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00:12
ERMAHGEHERDHADJFHSKJDHFKJH! I HAVE THE PROOF!
@user1
@anon
@robjohn I'm wondering if you're in the room ...
Can you please delete my account?
How can I delete my account on math stackexchange?
@DannyCheuk Why would you want to do that?
I spent literally too much time and I don't really feel like I'm learning anything (well, at least not a lot)
@DannyCheuk Don't delete it, just take a break.
@DannyCheuk I would like to tell you something, too.
That really upset me.
Please, refrain from making major edits on posts that are not "yours", that is, changing notation, formulas, or things like that. If you'd like to make major changes to a post, ask the poster first!
Yes, I won't do that again. Apologies
00:21
@DannyCheuk I know you do it in your best intentions.
@robjohn I did it! I got the proof of Faulhaber's formula.
Maybe I should throw 500 bounties out until I ran out of reputation ...
@DannyCheuk Just take a break.
Well I have already ask the support team to delete my account
Isn't that irreversible?
I spent too much time online and on non-academic stuff, last school year I literally accomplished nothing, and now I'm forced to transfer to a new school and start things all over again
I'm just trying to literally ... eliminate ... everything that's spending my time
@DannyCheuk Ah, if its that serious, then do it, I guess...
Maybe you're right, I need to take a break ... from school in general, that's what my advisor said
But, anyway, have fun in MSE! There's lots of great mathematicians!
gg
00:36
@DannyCheuk Instead of putting up bounties on your questions you can award it to answers you think deserve it!
Like that, it won't be wasted.
Links?
@DannyCheuk You can just choose the one you like.
Will do!
After the 3 of mine ... 24 hrs
"Nobody hacked my account guys, don't worry!" That is exactly what a hacker would say!
....
seriously?
00:40
I'm joking, of course!
Oh lmao
 
1 hour later…
kan
kan
01:50
Does somebody have quick access to Kantorovich Akilov Functional Analysis? I'd be grateful if you can email me a soft copy, if you had one. Thanks.
 
2 hours later…
03:45
@robjohn can you delete my account now? I've asked you hours ago ... to do so
03:57
@HerpDerp Since I noticed you were trying to give away your reputation via bounties, I figured you wanted to handle that first. If not, I will delete your account.
04:14
@robjohn Please delete my account
@PeterTamaroff Nice work. I would say it's a clever way to go from () to (*).
@PeterTamaroff I'm going to steal your $\blacktriangle$.
Oops, I am not sufficiently clever to type that.
 
3 hours later…
07:17
@AlexanderGruber May I ask what the image in your profile description is? (The one with the circles)
@user1 that's a (5,5)-cage.
i have a tattoo of it, actually.
@AlexanderGruber Cool
was my user logo, too, before i was elected emperor and had to start lookin' more stately.
lol
 
3 hours later…
09:58
@HerpDerp why don't you just leave your account unused, then you can come back to it some day if you need it?
 
1 hour later…
11:11
is anyone familar with the max flow min cut theorem ?
 
2 hours later…
13:17
A variable $x$ is said to have a domain;
yet the notation $x \in$ real numbers flips the possession.
Do you know why? @robjohn
why did you copy the picture of amswhy ?
She said we were going to forget her while she is gone, so this is a reminder for her to get well soon :-)
+ I like it.
13:33
Greetings
14:00
Hello
14:38
@skullpatrol the nomenclature "$x$ has a domain" does not really say anything in itself. Nothing belongs to $x$. It really means that whatever function $f$, sometimes called $f(x)$, has a domain and that domain restricts that $x\in\mathbb{R}$. It is very contextual.
15:12
Guys, In a group, when checking the associativity of the operation $a(bc)=(ab)c$, do $a,b,c$ have to be all distinct or they can be similar. Because there are some groups like $\{0\}$ or $\{1,-1\}$ that have less than 3 elements
Okay, the definition says any a,b,c so a,b,c can be the same
Can anyone help with number theory?
Just in case: is there any way of quickly finding the set of integer $n$ for which $\frac{\prod_i (a_i+b_in)}{c_i+d_in} \in \mathbb{Z}$, where $a_i,b_i,c_i,d_i \in \mathbb{Z}$?
15:38
@Chris'ssis I have now. I will have to look later.
15:49
@robjohn Rob.
@PeterTamaroff is it quick? I have to go out for a bit.
@robjohn I am stuck in proving the Bernoulli odd numbers arezero.
(except $B_1=-1/2$, of course)
And this is key in what I'm doing.
@PeterTamaroff Do you know their relation with the series for $\frac{x}{e^x-1}$?
I define them recursively as $B_0=1$, $$\sum_{k=0}^n\binom nk B_k=(-1)^nB_n$$
@robjohn Yes, but I wouldn't want to use that.
Want to keep it as "discrete" as possible.
@PeterTamaroff Then I will have to look when I get back.
15:56
@robjohn OK.
@AntonioVargas Hey!
@PeterTamaroff Yo.
Check it out. Pretty proud of this answer.
@robjohn OK
16:11
@AntonioVargas Nice, let me see! I am proud of this one =)
@PeterTamaroff Oh I just saw that the other day. I've been meaning to read it.
@AntonioVargas I have cleaned it up a little now.
@PeterTamaroff There's a small typo at the top, in your definition of the sequence y you have an x_n.
(thought you'd want to know)
hmmm, I'm trying to precisely compute $\displaystyle \int_0^{\infty} \sin(x) \sin(x^2) \sin(x^3) \ dx$
(and then perform the generalization ...)
@AntonioVargas Ah, thanks.
@AntonioVargas I'm reading your answer.
16:31
@PeterTamaroff I'm having a hard time going from ${\bf B}\star {\bf 1}={\bf B}+[n=1]$ to $\sum\limits_{k = 0}^{n}\binom {n+1}k {{B_k}} = 0$. How should I be looking at it?
@AntonioVargas Well, $$\sum\limits_{k = 0}^{n - 1}\binom nk {{B_k}} = \left[ {n = 1} \right]$$ from the definition. Now make $n\to n+1$.
You actually get $$\sum\limits_{k = 0}^{n }\binom {n+1}k {{B_k}} = \left[ {n = 0} \right]$$
But the Iverson bracket is $0$ if $n>0$.
I don't see why the first one is true.
OHHH
Thanks, now I do.
@PeterTamaroff Damn nice proof of Faulhaber's formula.
@AntonioVargas ;)
@AntonioVargas Your graphs remind me of bacteria =P
Damn, no one noted the pun? The vanishing of the Bees!
@PeterTamaroff lol
@PeterTamaroff The unit circle is my petri dish.
@AntonioVargas Exactly! =)
@AntonioVargas Man, I need time to read your answer.
16:52
@PeterTamaroff I appreciate that you took a look!
@PeterTamaroff Btw I have a sketch of an answer for your question about zeros. I don't know when I'll finish it though.
@AntonioVargas Ah, no rush.
17:07
@PeterTamaroff Is the formula $B_n=\sum_{k=0}^n\frac1{k+1}\sum_{r=0}^k(-1)^r\binom krr^n$ a consequence of one of your corollaries?
@AntonioVargas I haven't been able to pin that one down.
But I have an idea.
@PeterTamaroff Yeah, it's equal to $\sum_{k=0}^n \frac{(-1)^k}{k+1} \left( {\bf H}^n \star \mu \right)_k$, and I don't see how to deal with the ${\bf H}^n$ easily.
@AntonioVargas No, no, you mean $(\mu \star j^n)_k$
What do you mean by ${\bf H}^n$?
17:13
@PeterTamaroff I mean $H$ juxtaposed $n$ times.
@AntonioVargas Ah, OK. But I don't see how that is true. I am getting $${B_n} = \sum\limits_{k = 0}^n {\frac{{{{\left( { - 1} \right)}^k}}}{{k + 1}}} {\left( {{\mu _j} \star {j^n}} \right)_k}$$
So ${\bf H}^2 = {\bf H H} = \{0^2,1^2,2^2,\ldots\}$
I think that should be the same thing
if you mean j to be the "variable" of the sequence
@AntonioVargas But ${\bf H}$ is the harmonic sequence =)
Note that $${\left( {{\mu _j} \star {H_j}} \right)_k} = {\mu _k}{H_k}$$ so the equation is $${B_n} = \sum\limits_{k = 0}^n {{{\left( {{\mu _j} \star {H_j}} \right)}_k}} {\left( {{\mu _j} \star {j^n}} \right)_k}$$
17:16
So I guess I should write ${\bf H}^{-n}$ then!
And yes, $j$ is the variable of the sequence, just a placeholder.
@AntonioVargas Woah, cowboy!
${\bf H}^{-1}={\bf B}$
haha I know
That is the importance of Bernoulli numbers.
17:28
Is there some magic way to get MathJax working here in chat? I'm guessing no....
@PeterTamaroff Is that how you are defining the Bernoulli numbers?
@ThomasAndrews Check out this link.
@ThomasAndrews Basically you can create a bookmark that will enable a mathjax renderer for the chatroom. robjohn made it. It's awesome.
@robjohn Yes.
@robjohn See here
17:51
Cool, thx.
@ThomasAndrews Hey, there.
@ThomasAndrews No, we have magical TeX rendering eyes =)
18:23
huhu
how are you?
thinking about the mergesort algorithm
19:02
hi @skull
Hi @Charlie how are you?
@skullpatrol so so, and you?
@Charlie Fine thanks.
@skullpatrol good
@skullpatrol anything to tell me?
@Charlie ...nothing all that interesting :)
19:11
@skullpatrol :-/
@peter hi pedro
@Charlie more like :-|
what is: 331.91 - 1.03 - 19.90 + 150.00 = ?
equal to ?\
460.98
but that's wrong if you do it in your head. following the order of operation
@skullpatrol more like :(
19:16
@Charlie I know, but remember what I said, try not to think too much about it...
@Charlie Yo.
I'm not good with numbers, sorry
@PeterTamaroff como está?
me neither I am just filling out an application. damn it!
how many nickles in a dollar
@NelDoozy An application for what?
@NelDoozy Try changing it to 331.91 + (-1.03) + (-19.90) + 150.00
@NelDoozy 20 nickles are in a dollar
19:19
barista.
@NelDoozy (Now this makes sense)
if a train leaves chicago at 12 noon, heading east at 60mph, when will the train arrive in oakland(the distance is about 2100)?
stupid fucking applications!
@NelDoozy Why don't you do that yourself? Is there a time limit? Do you know that distance = speed x time?
no, I suck at numbers
there is time limit
helppppppppppppppppp
skip the number questions :D
19:24
@NelDoozy East?
@NelDoozy use a calculator....
If you suck at numbers and the application requires you to have a baseline competency for numbers then...
2100/60 will give you the number of hours
That is 35 hours, there are 24 hours in a day, so 35-24=11. The train arrives 11pm the next day.
fuck it! thank you all anyways! bye~
19:30
@NelDoozy You could always point out that a train will end up in the ocean before it reaches oakland, california if it's heading east.
can't trains turn?
That would throw off the whole question. You then can't just divide distance by speed.
(the distance is about 2100)?
it doesn't say a "straight" line distance
It is starting off going toward the atlantic ocean rather than the pacific.
True.
3 mins ago, by skullpatrol
can't trains turn?
19:36
There is no way of knowing how long it will go before it doubles back and heads in the right direction.
That is where the "about" comes into it.
It could reach the atlantic then double back.
That pretty much doubles the distance.
2100 +-?
is "about"
Anyway, I think I finally see your point that we should assume distance means distance traveled.
They probably purposefully put that kind of thing on the application to widdle out people like me who have no common sense.
distance travelled = rate * time travelled
20:07
@user1 “Common sense is merely the deposit of prejudice laid down in the human mind before the age of 18”
20:24
Hi @amWhy how are you?
@skullpatrol I'm okay. Another couple of weeks of daily visits to the hospital/clinic. (Weekends off, yay!!)
My reputation is going to plateau for awhile, meThinks!
@amWhy Plateaus are good places to rest and look at the view.
@skullpatrol Yes, that's a great "positive take" on it! ;-)
@amWhy Put yourself into the right frame of mind.
@skullpatrol Hehehe...Nice video!
20:31
:D
@amWhy did you see robjohn's concise answer to my question in chat?
@skullpatrol What question? Where in chat?
7 hours ago, by skullpatrol
A variable $x$ is said to have a domain;
yet the notation $x \in$ real numbers flips the possession.
Do you know why? @robjohn
6 hours ago, by robjohn
@skullpatrol the nomenclature "$x$ has a domain" does not really say anything in itself. Nothing belongs to $x$. It really means that whatever function $f$, sometimes called $f(x)$, has a domain and that domain restricts that $x\in\mathbb{R}$. It is very contextual.
@amWhy
Good answer!
Indeed.
One should not be too rigid in thinking of where some $x$ lies. That seems to be the mistake the asker made here.
20:44
:O 43 views and only 1 upvote?
Have you guys seen this: youtube.com/watch?v=czVkT-JrXd0 so beautifurr!!!
@user2357 Thanks for sharing :D
21:21
@robjohn I convinced the Homotopy Theory chat room owner to embed your mathjax link into the room description so it doesn't have to be continuously re-pinned.
@skullpatrol I thought we tried that here and it didn't work.
@robjohn It cannot be formatted.
@skullpatrol So it appears as an http address?
@robjohn Yes.
Homotopy Theory

A room for anyone interested in homotopy theory, or any nearby fields (e.g. category theory, algebraic geometry). To activate chatjax in this room go to math.ucla.edu/~robjohn/math/mathjax.html
@skullpatrol I would prefer they link through the meta post. That way I can move that page if need be. Besides, stackexchange.com links are just better.
21:28
@robjohn OK, I'll let him know next time.
22:55
Sup ?
23:49
This one was pretty cool
$$ \int_0^\infty \frac{\mathrm{d}x}{a^2 + \left( x - \frac{1}{x}\right)^2} = \frac{\pi}{2a} \qquad \forall \: a \geq 2$$

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