Mathematics - 2013-03-27 (page 2 of 4)

Dominic Michaelis

08:04

someone said that i am wrong, cause wolfram says the function doesn'T have a pole

@jasper hi

user19161

@DominicMichaelis Huhu!

Dominic Michaelis

i still find this funny

Dominic Michaelis

08:40

How you prove that the sum of 1, when sin(n) > 0 and -1 else is bounded here

awllower

08:59

periodicity of sin?

BTW, I cannot understand why here wolfram fiinds no poles at all.

while here it claims to have a pole...

Dominic Michaelis

i don't unterstand that too

awllower

:D

Dominic Michaelis

i guess it is to easy for wolfram

awllower

@JayeshBadwaik I am studying variational analysis from Enrico Giusti book, if this was what you asked?

@JayeshBadwaik I mean this one.

Dominic Michaelis

@awllower as i usually only use mathematica I never ask wolfram for poles, just mathematica for hte residues

awllower

09:03

Oh
I know nothing about mathematical softwares except matlab...

@JayeshBadwaik And PDEs I learn a little from Evans.

Dominic Michaelis

bro matlab is no mathematical software

matlab is crap

Jayesh Badwaik

@awllower yes, Van Lint is another book. Someone from chat was using it, I forgot who and thought it might be you, hence my question.

awllower

Really!

@JayeshBadwaik I see.

Dominic Michaelis

in matlab taking derivates of polynomes is not linear

awllower

@DominicMichaelis @DominicMichaelis Might I ask why you said so?

You mean: it uses approximations?

Dominic Michaelis

09:06

i think all the syntax is just an error and those autoscaling of matrices and that you can't enter a single scalar

awllower

oh

Dominic Michaelis

try: 1-uint8(2)

awllower

Sadly I must have taken that course in my university...

@DominicMichaelis I do not understand: is it some kind of algebraic groups??

:)

Dominic Michaelis

uint8 is an 8 bit integer without a sign

awllower

I see.

Dominic Michaelis

09:08

and matlab autoconverts to the lowest format

so 1 -2 = 0 here

awllower

Indeed: I encountered that problem before as well.

Dominic Michaelis

or [1 -2] = (1,-2) but [1 - 2]= [-1]

awllower

I once laughed out loud at that . :D

Dominic Michaelis

good luck finding an error if a library makes it ;)

awllower

:)

Dominic Michaelis

09:12

or try [pi e int8(3)]

awllower

Alright: depart time again!
Bye!

Dominic Michaelis

bye

awllower

@DominicMichaelis I shall try later. :D

Jayesh Badwaik

@DominicMichaelis matlab is good for engineering. it has a niche there, similarly as the R language is good for statisticians

Dominic Michaelis

maybe but i am not an engineer

real men need real numbers, not machine numbers g

Jayesh Badwaik

09:15

@DominicMichaelis bleh..... :P don't get into real men and stuff. ;-)

Dominic Michaelis

just a joke ^^

Jayesh Badwaik

Yeah....

Dominic Michaelis

i prefer my numbers to be variable ^^

Jayesh Badwaik

Hmmm, there is sym keyword in matlab which goes to help somewhat, but matlab is not for mathematicians, that is true...

Dominic Michaelis

by the way what does NM means here

Jayesh Badwaik

09:23

no idea

Michael Corleone

@DominicMichaelis never mind

He apparently had made comment suggesting something earlier but it didn't apply

so he deleted the comment and said never mind

user68578

10:40

Don't you worry, don't you worry now!

CBenni

10:59

Dantzig’s Two-Phase Method for MINLP
1. Convince the user that he or she does not wish to solve a
mixed integer nonlinear programming problem at all!

good to see mathematicians have some humor

Dominic Michaelis

11:10

@CBenni after reading Mixed integer nonlinear programming problem

i absolutly sense no feel of solving something like that

CBenni

I dont either, tbh.

But I am searching for an easy solution...

too bad I wont be able to find one.

Dominic Michaelis

procrastination ?

CBenni

@DominicMichaelis How is that procrastination? Its just that MINLP is NP-hard. So basically, there is no easy solution to it

I might just use the NLP+roundoff approach

Dominic Michaelis

procrastination is doing it tomorrow

CBenni

when trying in mathematica, that gave decent results

Dominic Michaelis

11:14

i think that should work :D

CBenni

however I have had results of like 1.4 for variables

rounding there is... welll. nonoptimal

might then try both values and pick the one that is better

awllower

11:48

This edit has been wrongly reviewed by me. Maybe someone else could repair my error? Thanks...

eXtremiity

Hey guys, I hope i'm not breaking any rules here, but:
An abelian group of order 4 is either isomorphic to...

what is the logic behind coming up with an answer

can anyone run me through it?

awllower

Do you know the Lagrange theorem?

eXtremiity

sure do !

awllower

Then every non-identity element of the group is either $2$ or $4$.

eXtremiity

sorry what is $2$ ?

awllower

12:00

2

Just ignore $.

eXtremiity

Oh, I see the habit you're in :P.

but yes.

awllower

And every subgroup of an abelian group is normal, right?

eXtremiity

is that a theorem?

have not seen that

Commute -> Normal.

OBVIOUSLY.

awllower

Do you know what is a normal subgroup?

eXtremiity

apologies.

awllower

12:01

OKOK

caveman

hello

awllower

Then, if there is an element of the group of order =4, then surely that element is a generator of the group, and the group is cyclic, right?

@caveman Hi!

eXtremiity

right.

awllower

So suppose that every non-identity element is of order 2.

eXtremiity

Yep, I'm with you.

awllower

12:04

And show that, for two distinct elements x, y, the group is isomorphic with the direct product of <x> and <y>.

<x> is the subgroup generated by x.

eXtremiity

hmm alright.

awllower

Maybe this is too formal, lack of intuitions?

eXtremiity

I shall give that a go. Thank you for your help. Muchly appreciated

awllower

np :D

@caveman How do you do today?

caveman

feel bad

awllower

12:07

What for?

caveman

maybe since I just woke up

awllower

I see.
:D

caveman

are you recovering well

awllower

Oh yeah!
One can barely find any remaining charcater of the wounds!

caveman

that's wonderful

awllower

12:09

ja :D

I can even play basketball again!

although I am a bad player, haha

κρανίοπεριπολία

Wow, you are a fast healer.

awllower

It seems so. :)

maybe I am some monster---group? haha

eXtremiity

Sorry to seem very rude (I have an exam tomorrow), but what is Z/3Z , where Z is the set of integers.

Is it related to cosets?

Z not 3Z

awllower

Of course it is related to cosets!

3Z is a subgroup of Z
And Z/3Z is the set of cosets of 3Z in Z.

eXtremiity

Excellenteeee' !

awllower

12:20

:-)

Thanks then.

eXtremiity

no, thank you ^_^

awllower

:)

caveman

12:33

I got a lot of attention form y diophantine question

here math.stackexchange.com/questions/337053/…

but no theoretical insight

awllower

What do you mean by theoretical insight?

caveman

it's just strong computer power applied to the question

awllower

I see.

But the answer by Yimin provides some insights at least?

eXtremiity

You guys are amazing. Eat and breath mathematics.

awllower

Albeit in the nature of comments...

We are no more than cavemen! :D

eXtremiity

12:39

:p

caveman

ok his answer is very interesting

awllower

But apart from that there is nearly nothing, all numerical... At least in my view, as I know nothing about numeric anamysis...

Tobias Kildetoft

@caveman As soon as I saw it it reminded me of part of the content of one of the answers (the part about it being congruent to something divides by $e$ rounded down mod $p$)

since showing that was a problem of the day on the EFNet IRC channel some years ago

caveman

the e trick is very interesting

Tobias Kildetoft

an unusually slow day on Arxiv

awllower

12:45

@caveman Hey look you are here!

Tobias Kildetoft

only 2 in group theory and 5 in representation theory

caveman

nice

awllower

haha

user67848

@awllower Think I got a badge for going to that link. Thanks. :)

awllower

haha
:D

NP

Tobias Kildetoft

12:51

yeah, there is a badge for reading the entire thing (or at least scrolling to the bottom of the page)

awllower

I think that the photo of caveman is the symbol of this site. :P

A bunch of cavemen is crowding around a fire.

caveman

lol

awllower

:)

user19161

@eXtremiity Breathe is the verb and breath is the noun.

awllower

Hm...
I think I am tired enough, so i shall take a rest.
Later then!

caveman

13:02

good night

eXtremiity

13:15

Haha! Thanks @jasper

man !! i hope I do well in my abstract algebra test tomorrow

pretty excited.

eXtremiity

13:48

Oh cool. My name is Gustavo too.

Gustavo Bandeira

@eXtremiity =)

amazon.com/Naive-Theory-Undergraduate-Texts-Mathematics/dp/…

It seems nice.

caveman

> if all time ever wasted on Failbook would have been invested in fusion research, the first commercial reactors would be under construction by now.

Gustavo Bandeira

@caveman Yes.

It's ' nice quote. Sad but true.

anon

@GustavoBandeira the book is basically one giant table of properties of specific matrix lie groups with derivations

Tobias Kildetoft

that sounds really dull

Gustavo Bandeira

13:59

@anon Is this good or bad?

anon

your mileage may vary

caveman

i cant brain today what should i do isntead

user19161

@GustavoBandeira This is too advanced for you, wait a few more years.

user19161

In fact, there is no need for any Lie thing in undergrad...

user19161

Today I got 100 points for doing a factorisation.

user19161

14:14

Also, today I did my 400th post.

caveman

14:54

UGH math.stackexchange.com/questions/342798/…

anon

15:07

frankly I find your answer close to useless (it's ad hoc and not amenable to obvious generalization, whereas a sleek cyclical solution is a standard textbook answer here), and the displayed method of handling obsolete comments ("remove it," "leave me alone") inappropriate and whiny.

2

caveman

see math.stackexchange.com/questions/342798/…

Charlie

15:27

Hellooooooo

@κρανίοπεριπολία hi skull!!!

Jayesh Badwaik

hilo...

Charlie

No one else will say hello?

Arkamis

@Charlie I just got here!

Charlie

Hi Ed

Arkamis

so, Hello!

Jayesh Badwaik

15:34

hilo...

Charlie

@JayeshBadwaik halo

Jayesh Badwaik

@Charlie hilo....

Charlie

@JayeshBadwaik wtf?

user1932595

someone can help me with technical issue?

Charlie

Ask

Jayesh Badwaik

15:48

away....

Jorge Fernández

Hi guys

user1932595

I alresy asked it as a questions, but I will write it also here:

Charlie

@JorgeFernández ¡Hola!

user1932595

I try to post question but I always get the message: This post does not meet our quality standards.

For example: I try to understand why by definition

[c0,c1,...cn]=[c0,[c1,...cn]] and also
[c0,c1,...cn]=[c0,c1,...c(n−2),[c(n−1),cn]] .

But not [c0,c1,...cn]=[c0,c1,[c2,...cn]] for example.

or this:

P is a prime such that q=p+2 is also a prime.
I need to prove that there is an integer a such that p|a2−q if and only if there is b such that q|b2−p.

Jayesh Badwaik

@user1932595 do not write twice, just link....

user1932595

15:50

good idea :)

0

Q: This post does not meet our quality standards.

I try to post question but I always get the message: This post does not meet our quality standards. For example: I try to understand why by definition $[c0,c1,...cn]=[c0,[c1,...cn]]$ and also $[c0,c1,...cn]=[c0,c1,...c(n-2),[c(n-1),cn]]$ . But not $[c0,c1,...cn]=[c0,c1,[c2,...cn]]$ for e...

support

Jorge Fernández

@user1932595 try to add the tags, good title and then just fill it up with random words which you can delete after the question is posted

it needs you to have a certain number of words and stuff

Jayesh Badwaik

In the first question, you have not described what do the brackets mean. Explain the question in more detail. Also show your work and similar things,

Tobias Kildetoft

@user1932595 well, the first example really is a bad question

and the second one may simply have been because of the short length, but that does suggest you should add some thoughts

user67848

Hm.. I wonder if one can approach this question by constructing a cycle decomposition like one would for a bijection.

Jayesh Badwaik

@JorgeFernández that's some really bad advice. The quality control software is not yet so bad that we should advice people to ignore its restrictions. So, rather, we should try to improve the question rather than to bypass the system.

Tobias Kildetoft

15:56

@user67848 I doubt that would work, as the assumption from the start is injective and bijective is what you want to show

user67848

@TobiasKildetoft But it really is a bijection, so we pick an element in the codomain and show that it comes up again after repeated application of $f$ (of course, through other means than just assuming it is a bijection).

Tobias Kildetoft

@user67848 but what would that tell us?

user67848

@TobiasKildetoft That it is surjective!

Tobias Kildetoft

ahh, right

user67848

I think it really just obfuscates the normal induction argument though.

Tobias Kildetoft

15:59

probably

Jorge Fernández

16:14

@JayeshBadwaik Sometimes the question can be posed concisely and adding more things just makes it worse.

Henning Makholm

I think Caveman left in anger ...

Dominic Michaelis

16:49

hi

anon

16:59

@HenningMakholm yes, that's unfortunate

Jorge Fernández

@DominicMichaelis hi

Guys, how can I learn math without becoming mentally instable?

Also: does anyone know when debian 7 will be out?

Arkamis

Easy -- you learn math. Mental health is unrelated to your ability to do math.

Jorge Fernández

@arkamis Not if you are born being good at it, but studying a lot of time does.

Arkamis

I still fail to see how an innate proclivity to learn has anything to do with mental health. As far as is known, the two are uncorrelated.

If you are going to become mentally unstable, it is going to happen regardless of whether you learn math, ballet, the piano, or chinese.

Henning Makholm

@JorgeFernández You'll need to be a lot more specific about what problems you have if you want to have any chance of a relevant answer here.

Jorge Fernández

17:07

Have you ever found that your mind becomes stuffed and you can't concentrate after some time of studying?

Arkamis

Yes, that's called "fatigue", and the same effect happens after a long period of video gaming, reading, cleaning, repairing your house, or playing a sport.

It also happens because active thought actually does use energy, and people tend to neglect nutrition and/or adversely modify their diet during prolonged study sessions.

Jorge Fernández

oh

Arkamis

Because of the structure of our working schedule, prolonged study sessions tend to go late into the night, which means that the fatigue is also an effect of natural circadian rhythms.

Jorge Fernández

what is a circadian rythm

Arkamis

Your wake/sleep cycle

"circadian" coming from "circa" or "around" and "dia" from day. So literally, the rhythm of the cycle of a day

If you want to be effective at studying, do it in between normal meals, during normal waking/working hours, and take breaks frequently.

Drink plenty of water, and avoid high-sugar foods.

Jorge Fernández

17:12

why avoid high sugar?

Arkamis

They're basically terrible for you, and affect your ability to concentrate

fruits are good, candy is bad. I actually like to have beef jerky when I study. High protein, a little salt, something that you can munch on slowly.

Tobias Kildetoft

@Arkamis how is the fruit sugar better for concentration than regular sugar?

Arkamis

fitday.com/fitness-articles/nutrition/carbs/…

Tobias Kildetoft

@Arkamis but regular sugar is a disaccharid, not a polysaccharid

just like fruit sugar

ohh, woops, I recalled wrong

Dominic Michaelis

which theorem does she mean here ?

Tobias Kildetoft

17:17

fruit sugar is mono

Henning Makholm

@TobiasKildetoft The sugar is probably more or less the same (though fruit generally contains fructose whereas refined sugar is almost 100% sucrose), but fruit also has a fibre content which you won't find in candy.

Arkamis

@TobiasKildetoft I mean more generally like HFCS-based foods.

Tobias Kildetoft

right, but the entire argument about sugar being bad for concentration was what I was objecting to

Arkamis

fi.edu/learn/brain/carbs.html

I should have been more specific when I said "high-sugar"

Jorge Fernández

what about music?

Arkamis

17:20

There are various studies. I personally prefer music that I enjoy but that is quieter and slower-tempo

I don't want to get so caught up in the music that I start listening to the song.

Henning Makholm

@JorgeFernández What about that? Some people concentrate better with some background music; others like silence. Do whatever works for you.

Jorge Fernández

what about narcotics?

Charlie

Hmm

Arkamis

Generally narcotics are a bad choice, not only for learning math, but also life in general.

Henning Makholm

@JorgeFernández Definitely yes, if you're Erdös. Otherwise stay away.

Jorge Fernández

17:22

caffeine

Charlie

Caffeine? I think you mean cocaine

Henning Makholm

@JorgeFernández Okay, the answer to your next 10 questions is going to be "find out whether it works best for you with or without, and then do that".

2

Arkamis

But don't do drugs. Drugs are bad, mmkay?

Jorge Fernández

mmkay

Charlie

Yes

Don't do drugs,.that's today's lesson

Cтарый Джон

17:24

Hi folks

Jorge Fernández

hi

Arkamis

When I mentored students, they would often ask how to cram for an exam. I used to tell them to sleep. You have weeks to learn the material; the chances of you truly absorbing and retaining advanced math while sleep-deprived, some three hours before a test, are minimal, and often to the detriment of the things you already know.

I used to read for pleasure the day of my exams. Nothing I was gonna learn then that I didn't learn in the preceding weeks.

Dominic Michaelis

@CameronBuie you just made the same proof as I did, with your edit

Arkamis

@CтарыйДжон Evening!

Jorge Fernández

Does anyone here know about Prüfer code?

Arkamis

17:32

Can't say I do

Jorge Fernández

has anyone read a course in combinatorics van lint and wilson=

?

Dominic Michaelis

17:55

nope sry

it is much easier to get reputation when you already have a lot of reputation lol....

Jorge Fernández

why?

Arkamis

credibility

Dominic Michaelis

if 2 users give the same question usually the one with higher repuation get's a lot of more upvotes

Jorge Fernández

yes

Dominic Michaelis

18:40

capped :)

κρανίοπεριπολία

congrats :)

Dominic Michaelis

thanks

κρανίοπεριπολία

yw

Karl's students

@robjohn: Excuse me. Is there an option for Moderator to implicitly assign wiki to one's answer such that he/she will not get reputation? "Implicitly" mean the wiki label does not appear visually. I wonder some of my answers get upvoted but my reputation does not increase while my rep has not exceed the daily limit of 200 upvotes.

I am talking for tex.sx site.

It should be the same moderation panel i think.

κρανίοπεριπολία

CW

Karl's students

18:49

Just for a reference, please kindly look at this: tex.stackexchange.com/users/19356/karls-students?tab=reputation and see "How to plot functions like ‎‎‎‎‎x=f(y)‎‎ using TikZ?" does not contribute any reputation to me while it is not wiki answer. :-)

Dominic Michaelis

ask in meta ?

κρανίοπεριπολία

Look up "Community Wiki" or CW.

Karl's students

@DominicMichaelis NO. I am talking about the main site rather than the meta site.

My answers in question are not in wiki type.

Jayesh Badwaik

@Karl'sstudents he is saying, ask the question about "not getting rep" in meta.

Karl's students

@JayeshBadwaik Maybe. :D

Henning Makholm

18:59

@Karl'sstudents The 200-points-a-day limit applies before what you spend on bounties is deducted.

Karl's students

@HenningMakholm Wait... I am checking the time stamp first.

Jayesh Badwaik

@Karl'sstudents OT: Why should I use pdflatex \input{filename} instead of pdflatex filename?

Karl's students

@JayeshBadwaik OT?

@HenningMakholm You might be correct! THanks!

robjohn

@Karl'sstudents nope, the only way you wouldn't get votes should be if you've capped or the answer is marked CW

Jayesh Badwaik

@Karl'sstudents Off Topic.

Karl's students

19:05

@JayeshBadwaik It has been asked by someone in the main site. I will give you the link shortly.

κρανίοπεριπολία

>8(

Karl's students

18

A: Rationale to use \input{filename} on the pdflatex command line?

Advantages It is a good trick, if someone wants to put TeX code before. Examples: pdflatex '\def\foo{bar}\input{filename}' pdflatex '\includeonly{introduction}\input{filename}' or inside \write18 (shell escape feature): \immediate\write18{\detokenize{pdflatex '\def\foo{bar}\input{filename}'...

@JayeshBadwaik My answer is tex.stackexchange.com/questions/97135/…

Henning Makholm

@Karl'sstudents The comment above yours, "Chatting requires 20 pts", confused me, because I'm seeing chat with a way smaller font than that :-)

5

Jayesh Badwaik

@HenningMakholm Hahaha

Dominic Michaelis

lol :D

κρανίοπεριπολία

19:12

:)

Henning Makholm

Has anyone noticed the vote counts next to the "related questions" column in a question page before?

κρανίοπεριπολία

yes

Hi @JasperLoy

Karl's students

@HenningMakholm When did this feature start appearing?

user19161

@κρανίοπεριπολία Hey hey.

user19161

Is caveman gone?

user19161

19:20

OMG, caveman is gone!

κρανίοπεριπολία

In anger...

user19161

I really got pissed with caveman too for calling people rude again and again and again.

κρανίοπεριπολία

Look at that caveman go...

user19161

Nobody is being rude to caveman, but he keeps calling people rude, which is a kind of insult to me.

user19161

@κρανίοπεριπολία I might be gone soon too...

κρανίοπεριπολία

19:24

...we all have to go sometime.

Life is a journey with death as the destination.

Dominic Michaelis

NONONONONONONO i can't watch it on youtube

@jasper huhu

user19161

@κρανίοπεριπολία And in my belief, there is rebirth.

user19161

@DominicMichaelis Huhu.

Dominic Michaelis

i reached the 8 k

12 k to go

Karl's students

Someone stole my egg in the refrigerator. :D

Henning Makholm

19:28

@Karl'sstudents A few hours ago, I think.

Karl's students

@HenningMakholm Thanks. So a few users realize it.

κρανίοπεριπολία

cool feature

user19161

Hey @henning nice to see your beard!

user19161

Hey @alex finished thinking about your proof to my question?

Jorge Fernández

what question?

user19161

19:31

@JorgeFernández He knows. Look for my most lowly voted question...

Alex Becker

@JasperLoy Oh that one? I don't think there's a way to rescue it that hasn't been covered by the other answers.

@JasperLoy I should probably just delete it.

user19161

@AlexBecker Yes, I think so too! Anyway, I look up to you as an extremely smart undergrad!

user19161

Hey @jayesh actually I still think your answer to my question is wrong. If you feel so too you can delete it...

Alex Becker

@JasperLoy It's done. Thanks for your kind words blushes.

user19161

Hey @jorge you asked when Debian 7 will be out? I am waiting too, maybe this weekend, maybe another month.

Jorge Fernández

19:34

thats cool, so it isn't long then?

user19161

Hey @jayesh sorry but I have removed the upvote on your post.

Henning Makholm

@JasperLoy Back to blue, I see.

user19161

@HenningMakholm Yes, and trying not to change my username so often, lol.

Henning Makholm

@JasperLoy I never know if it's you when I see someone with a plain monochromatic square beside them.

user19161

@AlexBecker Just don't forget me when you win the Fields medal!

user19161

19:38

@HenningMakholm Haha, just look out for the few stupid questions I have asked!

Alex Becker

@JasperLoy Out of curiosity, are you a university student?

user19161

@AlexBecker No, I finished my undergrad long ago. I will be turning 32 later this year. I hope to apply to grad school some time in the future. Maybe I will try to enter when I turn 35 and finish my PhD at 40...

Alex Becker

@JasperLoy because they're round numbers?

κρανίοπεριπολία

ha ha ha @(removed)

user19161

@AlexBecker Well, because some life events cause me to make plans this way, and that is one possibility which I have been thinking about for a while...

Henning Makholm

19:41

@Karl'sstudents There were a few minutes of downtime right around the time I posted this comment. I assume that was it.

Karl's students

@HenningMakholm Nice "debugging" skill.

user19161

7

Q: Existence of $\vee$ or $\wedge$ for non-monotonic functions

This question is inspired by a discussion in chat with wj32. We allow for equality in the definition of increasing and decreasing and call a function monotonic if it is increasing or decreasing. If $f:R\to R$ is not monotonic, are there three points $x<y<z$ such that $f(y)<f(x),f(z)$ or...

functions

user19161

By the way guys, I really feel like advertising this question of mine again, which is what is being talked about above...

user19161

It is something which seems straightforward at first, but the only proofs so far seemed rather nontrivial...

Dominic Michaelis

@robjohn i closevote cause of his comment

and there have been an answer to that time

user19161

19:55

@AlexBecker I actually hope to apply to Chicago, but I think they will never accept me...

robjohn

@DominicMichaelis yes, but now others who might want to answer cannot. This sounds more like a personal disagreement. At least 4 others agree with you, so I am only commenting.

Dominic Michaelis

thats always the way when a question is voted and i read it several times

user19161

In other news, I have decided to use mathbb for my reals etc from now...

Dominic Michaelis

good dicision i do it too

user19161

Also, I think I will take a break from answering and try to edit my existing posts into better shape instead.

robjohn

19:58

@JasperLoy I have never used anything else. I don't even know the alternatives :-)

user19161

After I have edited them to my satisfaction, I may consider deleting my account.

robjohn

@JasperLoy again?

Henning Makholm

Are we talking about this?

user19161

So Chicago you heard it, I am coming for you...

Transcript for

$Mathematics$ Mathematics