Mathematics - 2012-12-09 (page 3 of 7)

Peter Tamaroff

02:04

@MarianoSuárez-Alvarez DOes this work?

Mariano Suárez-Alvarez

perfectly

Peter Tamaroff

@MarianoSuárez-Alvarez Superb. Enjoy your friends and your martini.

Mariano Suárez-Alvarez

:-)

people using math.se to cheat on contests and such things are ample justification for someone to develop a way to slap-people-over-the-internet...

Peter Tamaroff

@MarianoSuárez-Alvarez is that happening right now?

Mariano Suárez-Alvarez

it would be the first software patent I'd aggree with

no

we've had a non-negligible number of occurrences of that, though

Peter Tamaroff

02:10

@MarianoSuárez-Alvarez Yes. I've seen some. I get easily annoyed by those which start with "URGENT"

ALL CAPS

Ugh,

Mariano Suárez-Alvarez

yeah

Argon

@Charlie

Peter Tamaroff

@MarianoSuárez-Alvarez Do you have any recomendation about what I should move on to after Spivak?

Mariano Suárez-Alvarez

You could ppick an algebra book

Peter Tamaroff

@MarianoSuárez-Alvarez I am kinda nibbling off your colleague's linear algebra book

Mariano Suárez-Alvarez

02:12

Rotman's book on groups is nice

linear algebra is not algbera

Peter Tamaroff

@MarianoSuárez-Alvarez oh, you mean abstract algebra?

Mariano Suárez-Alvarez

linear algebra is plain math

Peter Tamaroff

@MarianoSuárez-Alvarez sorry

Mariano Suárez-Alvarez

:-)

Peter Tamaroff

@MarianoSuárez-Alvarez what do you mean with that?

Mariano Suárez-Alvarez

02:13

linear algebra is like punctuation

Peter Tamaroff

@MarianoSuárez-Alvarez everythingismessywithoutit?

Mariano Suárez-Alvarez

heh

it is in the background of everything

Peter Tamaroff

@MarianoSuárez-Alvarez OK. I will continue with that. Like you said, I have to get used to computation...

I bought two books by a guy named Shilov.

Mariano Suárez-Alvarez

you could also pick apostol's book on analysis

Peter Tamaroff

G. E. Shilov

@MarianoSuárez-Alvarez Principles? I'd love that too.

I don't personally like Rudin that much

Mariano Suárez-Alvarez

02:16

I forget the title; the one which is not calculus :-)

a great book to get started on algebra is Herstein's

its only problem is that he writes functions to the right

peoplepower

@MarianoSuárez-Alvarez Why is that a problem?

Mariano Suárez-Alvarez

well, no one does it anymore

Sanchez

Herstein's notations are terrible..

Mariano Suárez-Alvarez

heh

it is an oldish book

there is a reason why he does that, in particular

Sanchez

and it doesn't talk about group actions, which is weird

peoplepower

02:18

Isaacs does it in Algebra.

Mariano Suárez-Alvarez

people who did ring theory usually did that

because that way one minimizes the need to turn around rings

(that is, use opposite rings)

Peter Tamaroff

@MarianoSuárez-Alvarez you mean $xT$?

peoplepower

Yes, I remember Lam used both sides of a module.

Mariano Suárez-Alvarez

at some point, when Auslander ruled the universe, he decided to make everything a left module, and then the rightfunctionists withered

Sanchez

haha

BenjaLim

02:20

@MarianoSuárez-Alvarez The ring is $\Bbb{Z}[w]$ where $w = e^{2\pi i /m}$ for $m \geq 3$ which is certainly not contained in $\Bbb{R}$.

Mariano Suárez-Alvarez

I know, Ben :-)

BenjaLim

@MarianoSuárez-Alvarez so it's ok?

there is no problem then?

Mariano Suárez-Alvarez

I ws doubting your idea that one can pick in general a basis with half real elements and half complex :-)

BenjaLim

ah in general

but I have a specific basis here

Mariano Suárez-Alvarez

it is not obvious that the part of the basis which is in real will be a basis of the real part

Peter Tamaroff

02:21

@MarianoSuárez-Alvarez So much win

BenjaLim

@MarianoSuárez-Alvarez the basis is :

@MarianoSuárez-Alvarez $1,w, \theta,\theta w , \theta^2, \theta^2w,\ldots, \theta^{n-1}, \theta^{n-1}w$

@MarianoSuárez-Alvarez $\theta = w + w^{-1}$

@MarianoSuárez-Alvarez so there is the explicit basis.

Mariano Suárez-Alvarez

for that basis, it is true that the real elements form a basis of the real part of the ring

Peter Tamaroff

@BenjaLim DUde, you'll drive people mad with constant pinging!

Mariano Suárez-Alvarez

but it requires a proof

BenjaLim

@MarianoSuárez-Alvarez yewww

hmmmmm

@MarianoSuárez-Alvarez how come proof is required?

Mariano Suárez-Alvarez

02:24

proof is always required

BenjaLim

@MarianoSuárez-Alvarez but when you intersect with the reals you just throw away the complex guys no?

Mariano Suárez-Alvarez

but that does not apply to bases

it is quite false that if B is a basis of a vector space V and W is a subspace, $B \cap W$ is a basis of W

BenjaLim

yes.

Mariano Suárez-Alvarez

why would this work magically here?

BenjaLim

hmm

I'm thinking of maximal real subrings

Mariano Suárez-Alvarez

02:26

you may be trowing too much

if you start with a basis with the maximal number of real numbers, then I could believe you

but then you have to prove that your basis has the maximal number of real numbers :-)

BenjaLim

ah but it has to be

because an integral basis is also a basis for the number field

and we already know that $[\Bbb{Q}(w) : \Bbb{Q}(\theta) ] = 2$

Mariano Suárez-Alvarez

well, now you are about to have a proof

BenjaLim

@MarianoSuárez-Alvarez ah crap I have to go shit

will you be here a bit later?

crap fuck

Mariano Suárez-Alvarez

that idea will get you to a proof

BenjaLim

that guy is the maximal real subfield

bye!!!
thanks mariano mwah

Mariano Suárez-Alvarez

02:29

bye ;-)

Peter Tamaroff

@MarianoSuárez-Alvarez Rotman's text is lengthy

Mariano Suárez-Alvarez

sure

no one expects anyone to go throught the whole of it tho

3 chapters or so would be quite enough for a summer vacation :-)

Peter Tamaroff

@MarianoSuárez-Alvarez Oh, OK. Herstein's is like halve of Rotman's

Mariano Suárez-Alvarez

that is irrelevant

because, again, reading the whole of Rotman would be crazy

Peter Tamaroff

@MarianoSuárez-Alvarez yeah, heh

I'll try and organize some reading. I'll take a trip to mendoza in january though

some aire changing is nice now and then

good for the brainss

Mariano Suárez-Alvarez

02:37

if you say brainss you sound like a zombie

Peter Tamaroff

@MarianoSuárez-Alvarez I am a little too hooked up with the walking dead, yes...

though they just breathe annoyingly

Mariano Suárez-Alvarez

haha

with a longer a it sounds better

braaainss

Peter Tamaroff

@MarianoSuárez-Alvarez hahahah yes

do you like any particular sitcom?

Mariano Suárez-Alvarez

hm, not right now

I do watch TBBT

irregularly

Peter Tamaroff

curious... I'm catching up right now to the last season, now that I have good internet !

Charlie

02:43

@Argon Good night, Aaron! too late here..must sleep...

Peter Tamaroff

it is funny that making a similar show about mathematicians rather than physicists would be probably impossible

Argon

@Charlie Good night

Peter Tamaroff

(IMO)

Mariano Suárez-Alvarez

they'd kill each other in a couple of episodes

mathematicians always are serial killers

Peter Tamaroff

@MarianoSuárez-Alvarez you're frightening me... =O

user57925

02:54

I'm annoyed I can't prove the xyx = x thing is a group

Limitless

@Argon This is the first time I've seen a circular arrow in a question.

Mariano Suárez-Alvarez

that is just a(n ugly) picture for the directed graph with one vertex and one arrow

Argon

@Limitless That's awesome!

user57925

let X be a set with associative composition and forall x, exists a unique x' such that x x' x = x. Then I showed x'' = x and (xx')' = xx' and b'b(ab)' = (ab)' = (ab)'aa' but I can't show (ab)' = b'a'.

user57925

I can't show a a' = b b' either

amWhy

03:00

@Limitless Hello, Limitless! You pop in just about when I'm thinking of "popping out."

Limitless

@amWhy Hey there! I have been drifting.

amWhy

@Limitless Yeah...I came in a bit ago hoping to "vent" a bit ago...but it seemed the conversations were in progress...

Limitless

@amWhy You can vent to me any time on my email or, if you prefer, via private IMing. :-D

Don't be a stranger.

amWhy

@Limitless hehehe...Of course I won't be a stranger!

Limitless

@amWhy What's your username about?

amWhy

03:03

@Limitless A-M-WHY...spell it out ;-)

Peter Tamaroff

@amWhy Dudette.

amWhy

@PeterTamaroff Hey, dude!

Limitless

@amWhy "I am why"?

Peter Tamaroff

@Limitless AMY

@amWhy What are you doing?

Limitless

@PeterTamaroff My sounding-out is bad. I failed that for several weeks as a little kid. X-D

amWhy

03:06

@Limitless Not much, thinking of heading to bed. Bad day...

Limitless

We've all got our hard times.

Today was good for me, though, thankfully.

amWhy

@Limitless Good to hear. Hopefully, tomorrow will be better...it likely will. I just need a little break from Math.SE

Limitless

@amWhy Politics or drudging questions?

user57925

21

A: Reference request for tricky problem in elementary group theory

I believe this is well-known to those working in regular/inverse semigroups. So well-known in fact that one can even find proofs on the web, e.g. see this proof on PlanetMath. Alas, I cannot recall the history of this result, though I vaguely recall reading something about such decades ago. For...

amWhy

@PeterTamaroff Politics...competitive tone...sarcasm (not directed at me - but to those posting...). I just work to keep things welcoming here.

@sunflower...yes, I saw that yesterday!

@Peter: Oops, I was trying to respond to Limitless...

Limitless

03:10

@amWhy Ah. It is very frustrating at times. Have you heard of REPT?

amWhy

@Limitless What's REPT?

user57925

I don't really get why idempotents are so important

Limitless

It's a type of therapy a psychiatrist I know mentioned. I met him and we discussed a lot of stuff like that. At one point he mentioned a key component of therapy is realizing that no one can make you mad. He empowers his patients to realize just how powerful they are.

@amWhy I was very impressed by him. A wonderful and fabulous guy.

amWhy

@Limitless Yeah...I've encountered similar statements. I don't get "mad", but I get "hurt" easily...I do need to lighten up. And I care about people, so when others demean them, I cringe.

Limitless

@amWhy Mathematics is one of those domains where I think many people develop much, much more sensitivity than they usually have.

For me, this is because I put a lot of value in my work and I take pride in what I write. I think this happens with everyone in mathematics. (Most likely other academic fields, as well.)

amWhy

03:16

@Limitless Yes, I agree. But also, many OPs come in with bad experiences in math...feeling intimidated. It takes courage for them to post, at least for some OPs. I just wish people would respect those seeking help a bit more.

@Limitless I didn't have an "off" day, in terms of my answers, etc. Just witnessing ... unpleasantness.

Limitless

@amWhy Mathematics is a very, very concrete place at times. It is harder to portray respect and appreciation at times. For example, I find incorrect proofs as useful and valuable at times, but a lot of people here would rather just downvote them and move on.

amWhy

@Limitless Yes...I do think I need to take a break from the site, though. But I do my best to participate in a manner that is respectful, and welcoming...Perhaps leading by example...

Limitless

@amWhy What's your theory when it comes to social change?

amWhy

@Limitless Well, as we discussed yesterday, I am a rebel of sorts... I can't keep quiet when I see injustice...and as a result, I have to accept that doing so isn't always well received. First and foremost, though, I try to live as honestly, respectfully, and compassionately (and passionately) as I would hope others would relate to me.

Limitless

@amWhy You have rather lovely dichotomy going on there. Do you know what I mean?

amWhy

03:26

Little ripples, if nothing else..."small acts of kindness"

Kevin Duke

Quick question: Does anyone know of a website where I can type in an equation and I can link back to it from other websites as a png/jpg similar to how image hosting websites work?

Limitless

@KevinDuke this?

Kevin Duke

If not, I can just write the equation and take a screen shot, then host it on an image hosting site. Just wondering if anyone here knows of one

Limitless

@KevinDuke this seems to be the best so far.

amWhy

@Limitless Yes, I do...I decided long ago that I would rather be a flower than a cactus...(sensitive rather than calloused) even in the face of the pain that might bring. My 10th grade teacher wrote to me: "We, among others, realize there is great pain and great joy to be faced. Despair is so easy. But we can not give up. If not for those who care and continue the Good Fight, who will preserve tomorrow?"

Kevin Duke

03:29

That second link looks pretty good. Thanks!

Limitless

@amWhy I am the same way. Although, I am not as inclined toward change. I do not seek nor want to change 'the world' (in the context of 'the world' meaning society as a whole), but I do want to change the environments directly specific to me.

Kevin Duke

Yep, thats just what I needed @Limitless. Thanks! bookmarked

Limitless

@KevinDuke Splendiferous!

amWhy

I have no illusions that I am powerful enough to change the world...but we can all make "ripples"... And, change is best achieved from the inside out.

Limitless

@amWhy You can change the world, and so can I. I simply choose not to because it is far beyond what I want out of life.

amWhy

03:36

Any way, I need to put my truth/beauty/peace/-loving soul to rest for the night.

Limitless

@amWhy Sleep well!

amWhy

@Limitless I shall! Be well!

Limitless

@amWhy You, too!

Gustavo Bandeira

04:47

@AntonioVargas Are you from Brazil?

Antonio Vargas

@GustavoBandeira No, I'm from California :)

Mexican heritage.

user19161

I have decided not to cap anymore and slow down, having capped the last 7 days...

Jayesh Badwaik

05:23

I see a ping and no corresponding message. Hmm.

user19161

@JayeshBadwaik Probably deleted.

Jayesh Badwaik

@JasperLoy yes.

user19161

@JayeshBadwaik I just posted an answer I like very much on Eng, but nobody liked it, would you like to look at it?

Jayesh Badwaik

@JasperLoy Okay.

user19161

@JayeshBadwaik Here english.stackexchange.com/questions/93718/…

Jayesh Badwaik

05:38

yours is the most correct answer there.

user19161

@JayeshBadwaik Of course, I understand how it probably refers to the same thing. I am just saying that the sentences have different definitions inherently, but could refer to the same thing.

user19161

@amWhy Did you watch Evan Almighty? How does one change the world? ARK, one Act of Random Kindness at a time. QED.

user19161

@amWhy You usually pop in after I pop out...

Gustavo Bandeira

@AntonioVargas Got it. In Brazil, there's a Vargas family.

user19161

@amWhy Well, it is often hard to determine exactly what people are thinking when they type something online. Something may seem offensive but may not be the intention, and vice versa.

Gustavo Bandeira

05:49

@AntonioVargas He was a dictator: en.wikipedia.org/wiki/Get%C3%BAlio_Vargas

Jayesh Badwaik

06:14

@JasperLoy it usually doesn't

@ctype.h what a username!

user19161

@JayeshBadwaik That makes my answer even more relevant then, if you say so.

Jayesh Badwaik

@JasperLoy yes. It does.

Gustavo Bandeira

@JayeshBadwaik Still trying to upload, I've tried it through Google Drive but it's kinda impossible, I'm giving dropbox a chance.

user19161

@JayeshBadwaik I dislike Eng SE now. The native speakers there pile on downvotes whenever a non-native speaker asks an alright question.

Gustavo Bandeira

@JasperLoy Hipsters!

user19161

06:24

@GustavoBandeira Also, what often is a question about subtle differences between two words is taken to be too basic when it is actually very deep and cannot be gotten from checking a dictionary.

Gustavo Bandeira

@JasperLoy Do you have an example on this situation?

user19161

@GustavoBandeira You just need to look at all the closed and negatively voted questions and ask whether they deserve so many downvotes.

Gustavo Bandeira

@JasperLoy I guess MSE is one of the most fair SE's, even some very basic questions here are not downvoted.

user19161

@GustavoBandeira That is because mathematics is a relatively objective discipline and mathematicians are smart.

Gustavo Bandeira

@JasperLoy Haha

user19161

06:27

On Eng SE, any native speaker Tom Dick Harry just clicks "downvote" and "closevote".

Gustavo Bandeira

@JasperLoy Do they have any question on the meta about it?

user19161

@GustavoBandeira It has caused many people to be upset before. So ELL was proposed on Area 51. English for Language Learners.

Gustavo Bandeira

Yep.

Kill these native speakers!

Antonio Vargas

@GustavoBandeira Awesome.

user19161

06:59

Enjoy your weekend everyone, over and out!

anon

08:00

Ah, tensoring with torsion to prove that if finitely generated free abelian groups are isomorphic then they have equal rank. Brilliant.

robjohn

@anon an interesting answer?

user19161

@anon Hey! Work again this weekend?

robjohn

@JasperLoy cap yet?

anon

erry weekend until I tutor next semester

user19161

@robjohn Nope, need 70 more. I decided to take a break, but I think I will still try to cap today... There's plenty of time left...

anon

08:08

dislike: when you begin reading a question you anticipate enjoying answering, that has gotten zero votes, zero comments, zero answers, and few views for over an hour, and fate picks that moment for another user to answer.

shakes fist at the sky

user19161

@anon Life is unfair. Those who say life is fair just have not met enough problems.

anon

@robjohn Yes, proving that $\Bbb Z^n\cong\Bbb Z^m\iff n=m$ by tensoring with $\Bbb Z/k\Bbb Z$ and then taking cardinalities.

user19161

But not too bad, I got 2 accepts today already, but none yesterday...

user19161

Also, I find that I have almost no stars these days in this room. That is a good thing, it means I am rep whoring on the main site and getting points instead of stars...

user19161

I am really dying to make it to 10k and see invisible posts on Math! I was really excited when I got 10k on Eng!

user19161

08:16

I am trying to type faster these days so that I am not scooped.

user19161

@anon I think that would be a better job for you.

user19161

08:34

Geezis, I just saw the MK meta post.

robjohn

@JasperLoy To quote Ghostbusters... "I'll tell you the effect; it's pissing me off!"

user19161

@robjohn I must say in defence of MK, I don't understand why that question of his on main got so many downvotes, so I have upvoted him.

user19161

08:58

In fact, I just edited that question of his to make it look a little better too, so it is now bumped!!!

user19161

But it doesn't appear on the main page because it is too negatively voted!!!

robjohn

09:20

@JasperLoy revenge upvoting?

user19161

@robjohn Actually I may have downvoted him in some places because the questions were book length with little motivation, but that particular one was short enough to be a good fit.

Nimza

09:40

Hello!

user19161

@Nimza Hello cookie monster!

Nimza

@JasperLoy Hello, Will! :)))

Do you know how to draw integral sign $\int$ with inverse slope?

user19161

What is an inverse slope?

user19161

Oh I see.

user19161

No, I am a TeX newbie.

Nimza

09:43

oh :(

user19161

@Nimza You can ask in the TeX room and they can give you an answer immediately!

Nimza

nice idea!

That don't give an answer :) Heh, @JasperLoy, which tradition of writing integral sign do you like more? English, German of Russian? If you're interested in typographics traditions, there is a nice article uni-giessen.de/partosch/eurotex99/zaitsev.pdf

user19161

@Nimza Wow, I never knew there were different traditions!

Nimza

@JasperLoy heh :) that's a cute topic!

user19161

@Nimza Yes, as cute as you!

Nimza

09:51

:D

Chris's sister

10:25

Hi.

BenjaLim

@JasperLoy I saw your deleted answer.

@JasperLoy You need to tensor over a field to get it out :D

@anon did you see my ping in chat for you?

the one you said you would read?

user19161

11:07

@BenjaLim Yes, I delete some now and then because the question has changed or because someone posted essentially the same answer as me a few seconds earlier or because nobody likes it.

BenjaLim

11:28

@JasperLoy you deleted it because the answer was wrong.

user19161

@BenjaLim Ah yes, I just figured which you were referring to. That one was because I misread the problem.

Jayesh Badwaik

11:47

@GustavoBandeira Ahh, let it be, not important, tell me where you got it from, I will get it myself.

user19161

Haha, I answered with a very funny answer, wanna take a look?

Jayesh Badwaik

@Nimza there are different traditions of writing integral sign? Well, I'll be damned... :P

user19161

1

Q: What does it mean to be a function of smth.?

There is a sentence in Sokal and Rohlf's classic text: "The variance of means is therefore partly a function of the sample size on which the means are based." [in R.R.Sokal F.J.Rohlf; Biometry, 3rd ed., 1994: p.132, chapter 7 "Estimation and Hypothesis Testing"] Well, in this specific case ...

functions

Jayesh Badwaik

@JasperLoy hmm.

user19161

@JayeshBadwaik Do you like my functions answer above? =)))

Jayesh Badwaik

11:53

@JasperLoy sweet gourds man, sweet gourds... they give me sugar rush..

user19161

@JayeshBadwaik No upvote?

user19161

@JayeshBadwaik Also, you asked me to remind you to upvote my reference request answer yesterday. =)))

rubenvb

Hi everyone.

BenjaLim

@JasperLoy do you know what is a tensor product?

That is the way to go

Jayesh Badwaik

@JasperLoy When? I forget

BenjaLim

11:57

@JasperLoy But if you see my answer it is a lot more elementary and does not use so many highfalutin tools

user19161

@JayeshBadwaik Well, you can search the transcript...

rubenvb

Is anyone here familiar with Clifford algebra (or more specifically geometric algebra, in my case)?

Jayesh Badwaik

@JasperLoy Ahh. Hmm. Kind of involved in many chats right now. Couldn't pay attention. :P :P

Upvoted btw.

BenjaLim

@rubenvb what's up?

rubenvb

@BenjaLim I'm doing the elementary exercises in Hestenes' "New Foundations for Classical Mechanics", and having trouble solving geom. alg. equations.

BenjaLim

12:00

right.

@rubenvb Though I consider myself to be an algebraist, I have never dealt with that kind of algebra before.

rubenvb

ah, ok.

user19161

@JayeshBadwaik Here math.stackexchange.com/questions/253576/…

Jayesh Badwaik

@JasperLoy Yes I remember now. I thought it was a really nice answer.

user19161

@JayeshBadwaik It is the only proof I know of. The two books that prove this are out of print...

user57925

12:18

I'm trying to decide whether one would expect the zeta-function to have zeros off the half-line, or whether one would expect this not to happen. — Gerry Myerson 27 mins ago

rubenvb

OK. A wedge of a bivector with a scalar is 0, right?

A wedge of a scalar with anything is zero, no?

hmm, nvm. That's not the case here.

user57925

@rubenvb, that fractal is very intriguing

rubenvb

@sunflower it's called buddhabrot, a 3D Mandelbrot.

user57925

Gustavo Bandeira

12:39

@JayeshBadwaik Done.

user57925

im bored

Gustavo Bandeira

@sunflower We're not your toys!

user57925

nice

Gustavo Bandeira

Haha

What ya doing?

user57925

listening to it

Charlie

13:08

@jayesh !!!

Jayesh Badwaik

@Charlie Hello!!

Did you ping me last night?

@Charlie ??

skullpatrol

13:30

@JayeshBadwaik I think I scared her away :(

@robjohn How did you like the documentary?

robjohn

@skullpatrol which documentary?

skullpatrol

@robjohn Horizon A Mathamatics Mystery Tour

robjohn

13:51

@skullpatrol it will take a while to watch the whole thing, but it looks interesting. A pretty standard documentary. Was there something specific you were asking about?

skullpatrol

@robjohn Nothing in particular, just of general interest.

robjohn

@skullpatrol Did you see the last comment on my profile?

@skullpatrol Where would math be if Fermat had Post-it notes?

skullpatrol

@robjohn Yes :)

robjohn

@skullpatrol The video is going over Fermat's Last Theorem (at length)

bitmask

Hi

skullpatrol

13:57

hi

bitmask

I was just pondering if every non-empty set M can be extended to a monoid with some +: M^2 -> M. I think yes, because one can always return the first argument to + to satisfy the requirements for a moinoid. Is that correct?

latex?

user57925

operation a*b = a is a monoid?

user57925

there's no identity

user57925

so that's not a monoid

N3buchadnezzar

Magic!

You need it, and you know it.

user57925

14:03

any finite set could be put in bijection with Z/mZ which is a monoid (since it's a ring)

Jaakko Seppälä

Does anyone knows for what values of a the integral( x^(1-a) / ((1+x^2)^a)) dx, from 0 to infinite converges?

bitmask

@sunflower Ah, yes, e + a should return a.

user57925

but what's e?

bitmask

the neutral element

user57925

I mean what element of X is e

bitmask

14:04

any?

user57925

no

bitmask

@sunflower Well, I think it can still be fixed. Just choose any e in M as neutral element, and use the + operation as given above, unless one of the arguments is e. In that case, return the other argument.

@JaakkoSeppälä Does Wolfram Alpha give up?

user57925

b = ba = (eb)a = e(ba) = a

Garbage Collector

@JasperLoy: Hi

Jaakko Seppälä

@bitmask It gave me hypergeometric and Beta function representation but convergence seems difficult

bitmask

14:11

@sunflower Good point.

No, hang on.

b = ba = (eb)a = e(ba) = ba = b

@sunflower I don't see how you derive e(ba) = a.

robjohn

@skullpatrol Even my calculator gets more of $\pi$ correct than this!

user57925

me neither

skullpatrol

@robjohn It is an old documentary :(

robjohn

@skullpatrol But they knew what $\pi$ was. I probably knew it to 100 places when that documentary was made.

@skullpatrol that is no excuse for getting $\pi$ wrong

Gustavo Bandeira

@robjohn Nitpicky!

robjohn

14:19

@GustavoBandeira It's nitpicky to expect that when a math documentary gives $\pi$ to a large number of places, that at least half of those digits are correct?

skullpatrol

It is known to 10 trillion digits, now that is nitpicky.

bitmask

@sunflower From any string of values of M arbitrarily grouped, the first non-e value will be returned, and e if there is no non-e value.

skullpatrol

@GustavoBandeira 10 trillion and 50 to be exact :-D

bitmask

I think you can even get to abelian monoids if you throw in a strict total order :)

Gustavo Bandeira

@robjohn I'm only kidding.

user57925

14:23

it is a monoid

Gustavo Bandeira

@skullpatrol Yep

Charlie

@JayeshBadwaik yes i did

@skullpatrol hahhahhahaha nice gravatar, Skull! I thought that you would do something like this

skullpatrol

@Charlie Am I getting that predictable?

Charlie

@skullpatrol :) maybe

@JayeshBadwaik i said: " @jayesh !!!"

user57925

I wonder why I was so sure it's not a monoid at first

bitmask

14:35

@sunflower Because it's an awkward definition :)

user57925

it's just function composition where the functions are all constant functions returning a single element plus the identity function

bitmask

@sunflower Sounds right.

Gustavo Bandeira

@JayeshBadwaik Can you look this?

@Charlie Heeeeeey! Sexy lady!

user57925

in practice an uninitialized variable will have some random value (usually zero) in it already, but the point is it's undefined so the behaviour of a program that uses it is undefined

skullpatrol

14:51

This could be because a variable is initially thought of as an "unknown."

@GustavoBandeira Or should I say that traditionally a variable is initially thought of as an "unknown."

Transcript for

$Mathematics$ Mathematics