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4:04 PM
Do you have an example where it doesn't work with coprime degrees?
 
@MikeMiller math.stackexchange.com/questions/691652/… Look at that answer. How can we assume that $g(x+\Delta x)-g(x)$ is always nonzero around $x$ ?
 
That's the nonconstant around $x$ assumption @Hippa
 
@MikeMiller I don't. Do you know whether we always have equality with coprime degrees?
 
@MikeMiller It could be nonconstant, but be $0$ (at least once) in any neighborhood of $x$
 
I don't, @DanielF, but probably we do.
 
4:16 PM
@MikeMiller Like $\displaystyle f(x)=\exp\left(-\frac{1}{x^2}\right)\sin\left(\frac{1}{x}\right)$
 
@Hippa Yes, that's fine. He only needs it to be defined on a sequence of $\Delta x$ converging to $0$.
 
@MikeMiller Oh, so we say that's not a problem by choosing a "good" $\Delta x$, right ?
 
Yes.
 
Thanks
 
I didn't read carefully - by this point, we know that the function is actually differentiable, right?
Because what I said doesn't suffice if we don't
 
4:18 PM
Yeah we do
 
I prefer the denominator-free version, @Hippa, that frees you of such concerns.
 
@DanielFischer Well is the proof "nice" denominator-free ? See math.stackexchange.com/questions/1073612/…
 
OK, then yes, we're fine.
 
@MikeMiller I just realized that if I had a phone I could be 5th or so in hats :O
 
nope - you don't have a hat they're not giving out anymore.
hehe
 
4:21 PM
Awww
 
(it's the one I'm wearing :) )
 
@MikeMiller What was it for ?
 
@Hippalectryon What is the "real" proof you know?
 
@DanielFischer Well I don't recall it well, but I supposed it's the "usual" one taught
 
@r9m don't post it (the double integral) on your blog. I'm going to send it to a mathematical magazine.
 
4:23 PM
@Hippalectryon With or without denominators?
 
@DanielFischer Without $g(x)-g(a)$ on the denominator
 
Hmmm.
 
Anonymous
@Chris'ssis What have you discovered recently?
 
@Ashwin I solved the famous Basel problem in a new different way, then I developed some of the Ramanujan's results and also developed some very nice multiple integrals.
 
Anonymous
@Chris'ssis I am sure you will do great.Keep up the hard work.
 
4:29 PM
@Hippalectryon For guessing what one of the secret hats is given for. They're given to the first 7 people to guess one, IIRC.
 
@Ashwin Thank you for encouragement. Yeah, the very hard work is one of the success keys.
 
@MikeMiller How do you "guess" that ? (I mean, hwo do they know you have guessed ?)
Because if I had known I would have got it immediatlly for the chameleon hat
 
@Hippalectryon I think they manually search chat.
 
Grrr....
The Cham hat was so easy
The warm welcome, too
That's a shame
 
Anonymous
@Chris'ssis Romanians and Hungarians don't quite get the English right :p
 
4:31 PM
@Ashwin Neither do you.
 
@Chris'ssis Will your papers be published in Jan or later ?
 
@Ashwin I think it's only me.
 
Anonymous
@JasperLoy LOL
 
@Hippalectryon I'll tell you when things are published. :-)
 
@Ashwin There should not be apostrophes there. It is not funny.
 
4:32 PM
@Chris'ssis :D
 
@Hippalectryon :D
 
Anonymous
@JasperLoy ?
 
Anonymous
@JasperLoy How you doing?
 
4:51 PM
Morning @robjohn.
 
@JasperLoy morning $e^{2\log(\text{blue})}$
 
Indeed, it is morning here, lol. It's almost 1 am.
@Chris'ssis I think your English is already very good. Good enough for all practical purposes.
 
@JasperLoy Well, well, it's just better when I don't have to write things at a very high speed. :-)
 
@Chris'ssis I don't think I can ever be that good at a second language.
 
@JasperLoy It's just a matter of practice I think.
@JasperLoy Today will you go jogging? I'm preparing to run for half an hour (or more?).
 
4:57 PM
@Chris'ssis Hmm, I think I will not go jogging this year. Maybe next year.
 
@JasperLoy The best moment for beginning good habits is today.
:D
 
@Chris'ssis Maybe I will go jogging after you tell me your name, lol.
 
@JasperLoy lol :-)
I'm out for some jogging.
 
Hello @TedShifrin.
 
hello mr @Jasper
hi @robjohn @RobertCardona
 
5:02 PM
@TedShifrin how goes?
 
Semester's over ... just doing miscellaneous grad school recs. About to spend the afternoon with an old student and one of his students. How're you?
 
@robjohn My enemy likes to say 'How goes it?'
 
Be specific, @Jasper. There are so many enemies. Oh wait, that's just me.
 
@JasperLoy Your enemy?
 
@robjohn Yes, my arch enemy on SE, lol.
@TedShifrin You would need to do much more to piss me off.
 
5:03 PM
No, I meant that I already have enemies (plural) :)
I gather that @Hippa got Balarka into some blend of algebra and geometry earlier today. I may have to relent :P
 
Good day @Ted.
 
@TedShifrin @BalarkaSen is very sad that you are ignoring him, despite my consoling him.
 
heya @DanielF ... enjoying your last hours of freedom? :D
@Jasper: If he were older, he wouldn't care :P Well, maybe @Pedro and @Mike would care.
 
@TedShifrin Freedom's just another word for nothing left to lose.
 
LOL ... I'm just teasing, @DanielF.
@Jasper: I would volunteer to give you some interesting problems in the new year, but I already know what you think about exercises/problems :P
 
5:06 PM
But if it gives me an opportunity to quote Janis, I can't waste it, can I?
 
It was lost on me, @DanielF. Sorry.
 
@TedShifrin Sheesh, Janis Joplin must not be forgotten.
 
Hi Professor @TedShifrin that's a very athletic looking hat you're wearing. I thought you were anti-football?
 
@KhallilBenyattou What the heck am I supposed to say to that? =_="
 
@TedShifrin I see. I will ask when I need to. I think I already have more than enough stuff to learn.
 
5:09 PM
@KhallilBenyattou No worries
 
@skullpatrol After Saturday I'm anti-football too
 
@MikeMiller I saw :(
 
Sorry, @skull. Of course, you're right.
 
It's called "handegg," @skull. Where did football helmet come from?
 
5:13 PM
Skull never said football helmet.
 
HE said "athletic-looking." I say it looks like a football helmet.
 
So "football helmet" came from you.
 
Right. I'm asking how "handegg" is pictured as football helmet.
 
Is there anyone here with an issue that has bothered you for years and you just can't get rid of it?
 
@Ted By the way, did you want to see a proof that $O(2)$ isn't linked?
 
5:16 PM
Later, @Mike. I'm about to be invaded by a former student and his student for the afternoon.
But I'm glad my intuition was right, @Mike. Yes, I definitely want to see.
 
Enjoy yourself.
I got grades back, BTW. 6% increase in avg score on the final between my Tues and Thurs sections.
 
I don't know what sorts of queries will be thrown my way by the student^2. He's interested in top grad schools coming out of a mediocre college.
 
127
A: What’s a “handegg”?

oerkelensCBS Sports has this nice article explaining the origin of the word, including a newspaper snippet from 1909: “Hand-Egg,” Not Football. To the Editor of The New York Times: Football is certainly a misnomer, for the game is played not with the feet but with the hands, and the ball i...

 
Hello!
 
5:17 PM
Isn't that what you expected, @Mike?
 
@ted Do you know of a book that proves the Nash embedding theorem? Or do we have to go to the original paper itself?
 
@Ted student^2's goal can certainly be done... and yes, some improvement from Thursday was expected, but that's still quite a wide variance. Actually on the midterms the difference was 1-2%.
 
One of the things I must remember to learn is how to solve a cubic and a quartic equation.
 
Why must you remember that?
 
Well, I think it's something so basic that every serious mathematician should know. Yet it's often not taught to the undergraduate.
 
5:30 PM
Well, you're free to think that if you'd like.
 
Yes, I have strange ideas, as everyone knows, lol.
Everyone knows how to solve a linear or quadratic. I don't see why we should not for the cubic and quartic as well, especially when it stops for the quintic.
 
See Pedro's reply with 9 stars @JasperLoy
 
@DonLarynx Yes.
 
I don't know of any book that proves Nash. My impression is that the theorem isn't really useful for much anything.
 
I read in the biography that Nash almost won the Fields medal.
@MikeMiller I know that Taylor's PDE III proves the compact case.
I used to think poorly of differential equations until I realised they are so needed for differential geometry.
 
5:39 PM
@JasperLoy Yes, for his embedding theorem, AFAIK.
 
I am going to take a nap.
 
later pal
 
5:58 PM
Back from jogging! I'm exhausted!
:PPPPP (my tongue is outttttttt)
 
@Chris'ssis Your tongues are out :P
 
@robjohn This is so hilarious
-1
A: differentiability of $\tan^{-1}(\frac{1}{|x|})$

Dr. Sonnhard Graubnerwe have $\lim_{h\to 0-}\frac{\arctan\left(\frac{1}{|h|}\right)}{h}=-\infty$ and $\lim_{h\to 0+}\frac{\arctan\left(\frac{1}{|h|}\right)}{h}=\infty$ The slope of the tangent line doesn't exist at the point $x=0$ Sonnhard.

 
@robjohn Custom flags are reviewed by moderators only right? And all other are reviewed by ordinary users, right?
@Venus Did you saw it in review queue?
@Venus There were 2 more answers like that or maybe even worse!
 
@Integrator Ya, It was so funny, I burst out laughing :D
 
6:06 PM
@Integrator :'-( have mercy
 
@AlexanderGruber Looks like I over did it! Did I?
 
@Venus hmm... that computation of the derivative is missing something.
 
@Integrator That is an insanely large number of bad answers. You're right.
but, we get the point, we're looking into it.
thanks for bringing it to our attention
 
@AlexanderGruber Down-voting is not an option for me and I'm not 10k yet, So, Flagging is all that remains!
@AlexanderGruber Thanks!
 
ooh
 
6:08 PM
@robjohn I didn't see his answer, but I did see the comments
 
who are we talking about
 
hello, take your calculator and set $h=10^6$ or $h=-10^6$ Which number do you get? — Dr. Sonnhard Graubner Sep 20 at 15:40
 
ah, the german doctor
 
@Integrator This one made me LOL
Please do not ban him from MSE. We need more jokers like him around here :D
2
 
@Venus it's fine we won't
 
6:10 PM
@Venus the derivative does not exist, but it is because it is $1$ on one side and $-1$ on the other.
 
@AlexanderGruber I'm so grateful to hear that from the mod :P
 
Does anyone know what employers think of Coursera? I ask because some of the jobs I have been looking at want familiarity with R. I know how to use Python, Matlab, Mathematica, and I have played around with C but know nothing of R. So I was thinking of taking their free courses on R.
 
@dustin Workplace.SE!
 
@robjohn The derivative does exist. Take your calculator! :D
 
Indeed, here's a relevant Workplace post.
 
6:12 PM
@Venus You missed Hello!
 
@Integrator HELLo :P
 
And you might also find this helpful, @dustin.
 
@MikeMiller thanks. I suppose it wont hurt since it is free.
 
@Venus Hi dear :P
 
I suspect they will care more about your ability with it than your learning experience (as the second thing says). But one doesn't gain ability with a language without learning it, and Coursera seems like a good place to learn.
 
6:14 PM
@Integrator You maybe don't believe me, but he had flirted with me.
 
My dramatic opinion is that Coursera is not very useful now but that it will eventually devour and replace the entire university system
 
@Venus Oh I know he said You have a nice name :P
@Venus Or something similar to that !
 
@Integrator Ya, something like that & the comments has been deleted
 
I want to show that $PO(1, n-1)$ acts transitively on $G^{n-1}$, where the latter is defined by $$-x_1^2 + x_2^2 + \cdots + x_n^2 = 1$$ Any ideas? It is clear that any vector in $G^{n-1}$ is space-like, but I am having trouble constructing the desired matrix.
 
@Venus :O
 
6:18 PM
@Venus really?
 
@AlexanderGruber what is your opinion of it on acquiring new knowledge for job prospects though?
 
@dustin anything you could do with coursera you could do by yourself to equal or greater efficacy
with that said, if you like it, go for it
 
Just note that they will probably appreciate more to view projects you have done yourself in R, rather than to know you learned it on the net.
 
@Venus Ah... I just looked at the answer. I see I already commented to him.
 
^_^
 
6:21 PM
@robjohn I was joking, you're too serious :D
 
@Venus Without reading the answer, I did not get the joke. Now that I've read it, I do.
 
@AlexanderGruber anything you could do with coursera you could do by yourself etc; there's no good reason to believe the same is true for everyone ese
 
@AlexanderGruber!
 
@Venus He is mean squared :D
 
@Integrator Nice pun :D
 
6:25 PM
@Integrator that's $e^{2\log(\text{mean})}$ to you... ;-)
 
@Venus standard pun
 
"with one standard deviation and several unusual ones"
 
haha yeah that one is even better than mean squared
 
@MikeMiller I just think the whole thing persists due to announcement bias. Coursera is a product that advertises itself as an effective way to learn things, but it didn't invent learning things, there are plenty of other ways of doing so and they all require doing the same basic thing: studying
but it's kind of like StackExchange, you gamify it in a certain way and it will be a good system for some people
 
6:27 PM
@BalarkaSen But you can get a girl only using standard pun ^^
 
i'd rather not
 
@robjohn No, It's $$2\int_0^{\text{mean}}x\,\mathrm dx$$
 
standard puns work on standard girls
 
@Venus ^^
 
@skullpatrol Please...
 
6:29 PM
Oct 23 '11 at 13:51, by t.b.
@robjohn: you're mean squared :p
 
I was here^
 
@AlexanderGruber I've never used it so I can't speak to its quality or any other aspect of it. I just think that education is a mysterious beast that works differently for different people, and would tend not to make judgements that it's no better than otherwise unguided study.
heh, I have Enthusiast on meta. Maybe one day I'll get fanatic.
 
You don't consider yourself one right now?
 
@MikeMiller Sure. I'm not claiming I'm right, it's just an opinion.
 
@Integrator that's the quote that inspired my avatar
 
6:33 PM
oh, fanatic is only 100 days, not a full year.
 
@MikeMiller 100 days straight?
 
@robjohn That's trivial!
 
yeah, @robjohn. Well, if I thought I might get fanatic when the requirement was higher...
 
hey @Studentmath
 
Heya @Balarka
Soon I can finally go back to some Algebra and Logics.. just need to finish multipicity spaces
 
6:41 PM
what's a multiplicity space?
 
@AlexanderGruber You got dangerously close to 20k again?
 
@DanielFischer it's a problem man they keep upvoting me
 
I bought a lottery ticket :o why do I have a feeling that I'm going to win :o
 
@Mike a bad translation of product space
 
lel
 
6:42 PM
@AlexanderGruber That might be related to the quality in this case.
 
you call a product space multiplicity space?
 
oh
I was excited to learn
 
@DanielFischer possibly.
 
We have the same word for product and multiply
@Mike I can make something up
 
Teach me something cool
 
6:45 PM
Oh. There is something close. arxiv.org/abs/1101.1700
 
@BalarkaSen that is making me laugh a lot.
 
What do you mean on TV?
 
click the link to find out!
 
@MikeMiller lel
 
6:48 PM
@MikeMiller That is incredible Mike
 
"and that other TV stations in other countries will catch on to the fact that low dimensional topology makes good television"
 
hahaha
oh i'm dying
there's even a nunchaku clip at the bottom!
 
Wow, I mean. Wow.
 
@MikeMiller So how do I get on Japanese TV?
 
6:52 PM
Read that Designer statement there.
@Mike how do you know so much about Japanese TV?
 
this is just following links from the first blog, which I read
 
speaking of japanese
have anyone of you ever looked at the site page of mochizuki?
 
the fashion itself is quite nice, even though admittedly I don't see how it relates to geometrization
perhaps it's too far above my level
 
haha
 
6:56 PM
Miyake is great
"but we didn't care. and he didn't care. :)"
 
Oh god damn it
Who messed up the icons on the map
there, whew, thank god it didn't forget the old labels.
 
I see I've been deleted
 
great. somebody's always got to come in and mess things up
 
i don't see a mess
 
@BalarkaSen i was able to fix a lot of it
does anybody know how to see the history of the map?
(if it is even maintained?)
 
7:04 PM
I see I'm undeleted
 
@Venus i had to wait for 2 days before giving the bounty, now i can
 
was somebody thrown in at greenland or north pole, @AlexanderGruber?
:P
 
@BalarkaSen No, everyone's icon was changed to a different style, and some of them were missing.
 
ah
that's not really a lot of mess
 
7:21 PM
man, sucking at probability really sucks
 
@Don some specific question you struggle with?
 
projecteuler.net/problem=494 I'm stuck on finding out the unique number of families of sequence prefix of length m. I know for sure if I was better at combinatorics I'd own this one. However I am stuck with doing it the long, hard way, lol
All I know is that two odd numbers cannot be in succession
and the last two numbers follow the sequence {$\dots, even, odd$}
 
i do not really see how this relates to probability.
 
not probability, combinatorics
but I also suck at probability :)
 
wonder what the fundamental group of $\Bbb R^3 - S^1$ is
 
7:31 PM
what do you mean by $S^1$?
 
i thought you were ignoring me @Mike
 
Guess the unit circle of $\Bbb R^2$?
 
I just haven't had anything to say
 
and by S^1 i mean a circle in R^3
oh wait i guess it's just Z
 
a circle? so you're asking what all the knot groups are.
 
7:32 PM
@MikeMiller eh.
well take R^3
 
Look
 
consider a copy of R^2 inside it
 
Like I tried writing down the different combinations of 0's and 1's of length 5 @Mike
 
then yes, it's $\Bbb Z$.
 
It should be 32
but I am getting 29
I did it twice
by hand
 
Huy
7:33 PM
You're clearly drunk again.
2
 
And cheers to that
 
No I'm sober
wow
 
And boo to that
 
I am asking for help
 
err
 
7:34 PM
I am unable ot provide it
 
oh yeah it deformation retracts to S^1 wedge S^2
 
Different binary words of length 5, @Don?
 
if you say so
 
Yes @Student
 
oh, yes, I guess I do agree
 
7:35 PM
$2^5$
5 spots each may be one of the two (0 or 1)
 
now, hmm, for a hopf link
 
I will try again.
 
heh
that was an old qual problem I had
 
which one, @Mike?
 
calculate the fundamental group and homology groups of the complement of the hopf link in $\Bbb R^3$
 
7:38 PM
ah
 
@Studentmath: How can I find out all the binary words with only two 1's?
of length 5
 
Precisely 2 ones?
 
and three zeros
 
It's the number of ways you can order 2 items in 5 slots (or 3 items in 5 slots, it's the same number of ways)
Since you have 5 slots, and the location of the 1's (or 0's) decides the location of the 0's (or 1's)
 
i guess that one deformation retracts onto S^2 wedge torus.
or not
it's probably just false though
 
7:44 PM
Thanks.
 
might be true
guess it is
in retrospect the actual problem was the complement in $S^3$
the missing point is where your sphere comes from
 
well you deformation retract the whole R^3 onto S^2
 
since when did project euler go back up?
 
and then you stick up something like a torus through the linked circles.
 
@robjohn did you try that double integral I showed? I'm thinking to send it to some math magazine together with my best solution.
 
7:47 PM
what you just said seems like nonsense to me, but apparently there's a method to you rmadness
 
everything i say is nonsense to you @Mike
:(
 
it's notoriously difficult to explain visual intuition via the written word
or spoken word, without pictures (and even then, pictures only go so far...)
 
@Venus so i've put a +150 bounty on my question
 
@MikeMiller i think i have an idea to compute $\pi_1(\Bbb R^3 - \mathcal{H})$
without going into complicated deformation retracts
 
Always define your symbols.
 
7:56 PM
H is the hopf link
 
You can do it with three applications of van Kampen's. Don't think you can do better than that.
There is a quite simple way to write down the desired deformation retract.
 
are you interested in listening to my method?
 
sure
 
ok. take R^3 and take the z-plane.
now draw two circles intersecting each other at two points.
 
in general you should write it down regardless of whether or not you think I'll listen; you gain by having your thoughts written down and made coherent
explain that last line
 
7:59 PM
well just project the hopf link on a flat plane
 
like oo where one of the o's is shifted slightly left?
 
yeah
 

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