM
@Chris'ssis: the sum that you pointed out yesterday that Mma got wrong... not only was it divergent, but it was negative. The value it gave back was positive.
 
@robjohn Exactly. That was pretty weird though. Do you figure out why Mathematica thinks like that?
 
@Chris'ssis I'm wondering if there is a regularized interpretation, like $\sum_{k=1}^\infty k=-\frac1{12}$
 
You look terrible, @AlexanderGruber. Far worse than the guy in your avatar.
this looks interesting.
exactly what I need actually.
 
@robjohn hmmm, interesting. Well, it might be ...
 
Oh @Balarka, back at Probability now
 
3:54 PM
@Chris'ssis Since it diverges in the other direction, there is a good chance.
 
@robjohn Indeed.
 
@alexander you are familiar with the fact that GL(4, 2) is exceptionally isomorphic to A8, aren't you?
 

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