Mathematics - 2012-11-03 (page 1 of 4)

sea turtles

12:00 AM

otherwise I just drink water plain and simple usually

user19161

@seaturtles Hmm, I will remember that. That makes it turtle pie plus mountain dew then. =)

Nick Kidman

an what am I??

user19161

@NickKidman You are a beautiful actress.

Nick Kidman

I can live with that

I like Dogville

user19161

I like Smallville.

Nick Kidman

12:03 AM

if I'm allowed to say so myself

it's funny you would say that

user19161

Why? Smallville is a nice drama series ain't it?

Nick Kidman

okay...

she's talking about an album I gave to her, including
http://www.youtube.com/watch?v=6W_0E1QRx84

Peter Tamaroff

Dude, she might not want you to be sharing that stuff...

MSE is REALLY PUBLIC

Google "Nick Kidman"

user19161

@PeterTamaroff Or PNT.

Peter Tamaroff

Darn. There's a photographer with your name. Or is it you?

Nick Kidman

12:07 AM

@PeterTamaroff: well okay, but it really just says "I watched smallville on Halloween". If I would have described the email you wouldn't have complained

but I catch your drive, so okay

user19161

@seaturtles This is the first time you are pinging me using typed @, very interesting.

user19161

@peter Did you say you have a beard now?

Peter Tamaroff

@JasperLoy Nope.

user19161

@PeterTamaroff Hmm, I must be hearing voices then.

Nick Kidman

I don't know of any photographers with my name

and Nick Kidman is not my name

user19161

12:11 AM

@NickKidman Neither is mine JL.

Nick Kidman

because when I signed up, I accedentely wrote nicole with k

user19161

LOL

Nick Kidman

shit happens

I just drank a litre of milk

with my müsli, that is

user19161

@NickKidman Yes, shit happens after milk, lol.

Nick Kidman

that's low

user19161

12:15 AM

Hi Mr Potato.

MJD

Is there a special name for a graph that is a product of two cycles, or a graph that is a product of $n$ cycles, or a name for the family of such graphs?

Hi Mr. Jasper.

user19161

Hmm, nobody I know in chat talks about graphs, lol.

MJD

Question seems too trivial to ask on the main site.

Nick Kidman

what's the short key for ", lol."

user19161

Anyway I am out of this chat for now. Have a great weekend @anon.

Nick Kidman

12:20 AM

he said he doesn't drink coffee and then he fell asleep

@JasperLoy: ciao

wj32

why is the front page blank for me?

using both chrome and firefox, logged in and not logged in

anon

it is for me as well

peoplepower

Is the right panel on main up to date?

amWhy

glad I'm not the only one with a blank front page!

the meta site (front page) is down too, so I suspect there's a SE issue...

peoplepower

There we go.

wj32

12:29 AM

looks like most of the SE network sites are like that

Peter Tamaroff

12:40 AM

$$\Huge{\text{THE QUESTIONS ARE GONE!}}$$

peoplepower

I see them.

Oops, I refreshed.

Nick Kidman

good night

peoplepower

Aha, after clicking on the big "Questions" tab, then clicking through the little tabs "faq", "votes", etc and cycling back to "newest" I see them.

Or, more likely, it is just luck.

user19161

Well, it is intermittent.

wj32

@PeterTamaroff do you remember this:

5

Q: Prove that $f$, such that $\forall\delta\gt0$ $|f(y)-f(x)|\lt\delta^2$ $\forall x,y\in\mathbb{R}$ and $|y-x|\lt\delta$, is a constant function.

The function $f$ is defined on $\mathbb{R}$ such that for every $\delta\gt0$, $|f(y)-f(x)|\lt\delta^2$ for all $x,y\in\mathbb{R}$ and $|y-x|\lt\delta$. Prove that $f$ is a constant function. So, what I know, is that I need to show that $f(a)=f(b)$ for all points $a,b\in\mathbb{R}$. Or for ever...

real-analysis

Peter Tamaroff

12:45 AM

@wj32 Yep.

wj32

i think your proof is a little... excessive

user19161

@wj32 What a sweet picture...

Peter Tamaroff

@wj32 Sorry?

wj32

if you are given $|f(x)-f(y)|\le(x-y)^2$ for all $x,y$, there is a shorter way to prove that $f$ is constant

user19161

@wj32 Yes, they are often rather convoluted. Pedro is still a Padawan.

wj32

12:47 AM

the OP's hint is complete BS

Peter Tamaroff

@wj32 Well, that is relative.

wj32

@PeterTamaroff just something you might want to know :)

Peter Tamaroff

@wj32 Defend your position!

=)

user19161

@PeterTamaroff Truth needs no proof!

wj32

@PeterTamaroff well, if you write $|f(x)-f(y)|/|x-y| \le |x-y|$ for all $x,y$ then it is obvious that $f'(x)=0$ for all $x$

from the definition of the derivative

Peter Tamaroff

12:49 AM

@wj32 No, it isn't.

wj32

let me explain

Peter Tamaroff

@wj32 I know why "it is obvious".

But it needs proof.

My proof is self contained. And I like that.

wj32

let $\epsilon>0$ and choose $\delta = \epsilon$. Then for all $0<|x-t|<\delta$, we have $|f(x)-f(t)|/|x-t|<\delta=\epsilon$

Peter Tamaroff

In fact, assuming $f'\equiv 0$ you just use the MVT and you have for $a\neq b$ $$\frac{f(b)-f(a)}{b-a}=f'(c)=0$$ whence $f(a)=f(b)$ for every $a,b$.

wj32

oh, so you want to avoid the MVT?

alright then

Peter Tamaroff

12:53 AM

I don't want to avoid anything.

There are several proofs. Pick your favourite, that's it.

user19161

@peter How many proofs of Pythagoras theorem do you know?

wj32

what is your definition of a triangle?

user19161

Me? Actually I dunno.

user19161

I should go to bed now. Over and out!

wj32

it's 12pm here

good afternoon

Peter Tamaroff

1:59 AM

@anon Man.

$\bf T $ Let $D$ be an integral domain. Then there is a minimal and unique field extension of $D$.

peoplepower

What have you tried? What examples of this phenomenon come to mind?

anon

surely you mean unique minimal, not minimal and unique

also, field-of-fractions, universal properties, yadda yadda

Peter Tamaroff

@anon Potato, Patato

@peoplepower The book suggests this extension is produces by considering the "field" (which should be proven is one) of the "quotients" $$\frac a b:=(a,b)$$

anon

@PeterTamaroff No, because it is not a unique extension, so you cannot treat unique and minimal as separate adjectives here. "unique" must modify "minimal" (note that many posets have nonunique minimal elements)

Peter Tamaroff

We just quotient by an appropriate equivalence relation?

anon

2:03 AM

quotient, yes

Peter Tamaroff

@anon =)

@anon Yes, the book says this

anon

a tiny bit sloppy

Peter Tamaroff

For each integral domain $D$ there exists and is unique a minimal field extension.

BenjaLim

@anon Hey

anon

show that the field of fractions exists and embeds into any field containing D

hey benjalim

I'm thinking of actually buying F&H

BenjaLim

2:06 AM

@anon

anon

what the gerbils is the point of an otherwise textless ping

BenjaLim

@anon That's my copy

anon

cool I need to check my pizza in the oven

BenjaLim

@anon Can I send you my final essay when it's done?

@anon It's one Schur - Weyl duality, comments are welcomed.

anon

sure, did you see my link?

BenjaLim

2:07 AM

@anon No.

anon

do you want to post it here or email it?

BenjaLim

@anon I'll email it to you.

@anon By the way weren't you going to send me a paper of yours on the bracket?

anon

@BenjaLim www11.speedyshare.com/T7s5S/download/groups1.pdf

heh

you have my email right?

brb

BenjaLim

@anon No.

@PeterTamaroff thinking of fraction fields?

got it

@anon Fulton and Harris is ok

@anon But they don't explain a lot of stuff

and a lot of stuff is left hanging

you have to kinda fill out everything by yourself

definitely not easy to read

anon

my next topics to talk about are root space decompositions and the BCH formula

the former will probably delve into some combinatorics, lattices, group theory (coxeter groups)

BenjaLim

2:16 AM

@anon You mean like in $\mathfrak{sl}_n$

you can decompose it into cartan + positive root spaces + negative root spaces

anon

isn't positive vs. negative roots somewhat arbitrary?

so I gather from wikipedia

BenjaLim

@anon No not really.

For example, we define the highest weight vector of a representation

to be one that is annihilated by all elements in the positive root space

anon

this says there are many ways of choosing a positive root set of a given root system. does lie algebra structure force one to make one particular choice over others somehow?

@BenjaLim so you define something in terms that assume a priori which roots are positive, that doesn't seem relevant to my question of whether or not the selection of which roots are positive or not is arbitrary

BenjaLim

@anon Sorry yes the assignment of whether you call something positive or negative I believe is up to you.

@anon But the one for $\mathfrak{sl}_n$ is natural: The positive root space is just those $E_{ij}$ for $j > i$

anon

when are you planning on finishing the schur-weyl thing

BenjaLim

2:24 AM

@anon Tomorrow night.

anon

ok cool

BenjaLim

@anon Right I'm going to take a shower and get started on it

@anon Just finished a 20km bike ride :D

anon

... started?

nice. I used to do those long rides in boy scouts, but only like once a year. exhausting.

Peter Tamaroff

Hey

Im on my mobile

So texing is impossible

anon

@BenjaLim I think representation theory should branch out into category theory by defining representations as functor categories $\mathcal{C}^G$, where $G$ is a group viewed as a category with one element. then morphisms between representations are natural transformations of the functor objects. for $\mathcal{C}=\rm Grp,Set,Vect_k$ we obtain homomorphisms, group actions, and linear actions (the usual representations), respectively. Sound cool?

actually, that reminds me, I can probably add to an answer qchu had using this

but first I must imbibe alcohol

Is there a name for the left adjoint of hom(X,-) in general? I think it's the tensor product in Vect, and the cartesian product in Set. It'd be nice if it were functorial and symmetric in both its argument and the parameter X, just like in those two cases. I should think about Grp.

Pilot

2:56 AM

Hello everyone.As usual I wanted to ask a question: how do we prove that f(x)=g(x) for all rational x s implies f=g, where f and g are continuous maps from R to R. I have proven that f(x)=g(x) is true for all real x s.Please help

Sanchez

What have you tried?

Pilot

I have shown from sequential continuity that f(x)=g(x) for all real x s,does this imply f=g if f,g:R->R??

anon

every real x has a sequence of rationals converging to it

Pilot

yes,I used that fact

anon

so f(x)=f(lim q)=lim f(q)=lim g(q)=g(lim q)=g(x)

Sanchez

3:02 AM

f = g means f(x) = g(x) for all x

Pilot

so does this imply f=g?

Sanchez

yes

they are the same thing

Pilot

i am trying to be as careful as i can with analysis,so sorry for my asking too many question

and thank you )

Pilot

3:25 AM

Is there a map that is continuous on rationals and discontinuous on irrationals,help please,I cant come up with any function

anon

@Pilot google.com/…

Jayesh Badwaik

${}$

taylor

4:54 AM

are odd numbers really all that odd

anon

no

Peter Tamaroff

@anon Man.

@Pilot Yes!

Jayesh Badwaik

@PeterTamaroff Dawg.

Peter Tamaroff

I read that the other way.

Jayesh Badwaik

hmm.

Peter Tamaroff

5:01 AM

@Pilot Do you know about The function $$f(x)=\begin{cases}1/q \text{ for }x=p/q\text{ rational}\\0\text{ for } x \text{ irrational}\end{cases}$$ ? That one is cont at irrationals and disc at rationals.

@JayeshBadwaik Hey

anon

@PeterTamaroff in other words, did pilot look at the search list he was linked to an hour ago...

Jayesh Badwaik

@PeterTamaroff Do you know about this?

Peter Tamaroff

@JayeshBadwaik Hahaha

I google search my head, not internet, man.

@anon How do I download this?

Jayesh Badwaik

@PeterTamaroff :-)

Peter Tamaroff

Oh. Done

:6750659 Go home man. You're drunk.

Jayesh Badwaik

5:05 AM

anon is being testy today.

anon

hovered over wrong arrow

made a joke that made no sense

Peter Tamaroff

@anon I had black bier today.

Jayesh Badwaik

@anon now you are wallowing in your sorrow
thinking whether you should just jump off the fence

Peter Tamaroff

Jonas will tell me it is a crappy brand, but fuck it. It was good.

anon

I am home. In fact I am under the covers!

Not even close to drunk.

Jayesh Badwaik

5:10 AM

__

anon

5:49 AM

@Zhen is there a notion of tensor-hom adjunction in Grp (not just AbGrp)?

user19161

@JayeshBadwaik You sent me a mail that just went into my spam box, weird.

user19161

This means gmail's filter is set a little too strongly.

Peter Tamaroff

6:04 AM

Anyone up for peer review??

user19161

@PeterTamaroff I was reading before you asked.

Peter Tamaroff

@JasperLoy Good, good.

user19161

@PeterTamaroff Now that I have reviewed yours, please review mine. math.stackexchange.com/questions/227760/…

Peter Tamaroff

@JasperLoy .4563 seg. Erros=0.

user19161

@PeterTamaroff I am really low hanging fruit eh?

user19161

6:09 AM

@PeterTamaroff What is black bier?

Peter Tamaroff

Bier

Im engeren Sinne ist Bier ein alkohol- und kohlensäurehaltiges Getränk, das durch Gärung meist aus den Grundzutaten Wasser, Malz und Hopfen gewonnen wird. Für ein kontrolliertes Auslösen des Gärvorganges wird meistens Hefe zugesetzt, selten auch Milchsäurebakterien. Weitere Zutaten sind Früchte, Kräuter wie Grut oder Gewürze. Der Alkoholgehalt der üblichen Biersorten liegt in Deutschland und Österreich in der Regel zwischen 4,5 % und 6 %. Im weiteren Sinne versteht man unter Bier jedes alkoholhaltige Getränk, das auf Basis von verzuckerter Stärke hergestellt wird, ohne dass dabei ein...

user19161

@BenjaLim Nice, I still don't have a single RIM series on my shelves.

user19161

@PeterTamaroff Geezis.

ガベージコレクタ

6:52 AM

@JasperLoy: I made a new animation only for you here tex.stackexchange.com/a/80203/19356.

user19161

@ガベージコレクタ Hmm, OK. I am out of here. See you.

ガベージコレクタ

@JasperLoy: Please don't go.

user19161

8:07 AM

Hey @jayesh I am brown now.

ガベージコレクタ

@JasperLoy: Hi, Welcome.

user19161

@ガベージコレクタ Anyway, that was not really an animation.

Jayesh Badwaik

@JasperLoy Hi!! That is much better.

ガベージコレクタ

@JasperLoy 2 frames are enough to be animated.

Jayesh Badwaik

@JasperLoy Your filter treats me as a spam? But I never sent you any kittens. :-(

user19161

8:09 AM

@JayeshBadwaik I have an answer which I like a lot but deleted it. I will undelete it now and perhaps you can reivew it. math.stackexchange.com/questions/14841/…

user19161

@JayeshBadwaik Hmm, you are not in my contacts list which is kept to a bare minimum, I like to remember emails instead of store them. That is one reason. But considering that it was a one to one email, the filter is very drastic.

user19161

@ガベージコレクタ Perhaps one is enough too, it will be termed the trivial case.

Jayesh Badwaik

@JasperLoy Your answer does not really put things in any physical perspective. I upvote it because it has the word "inflection", however, I feel I would like to be related it to the rate of change of radius of curvature of the motion object and may be something similar.

ガベージコレクタ

@JasperLoy While the result was acceptable, creating a single frame animation often turned out to be a funny process. ;-)

user19161

@JayeshBadwaik OK, the question asks for any meaning though.

Jayesh Badwaik

8:17 AM

@JasperLoy Yeah, to some level, jerk meaning is good as if inflection. I am not satisfied though. Not that I know the answer myself, but still.

user19161

And that inflection is the most immediate one which many are not aware of.

Jayesh Badwaik

@JasperLoy Yup, and hence, the upvote.

user19161

@JayeshBadwaik Yes, jerk is the physical interpretation. I am not a physicist, physics is ugly. =)

user19161

@JayeshBadwaik In fact on MO someone commented that he liked my answer, but that was long ago...

Jayesh Badwaik

A poet once said, "The whole universe is in a glass of wine." We will probably never know in what sense he meant that, for poets do not write to be understood. But it is true that if we look at a glass of wine closely enough we see the entire universe. There are the things of physics: the twisting liquid which evaporates depending on the wind and weather, the reflections in the glass, and our imagination adds the atoms. The glass is a distillation of the Earth's rocks, and in its composition we see the secrets of the universe's age, and the evolution of stars. What strange arrays of chemica…

@JasperLoy you deleted your answer there?

user19161

8:20 AM

@JayeshBadwaik I used to be interested in math and physics equally, but after that the math took over completely.

user19161

@JayeshBadwaik No, because OP posted question on MO as well and then linked to MSE post so people are aware of the posts here.

user19161

@JayeshBadwaik I have no business there, for I am only a banana.

Jayesh Badwaik

@JasperLoy I am equally interested in electronics, computer science, mathematics and physics and may be economics. In short, I am screwed

@JasperLoy Hmm.

user19161

Hey @jay thanks for telling me what you did in the email, and I actually found out myself before that too. =)

Jayesh Badwaik

@JasperLoy =)

user19161

8:23 AM

@JayeshBadwaik Nah, only I am screwed, you know why...

user19161

@JayeshBadwaik It's actually better that way, I don't have to put my hope only to lose it in the future. =)

Jayesh Badwaik

@JasperLoy Hmm.

user19161

@JayeshBadwaik Hey why did you change that?

Jayesh Badwaik

@JasperLoy You read it right? It served its purpose.

user19161

@JayeshBadwaik And no, I wasn't being not nice to whoever you are talking about. She just misunderstood me.

Jayesh Badwaik

8:25 AM

@JasperLoy hmm. May be.

@JasperLoy Yup. =)

user19161

@JayeshBadwaik Why should I be not nice to her? She hasn't done anything bad to me.

user19161

@JayeshBadwaik Anyway if there is any problem, whoever wants to talk about it can always email me again, anytime.

Jayesh Badwaik

@JasperLoy Yup.

user19161

@JayeshBadwaik Also, I don't tell lies. If I hate a person, I will say so. So no means no.

Jayesh Badwaik

@JasperLoy Hmm. Okay. I trust that.

Nimza

8:36 AM

good morning!

Jayesh Badwaik

@Nimza Hi!!

Nimza

Hi @JayeshBadwaik, that's nice you're here! How do you think, is it better to take numerically derivatives of holomorphic functions using integral than using differences?

Jayesh Badwaik

@Nimza well, derivatives have division with small numbers which is bad numerically, so I would prefer integration.

Nimza

@JayeshBadwaik me too)

user19161

@JayeshBadwaik You know what, I can also choose to flag a lot of things others say to me. But I don't. Because I think first what that person may have in mind, and if I have a problem I will talk to that person. What upset me is that what I said got two flags. This kind of thing always reminds me I don't belong to this world.

Jayesh Badwaik

8:40 AM

@Nimza yup, I had written a extra precision derivative program once. There I used $\frac{f(x+ih) - f(x)}{ih}$ as the formula to calculate derivative to enable more precision. This was one of the best methods to do so for real functions. This fails down in complex domain.

Nimza

@JayeshBadwaik ogo, And what did you do with this difference for real functions? (You have a division by small number still)

ガベージコレクタ

Centroid of human beings youtube.com/watch?NR=1&v=Mdk78fR0ihw&feature=fvwp

user19161

@JayeshBadwaik And yes, that flagging has upset me now and that has made me change my mind about certain things, I admit that. Of course, I can't be sure who flagged it.

Jayesh Badwaik

@Nimza Yes, but now, by separating the real and imaginary parts, your division is by a small number of a small number. So, the error is quiet less. I forget exactly which manipulations I used, but the main idea was above.

Subtracting two big numbers to give a small number is very very error prone again.

@JasperLoy Yes man. Too much flagging currently in the room. I haven't flagged anyone yet I assure you though.

Also, I cannot think of anything you said that could be "offensive". I missed the last night joke though , and do not know what happend there.

Nimza

@JayeshBadwaik to separate real and imaginary parts is so nice idea) but does this method work only for real analytic functions?

user19161

8:45 AM

@JayeshBadwaik Everything can be interpreted in multiple ways. I only get mad at people when I have thought carefully and assured myself that the person intends malice. But then again, different people see things differently and draw lines differently, so there is always conflict in the world, intentional or otherwise.

Jayesh Badwaik

@Nimza I would guess so. May be if you can convert the complex function into a two dimensional function and then take a third/four dimensional system and write the difference similarly? and then separate? I am not sure.

@JasperLoy Hmm. Yup.

Nimza

@JayeshBadwaik uh, I think that for complex (holomorphic) function integrating using Cauchy representation will give very exact formulas too, but I'll try at first to program it :)

Jayesh Badwaik

@Nimza yes integration will give quiet good formulaes.

user19161

@Nimza I never thought computers were so important for calculating things until recently.

Johan Larsson

morning

user19161

8:54 AM

@JohanLarsson I noticed you were quiet.

Johan Larsson

It's probably a good thing when I'm able to control myself :)

user19161

Did you have something to say?

Johan Larsson

Feeling red today?

Nimza

@JasperLoy :)

user19161

@JohanLarsson Nah, it does not mean anger. It is just an arbitrary colour. It is "brown".

user19161

8:56 AM

@Nimza Hey you should learn to use the arrows in here for replying.

Nimza

@JasperLoy why? I don't use them when it is obvious to what I reply

Johan Larsson

@JasperLoy I'm gonna ask a question some day

user19161

@Nimza Otherwise, I dunno what you are referring to.

user19161

@JohanLarsson You have no posts now on math?

Nimza

@JasperLoy okay, I'll remember that you like them)

Johan Larsson

8:58 AM

@JasperLoy It renders as ~wine on my screen

user19161

@Nimza It might be obvious to you but not the other person. I see things in 9000 ways when people see it in 1.

user19161

That's why I often get into quarrels.

Nimza

ok-ok-ok

Johan Larsson

@JasperLoy Nope, no posts, just lurking. Liked this chat a lot

Been ten years since I used math (school) extremely rusty on all lingo, notation etc.

user19161

@JohanLarsson By the way you look good without hair. Genuine, not sarcasm, in case someone thinks I am being sarcastic and flags me. See, everything can be flagged.

Johan Larsson

9:02 AM

lol, I could just flag it for being genuine!

This is my final haircut, not gonna do the comb-over phase

+ its low maintenance

user19161

I would like to ask your advice then. How does one make himself bald? Using scissors, razor, etc?

user19161

I am trying to determine the easiest painless way to go bald head.

ガベージコレクタ

@JasperLoy Who is she?

user19161

@ガベージコレクタ Not gonna tell you.

ガベージコレクタ

@JasperLoy Oh my ghost!

Johan Larsson

9:06 AM

@JasperLoy I use and Andis Agc atm, its intended for animals. Tried two consumer grade trimmers last year but they failed me

user19161

@JohanLarsson HAHAHA. You know what, I once used an electric shaver but that did not work well for ordinary shaving of face, so now I use the manual ones.

Johan Larsson

Are you a math student or professional or something else?

user19161

@JohanLarsson That's a secret. =)

Johan Larsson

ok

I never really studied math other than the contents of engineering school

but that is a while ago now and feels even longer when trying to remember anything

user19161

@JohanLarsson Not a bad thing. Some math courses have too little applied stuff. It's good to know how to solve differential equations and things like that.

user19161

9:14 AM

@old I would have overtaken you now if not for the Littlewood question of yours.

Old John

@JasperLoy Yes! I was a bit surprised how popular that question was

Johan Larsson

what is the difference between mathoverflow and math.stackoverflow?

user19161

@JohanLarsson You mean MO and MSE? One is for research level math and the other for all levels.

ガベージコレクタ

@JasperLoy: I give up about why we cannot divide any non-zero number by 0. Could you give me the answer?

Johan Larsson

ok I think I picked the right one at least

user19161

9:20 AM

@ガベージコレクタ It's just that when you write a/b you mean the number which when multiplied by b gives you a. If b is 0, anything times b is 0. So we just let division by 0 be undefined.

user19161

Of couse one can define 0/0=0, but there is no point in doing that in everyday life, so we omit this case as well.

Johan Larsson

why not 0/0 =1?

ガベージコレクタ

@JasperLoy: I think the yesterday guy ( I forgot his name) forced me not to assume division by zero from the beginning. Your explanation is what I already thought but I canceled it because of his statement.

user19161

@JohanLarsson Yes, in fact it can be anything on the right side, which makes things even messier, so that's another reason we don't define division by 0 at all!

user19161

There are various ways to look at any given concept.

user19161

9:26 AM

So just remember that when we talk about the set of real numbers, division by 0 is undefined.

user19161

Also, note that plus infinity or minus infinity are not considered real numbers.

user19161

However one can bring in infinity and division by zero in various ways for certain purposes, but these are not within the scope of the real numbers and their basic operations per se.

Johan Larsson

9:41 AM

How did you understand this question?:
http://math.stackexchange.com/questions/16282/what-is-the-probability-of-obtaining-a-triangle-when-choosing-3-points-from-a/16283#16283

Nine points are place in a 3x3 matrix wtf (for me)

Nimza

11:10 AM

hi again

Is it true that set $X$ in $\mathbb{C}P^2$ given by $w_0^2 = w_1 w_2$ intersects $w_0 = 0$ transversally? What does it mean?

skullpatrol

12:13 PM

hi @OldJohn

Old John

@skullpatrol Hi there

Johan Larsson

hej

skullpatrol

@OldJohn Did you watch "A Brief History of Time" yet?

Old John

@JohanLarsson Hej

@skullpatrol Not yet - maybe over the weenend.

Johan Larsson

@OldJohn Swede?

Old John

12:15 PM

@JohanLarsson No - but a "friend of Sweden" - and snus-er

Johan Larsson

lol, how did you find out about snus?

Old John

@JohanLarsson I am from UK, but Sweden is the country I have visited most -

Mats Granvik

12:30 PM

The sum of the smaller trigonometric curves adds to the straight line curves.

Johan Larsson

Standard fourier series? ^^

Mats Granvik

Not really. These are recursively defined. And instead of a Gibbs phenomenom there is a rounding of the curves.

Rounding of the straight lines curves corners that is.

ガベージコレクタ

@skullpatrol: What is your explanation about why we cannot divide any number by 0?

skullpatrol

Maybe @OldJohn can help us?

Old John

@skullpatrol With what?

dividing by 0?

skullpatrol

12:36 PM

@OldJohn Why can you never divide by 0?

@OldJohn In the set of real numbers.

Old John

simplest explanation I know of is that if $3/0$ had a value (say $x$), then we would have $3=0\times x$, and that is clearly impossible for any real $x$.

QED

If you try looking at $0/0$ by the same argument, you get $0=0\times x$, and now any real number is a solution.
Thus you always get either no solution at all, or everything is a solution, so there is no definition for dividing by 0 which makes sense - ever.

Johan Larsson

@OldJohn what if x = 0/3? (maybe not a value)

Montaigne

Maybe someone could help with properties of a matrix norm: math.stackexchange.com/questions/227001/trace-norm-properties

peoplepower

Since division is the inverse of multiplication, in dividing by $a$ you invoke an implicit hypothesis that $a$ is multiplicatively invertible. Now when we set $a=0$, that means in particular that $0r=1$ for some $r\in\Bbb{R}$, a false statement. (Tldr; what Old John said.)

Old John

@JohanLarsson That is just dividing by 3 - we know how to do that OK :)

Johan Larsson

12:43 PM

@OldJohn but to me it makes some sense so long as we are not to eager to do eval()

Nimza

Do you know about local fractional calculus?

Old John

@JohanLarsson I don't think dividing by zero ever makes sense - if you are working just with real numbers

Johan Larsson

@Nimza me? I don't know much (at all)

peoplepower

It follows that the only ring in which division by zero is possible is the trivial ring in which 1=0.

Old John

@peoplepower and that is not worth studying too hard :)

peoplepower

12:45 PM

@OldJohn Not much structure there, eh.

Old John

right - time to watch Man Utd v Arsenal - back later

Nimza

@JohanLarsson ho, I have a problem with it

Old John

@peoplepower indeed!

bye folks

skullpatrol

@peoplepower Your $r$ stands for the reciprocal of a, correct?

Johan Larsson

@Nimza Let me put it like this, you mentioning it was the first time I heard about it :)

peoplepower

12:47 PM

@skullpatrol It stands for a real number such that $0r=1$. No other restrictions.

In general $ar=1$ implies $r$ is a right inverse of $a$.

Johan Larsson

@Nimza But if you feel like it you can write your problem and, at best, I can ask a couple of stupid questions

Rajesh D

Hi there! Is anyone in here acquainted with harmonic analysis?

Nimza

@JohanLarsson I'm interested in question if there exist some local operator that sends $(x+a)^{n\alpha}$ to $C(n)(x+a)^{(n-1)\alpha}$. Fractional derivative of order $\alpha$ is nonlocal :( So I was looking for local fractional derivative

skullpatrol

@peoplepower What is the difference between a reciprocal and a multiplicative inverse then?

Johan Larsson

@Nimza sry, got to run gf called

Nimza

12:52 PM

@JohanLarsson aha, bye

skullpatrol

1:18 PM

@ガベージコレクタ Here are some explanations.

@ガベージコレクタ Remember that with a question like this it is easy to not be able to see the forest because the trees are in your way :-D

Nimza

Hm, help me please, if we define $f(x) = \sum\limits_{k=0}^{\infty} \frac{(x+a)^{\alpha k}}{\Gamma(\alpha k + 1)}$ then $\lim\limits_{h \to +0} \frac{ f(x+h) - f(x)}{h^{\alpha} } = 0$ for $x+a>0$, right? $0 < \alpha < 1$

Frank Science

1:56 PM

Hi, is there anyone familiar with Kronecker's density theorem?

Greg Ros

If $$a_{k} = (-1)^{k}$$ and $$b_{k} = (-1)^{k+1}$$ then would the sum of the series $$\{a_{k} + b_{k}\}$$ converge?

Frank Science

$a_k+b_k=0$

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