Mathematics - 2012-07-02 (page 1 of 3)

Dylan Moreland

00:09

@Eugene $k = k[x]/(x)$. Quotients of $A$ are $A$-modules!

Peter Tamaroff

@DylanMoreland Hey there.

Jonas Teuwen

00:26

@MattN That is what I say! 8-). But you can take the inner product ($x_1 y_1 + \dots x_n y_n$) and derive that thing with the cosine.

Dylan Moreland

00:37

@PeterTamaroff Hi Peter.

Peter Tamaroff

@DylanMoreland We were discussing about good analysis books. I'm reading Rudin now. What is your experience?

BenjaLim

01:03

@DylanMoreland Do you know that question on a degree 2 extension of $\Bbb{Q}$?

Dylan Moreland

@PeterTamaroff Oh, I don't know. I like Rudin. At Michigan they used Spivak which seems like a nice book.

BenjaLim

@DylanMoreland The OP surely meant "for $d$ not a square in $\Bbb{Z}$"?

that is different from asking for a $d$ such that $d$ is square free.

Dylan Moreland

@PeterTamaroff My friend likes Shilov. I don't hear that mentioned as often.

BenjaLim

Makoto's answer does not address that. All he has produced is an integer that is not a square in $\Bbb{Z}$

@PeterTamaroff I recommended abbott's understanding analysis. I think it is supremely beautiful.

Dylan Moreland

@BenjaLim I remember. One second.

Ah, you bumped it. I don't have to go searching :)

BenjaLim

01:06

Yes I had to edit my answer.

Dylan Moreland

Makoto doesn't seem to worry about the square-free bit at all.

Kind of an easy thing to patch up at the end, though.

Right?

Peter Tamaroff

@DylanMoreland I love Spivak. It is awesome.

BenjaLim

hmmm

@DylanMoreland perhaps...

but I think the OP is confused between a square free integer and an integer not being a square in $\Bbb{Z}$

Peter Tamaroff

But is has no "real analysis", rather very "advanced calculus"

Dylan Moreland

I didn't get that vibe. It's possible. Neither of them are being very explicit about that.

@PeterTamaroff I don't know what the distinction is.

It seems to teach you more or less what Rudin does, when combined with Calculus on Manifolds.

BenjaLim

01:09

@PeterTamaroff If you want a very rigorous treatment of several variables I suggest Duistermaat and Kolk

It is really full on

GTG guys

Peter Tamaroff

@BenjaLim I'm sticking to one variable now! =)

BenjaLim

@PeterTamaroff bye!!

Peter Tamaroff

@BenjaLim See you.

@DylanMoreland What I mean is that Spivak doesn't treat Topology, Cauchy Sequences, or Fourier Series as an example.

But I really like that book. It served me a bunch.

For example, Apostol has a chapter on Functions of Bounded Variation, while Spivak doesn't mention them (or the notion of Variation of a Function)

@DylanMoreland I'm considering to read Apostol's maybe, it seems really thorough.

@Eugene What did you write there?

Frank Science

01:24

Good morning, everyone.

How do you do?

What's partition of unity? Can anyone interpret in calculus? I googled and found wiki, but it's so far for me to understand.

Peter Tamaroff

@FrankScience It is very clearly explained in the first lines of the page. You have to read a little about topology to get it, that's all.

Frank Science

@PeterTamaroff I have no idea on topology.

Peter Tamaroff

@FrankScience Where did that concept arise, then? Where did you find it?

Frank Science

topological space, say, $\Bbb R^n$?

Peter Tamaroff

A simple example would be $\mathbb R$, and $\{ \sin^2 x, \cos ^2 x\}$

Frank Science

01:30

See it here

Yesterday I couldn't understand.

Today I read it one word by one.

Peter Tamaroff

@FrankScience Do you know what a topological space is?

(I don't)

Frank Science

No, I'm just learning calculus.

Breakfast, I'll go back.

Peter Tamaroff

@FrankScience LOL, it is 10:30 pm here!

Rajesh D

Hi

Dylan Moreland

@PeterTamaroff He certainly talks about Cauchy sequences, but only in $\mathbf R$, I agree. I guess I don't see general topology as being the hard part of that material, so I'm not upset with Spivak's choice.

I recall Fourier theory getting short shrift in Rudin as well. He does at least talk about it, though.

I think in general analysis courses are somewhat light on the analysis that people actually use.

Peter Tamaroff

01:40

@DylanMoreland OK.

@RajeshD Hey.

Dylan Moreland

@PeterTamaroff Let me know how you find Apostol. I've never read it.

Peter Tamaroff

@DylanMoreland It has cool excersices, for one.

Eugene

@DylanMoreland i don't see how nakayama applies either. also i see why you're saying $M$ is an $R$-module but i'm not so sure.

Frank Science

back now.

dilemma

It seems hot today.

Is it famous?

$\xi(t)$ is a $\mathcal C^n$-function such that $\xi(t)=0$ for $0\le t\le1$ and $\xi(t)=1$ for $t\ge1$.

Then $f(z)=\xi(|z|)$ for $z\in\Bbb C$?

We conclude that $f$ is $\mathcal C^n$ (I don't know why).

Dylan Moreland

02:08

@FrankScience This can't be right; you'd have a discontinuity at $t = 1$.

Do you want something that's say, zero on $[0, 1]$, between $0$ and $1$ on $[1, 2]$, and identically $1$ on $[2, \infty)$?

Frank Science

@DylanMoreland Sorry, $\xi(t)=1$ for $t\ge2$

Dylan Moreland

Okay cool.

Frank Science

@DylanMoreland $2$ is not important.

Dylan Moreland

No, none of the particular numbers really are :)

Frank Science

@DylanMoreland any $1+\epsilon$ where $\epsilon>0$ is acceptable.

Dylan Moreland

02:10

Then I think the argument is that at $z \neq 0$, $f$ is $C^n$ by the chain rule, and near $0$ the $f$ is identically zero, so it's certainly differentiable at $0$.

Frank Science

@DylanMoreland I wonder whether it is a famous construction?

Dylan Moreland

Right? Because the only worry is that $z \mapsto |z|$ is not smooth at the origin.

It's how you take a one-dimensional bump function and boost it up to $\mathbb R^n$. Look in any differential geometry book!

Frank Science

@DylanMoreland I'm just learning calculus.

@DylanMoreland I'm trying to understand the proof of a calculus problem.

Dylan Moreland

I see. Well, "bump function" is certainly another thing to search for.

Frank Science

Bump is not needed. $\mathcal C^n$ is smooth enough.

Dylan Moreland

02:16

It's one of those instances of the generalization being only superficially harder, I think.

Frank Science

For example, if we know $f,f',\ldots,f^{(m)}$ at some point, saying $x_0$, and $f,f',\ldots,f^{(n)}$ at some point, saying $x_1$, we can construct such $f$. Taylor polynomial $g(x)$ at $x_0$, and let $f(x)=g(x)+(x-x_0)^{m+1}h(x)$ where $h$ is needed to find out.

Applying this result to $\xi(t)$, we can construct one.

Peter Tamaroff

@BenjaLim I have to take a bow to that book, dude!

Frank Science

02:40

Awful.

Dylan Moreland

03:51

Hm. Don't understand that last one.

Frank Science

04:02

@DylanMoreland eh?

user19161

05:25

@DylanMoreland I like it too, but being a translation the definitions can be very weird.

Eugene

@DylanMoreland what does it mean to be an open point in Spec $R$?

for example $R = \Bbb{C}[x]$?

user19161

@Eugene Hi sir.

Eugene

@JasperLoy i'm not worthy sir. i touch your feet

user19161

@Eugene No need to worship me, I am not God.

Eugene

@JasperLoy you're not familiar with iyengar?

user19161

05:34

@Eugene I am. But did he mention feet as well?

Eugene

he used to

also meta.mathoverflow.net/discussion/1351/…

user19161

You know, I have to refresh chat like once every minute with chrome on linux.

user19161

Otherwise the messages do not display.

Eugene

oh well

user19161

In fact, I had to refresh it again to edit a message.

user19161

05:38

And the only reason I am using it is because it has the most recent built-in flash plugin which is impossible to get for linux otherwise.

Eugene

well i've had to grade like a bajillion papers today so...

@anon you online?

anon

yup

Eugene

so for example, is $\Bbb C$ a $\Bbb C[x]$-module?

anon

how is $x$ designed to act on $\Bbb C$?

user19161

@Eugene Nuts.

Eugene

05:40

@anon just the usual multiplication

anon

@Eugene I don't understand. What complex number is $x\cdot 1$ for example?

Unless you mean $\Bbb C[x]$ is a $\Bbb C$-module..

Eugene

@anon so dylan and i were talking about this today. he argued that $\Bbb C = \Bbb C[x]/(x)$ and so since the the quotient $A$ is an $A$-module (where $A$ is any ring).

anon

well, $\Bbb C\color{Red}\cong \Bbb C[x]/(x)$, but not $=$, if we want to be pedantic..

Eugene

@anon i was really confused as well

@anon yes i know that too

let's see if i can find the transcript

anon

of course you can make C a C[x]-module, it's just not faithful or whatever the correct term is

Eugene

05:44

so it starts with this:chat.stackexchange.com/transcript/message/5189231#5189231

i replied with this chat.stackexchange.com/transcript/message/5189569#5189569

anon

we have $\mathrm{Ann}_{\Bbb C[x]}\Bbb C=(x)$. it's well-defined and all that, I just don't see the point.

Eugene

then he says this chat.stackexchange.com/transcript/message/5190756#5190756

@anon so in this case we do have a counterexample?

anon

I dunno what the original lemma was

Eugene

it's in the transcript

here

anon

ah

Eugene

05:46

i'm trying to figure out if dylan's counterexample is wrong or the lemma is wrong

like dylan i cannot figure out how nakayama's lemma applies

@JasperLoy you're awake a lot

anon

interesting, I think it is a counterexample

Eugene

@anon hmm.

so we do have that $\Bbb C$ is a $\Bbb C[x]$-module?

anon

of course

$x\cdot m=0$ for all $m\in \Bbb C$.

Eugene

this is the case because $\mathrm{Ann}_{\Bbb C[x]}\Bbb C=(x)$ right?

anon

I'd phrase that the other way around.

Eugene

05:53

i don't think it's true in general though

anon

Using $k\cong k[x]/(x)$, we have $x\cdot(m+(x))$ getting sent to $0+(x)$, so $x$ acts trivially on $k$

Eugene

@anon yes i know this but i wasn't able to find any literature on this

anon

I don't see how that should be an issue. Though it's interesting if no text ever bothered to point out this sort of situation.

Eugene

i don't see the issue either and it is surprising that i wasn't able to find a mention of this

so i wanted to check to see what you thought

Frank Science

Is it of rigor?

Frank Science

06:15

Calculus, too complicated.

user19161

06:37

@Eugene I don't sleep at regular hours. I am not well.

user19161

06:50

@FrankScience Yes, calculus can be very hard even though it is the lowest life-form.

Old John

Hi Eugene

Matt N.

@JonasTeuwen There must be something wrong with it.

Eugene

07:14

@OldJohn hi

@OldJohn how's it going?

Old John

Not so bad, thanks - struggling with the Riemann paper :-)

Eugene

@OldJohn oh. are you trying to prove all his statements without looking at the proofs?

Old John

I tried that for a while, and then decided that might take months of work! - That paper is pretty "dense"

Eugene

@OldJohn lol. yes it is! and most of what he does is not incredibly intuitive. it's definitely an ingenious piece of work.

what more i heard that it was his only work in number theory

Old John

Yep - and it seems that his contemporaries didn't grasp the full significance of what he said in it until about 30 years later :-)

I think it was his only published work in NT, yes - although I believe he did other stuff

Eugene

07:20

@OldJohn yes mostly in analysis

Old John

Ah - I meant that he did other stuff in NT, but didn't publish it

Eugene

@OldJohn oh. i didn't know that

Old John

I also suspect that he was influenced by Gauss's preference for hiding some of the steps that lead him to some of his discoveries - Gauss seemed to like to "remove the scaffolding" after creating something (annoyingly!)

I think Gauss was his Doctorate supervisor (?)

Eugene

@OldJohn i thought it's because they were less interested in rigor back then

Old John

@Eugene probably that too!

Eugene

07:25

@OldJohn my algebra prof told me that rigor only came about in the 20th century

Old John

@Eugene Mostly - although I think there were a few guys before then who understood the need for it

Eugene

@OldJohn yeah i believe that is the case.

how is the foray into elliptic curves going?

Old John

@Eugene Not got very far with that, yet - but been reading some of Ireland and Rosen - the more I read of it, the more I like it - and it has some terrific exercises

Eugene

@OldJohn it is a tremendous book. i've never found another book that talked about gauss sums like it did

Old John

@Eugene That is about where I got to - I think I can cope with the Gauss sums, but not yet grasped the Jacobi sums

Eugene

07:33

@OldJohn that is very good stuff. i like that method for counting solutions

Old John

@Eugene Yep - looks to me like another area where Gauss was well ahead of his time

Eugene

@OldJohn silverman's book is really good once you pickup some algebraic geometry. you don't need to know about schemes and sheaves thankfully

Old John

@Eugene I might give that one a go - eventually - it sounds good from what I have heard

Eugene

@OldJohn it's the best IMO. milne is a softer intro and silverman is the meat

milne deals with them over $\Bbb Q$ mainly that's why

silverman talks about EC over general fields.

Old John

@Eugene I had the idea of printing out a few pages of Milne every few days and carrying them around until I understand them, then printing a few more etc :-)

Eugene

07:41

@OldJohn haha. that's nice.

anyway i'm off to bed. it's late here. good luck with your studies!

bye

Old John

@Eugene Bye - sleep well

Frank Science

The calculus problem:

$\int dx/(x\ln x)$

Matt N.

08:36

Can we tag this big-list?

user19161

@MattN Eric commented there are 42 proofs. Is that a joke?

Frank Science

How to relate a room to a question in MSE?

Gigili

@FrankScience Bookmark the part of discussion you want to link to it.

Frank Science

@Gigili Can you make an example?

Gigili

For example

Next to "leave" on top right, there's "room".

Click on it and "create new bookmark".

Frank Science

08:50

@Gigili I want to relate to MSE.

Gigili

Don't you want to link to a chat discussion in your question? Then I misunderstood you!

Frank Science

@Gigili For example, relate to this

@Gigili Can I do that?

Gigili

Umm, I don't understand what you want to do.

If you want to post a question here, well, you just did it.

Frank Science

I saw sombody having do it.

Sometimes here is a question discussed very hot.

Then a person create a room to discuss another.

He can relate the room to the link of the problem in MSE.

Gigili

Aha, that.

Creating the room to avoid extended discussion in comments.

Frank Science

08:56

I'm looking for that room.

Gigili

There's a link there, they just click on it.

@FrankScience Which room is that?

@FrankScience Of course.

Frank Science

@Gigili No, I see now.

Gigili

OK, good.

Frank Science

@Gigili He only created a room and made a desciption, which contained the link, not magic.

Frank Science

09:07

Are there many cranks in western countries?

Jonas Teuwen

09:23

@FrankScience You know it is quite stupid to just write down the result of somebody else in your own topic and then accept it?

Frank Science

@JonasTeuwen ？

Jonas Teuwen

math.stackexchange.com/questions/165260/…

Frank Science

@JonasTeuwen ?

@JonasTeuwen write down the ... in your topic

@JonasTeuwen what?

Jonas Teuwen

You copy the proof of Blatter, just add some words and then accept your own answer.

That's quite... strange/stupid/whatever.

Frank Science

@JonasTeuwen First

@JonasTeuwen You can see whose answer I accepted

@JonasTeuwen Not mine, ok?

Jonas Teuwen

09:25

@FrankScience Huh... It was a BUG.

I swear.

Frank Science

@JonasTeuwen Next

Jonas Teuwen

I refresh the page and it is gone!

Frank Science

@JonasTeuwen Why I write that?

Jonas Teuwen

@FrankScience Sorry, sorry :-).

I'm serious the page showed the V next to your post...

Frank Science

@JonasTeuwen You can see that he edited his answer 1 hour ago?

Jonas Teuwen

09:26

(including the votes).

Yes.

Frank Science

@JonasTeuwen You know what he edited?

Jonas Teuwen

@FrankScience Yes.

Frank Science

@JonasTeuwen Just the difference between my outline and his.

Jonas Teuwen

@FrankScience I know, I know. Just $2 mapsto 3$.

But the website said you accepted your own answer. Which appears to be false.

Frank Science

@JonasTeuwen and $\bar M$ is the idea I've contributed.

Jonas Teuwen

09:29

@FrankScience That idea... is everywhere.

You do that to get a compact set.

Otherwise: does not make sense.

If you start with a compact one you might get in trouble.

Frank Science

@JonasTeuwen In his original proof, it's $\mathcal L$, not $\overline{\mathcal M}$.

@JonasTeuwen And StackExchange is not an open source system, so bugs are stated unless the administrator finds it.

Jonas Teuwen

@FrankScience Yes, that is a mistake, (but I explained that "intuitively").

@FrankScience It is probably just a database relation thingie.

Some database systems are very fast but can make errors, like the ones on Twitter.

Does not have to be a bug.

Frank Science

@JonasTeuwen Not mistake. His original idea of $\mathcal L$, but a closer check is necessary.

Jonas Teuwen

@FrankScience Well, no it is necessary otherwise you might get in trouble.

Take the open cover your own set + neighborhoods.

And he constructs a partition of unity, but I think you can this with convolutions as well.

Hmm. 8-).

Frank Science

@JonasTeuwen Get it? I'll delete my latest post.

Jonas Teuwen

09:34

No.

Okay.

Frank Science

09:46

@JonasTeuwen Well, where is it shown that I accepted my answer?

Jonas Teuwen

@FrankScience Not anymore, I refreshed the page as I said before! Then it was gone.

Frank Science

@JonasTeuwen Such bug might not be found out. It's hard for a programmer to find out a random bug.

Jonas Teuwen

I don't think it is a bug, but just the database setup.

Mr.Anubis

10:00

I require some help with josephus problem , can anyone please help me with it?

user19161

What's a josephus problem?

Mr.Anubis

I'm unable to understand the derivation of recurrence relation

Josephus problem

In computer science and mathematics, the Josephus Problem (or Josephus permutation) is a theoretical problem related to a certain counting-out game. There are people standing in a circle waiting to be executed. The counting out begins at some point in the circle and proceeds around the circle in a fixed direction. In each step, a certain number of people are skipped and the next person is executed. The elimination proceeds around the circle (which is becoming smaller and smaller as the executed people are removed), until only the last person remains, who is given freedom. The task is to c...

user19161

If it's complicated you will do better to post on main. If not and if you are lucky someone will answer in chat.

Mr.Anubis

@JasperLoy I hope someone does that on chat :)

user19161

@MrAnubis If so you should start by posting the problem. Otherwise we cannot read your mind.

Frank Science

10:24

@MrAnubis

@MrAnubis Josephus problem?

user19161

Hey @frank. How is your study of calculus now?

Frank Science

@JasperLoy indefinite integration is started.

@MrAnubis Here?

Mr.Anubis

@FrankScience Hi :) , chat.stackexchange.com/transcript/message/5193386#5193386

Frank Science

@MrAnubis yeah

user19161

@MrAnubis Haha.

Frank Science

10:27

@MrAnubis Which kind confused you? $k=2$ or $k>2$?

user19161

@FrankScience So you are mainly computing antiderivatives?

Frank Science

@JasperLoy Today I started.

@JasperLoy What's wrong?

user19161

@FrankScience Are you going to major in math or CS?

Mr.Anubis

@FrankScience The derivation of recurrence relation : upload.wikimedia.org/wikipedia/en/math/7/3/6/…

Frank Science

@JasperLoy undecided, but math is necessary.

user19161

10:29

@FrankScience Nothing, whatever you are referring to. Hey you know you can use the right arrow to reply so that I know which message you refer to?

Frank Science

@MrAnubis $f(2j)=2f(j)-1$?

Mr.Anubis

@FrankScience yes :)

Frank Science

@MrAnubis For example $j=3$

@MrAnubis 6 people here: $1,2,3,4,5,6$

@MrAnubis At first $2,4,6$ is killed

@MrAnubis am I right?

@MrAnubis So $1,3,5$ remains.

Mr.Anubis

@FrankScience f(j) tell which number will survive , right? , why would we use it in recurrence relation f(2j)=2f(j)−1 on right side of equation to solve bigger problem ?

Frank Science

@MrAnubis Now it's 3 people's case.

@MrAnubis Am I right?

Mr.Anubis

10:32

@FrankScience right :)

Frank Science

@MrAnubis $f(3)$ denotes the case of 3 people

@MrAnubis It is labeled $1,2,3$.

user19161

@FrankScience Is physics one of your options as well?

Mr.Anubis

@FrankScience ok

Frank Science

@MrAnubis $f(3)=1$, corresponding to the $1$ of $1,3,5$. $f(3)=2$, corresponding to the $3$. $f(3)=3$, corresponding to the $5$.

@JasperLoy

@JasperLoy wait a moment.

@MrAnubis can you understand this? my english is bad.

Mr.Anubis

@FrankScience What's that supposed to mean? I'm confused in that line

Frank Science

10:35

@MrAnubis OK

@MrAnubis when $2,4,6$ are killed, there remain $1,3,5$. if we relabel them, say, $1,2,3$, the remain problem is just the problem when $j=3$. am I right?

Mr.Anubis

@FrankScience true

Frank Science

@MrAnubis Now can you see that $\textrm{old label}=2\cdot\textrm{new label}-1$?

Mr.Anubis

@FrankScience oh boy !! , now I can see :) , but How does relabeling leads to solution ?

or am I too much idiot to see that?

Frank Science

@MrAnubis As in new label, the survivor is $f(3)$, is it right?

Mr.Anubis

@FrankScience yep

Frank Science

10:39

@MrAnubis So in the old label, the survivor is $2f(3)-1$, right?

Mr.Anubis

@FrankScience aahhh, got it :)

Frank Science

@MrAnubis In general, at first, $2,4,\ldots,2j$ is first killed, and there remains $1,3,\ldots,2j-1$. Just use the same trick, we can see why $f(2j)=2f(j)-1$.

Mr.Anubis

Thanks @FrankScience

Frank Science

@MrAnubis If you can't understand, try to think small. It doesn't bother you to do that.

@MrAnubis Incidentally

@MrAnubis I suggest you a book

@MrAnubis CMath

Mr.Anubis

@FrankScience Thanks I'll consider that :)

Frank Science

10:42

@MrAnubis In that book, a very general algorithm to determine the survivor is shown.

Mr.Anubis

@FrankScience you're cs student too?

Frank Science

@MrAnubis oh, no, high-school graduate.

Mr.Anubis

@FrankScience my mother :)

user19161

@FrankScience And possible future Fields medallist.

user19161

@MrAnubis What? :-)

Frank Science

10:44

@MrAnubis If you're cs student, well, The Art of Computer Programming is suggested too.

Mr.Anubis

@FrankScience Then what you're doing with that cmath book I'm wondering?

Frank Science

@JasperLoy Failure is mother of Success, you know.

user19161

@FrankScience Yeah, shi bai nai cheng gong zhi mu.

Frank Science

@MrAnubis I just overviewed that book.

@JasperLoy That might be what he meant mother.

user19161

@FrankScience Exactly. He meant wo de ma!

Mr.Anubis

10:46

@FrankScience good lord, good luck with future medals :)

user19161

@MrAnubis You are very funny, first it was the mother, now it is the lord. :-)

Frank Science

@JasperLoy My physics is very bad. Now it's high time for dinner. Bye everybody.

Mr.Anubis

bye :)

AgainstASicilian

13:44

hallo

anon

when will ddd/doit learn?

Gigili

14:06

Why the question mark is not in the link?

That's not the point, but still.

anon

because I didn't put it in the link..

robjohn

@Gigili editorial license

Gigili

Ah OK. Why I did not think of that beforehand.

@robjohn I deserve one!

robjohn

@anon Would that be an imaginary question? Perhaps if we multiplied it by $i$ we could see a real question.

Gigili

The weird thing is I see no question or edit history there that they are talking about in the comments.

robjohn

14:19

@Gigili The content was probably deleted within the first 5 minutes.

Gigili

Yeah, that must be the case.

user19161

14:41

@FrankScience So how was dinner?

Frank Science

Is there any sufficient and necessary condition easy to check that $f(x,y)$ is differentiable?

@JasperLoy Fine.

It is sufficient that $\partial f/\partial x$ and $\partial f/\partial y$ is continuous, but not necessary.

Differentiable at $(x_0,y_0)$.

AgainstASicilian

15:11

hallo

unNaturhal

15:24

Hi guys!

AgainstASicilian

is anyone here familiar with the game nim

N3buchadnezzar

16:22

soup?

Jonas Teuwen

@N3buchadnezzar Soup sounds like a terrific idea.

N3buchadnezzar

=)

unNaturhal

17:27

I'm sorry guys, I've a trouble... When I study discontinuity in a function, after doing $f(x_0)$ and the right and left limit for $x\to x_0$, how I have to continue?

Gigili

17:38

@unNaturhal Umm, I think that's it. Except you should check its domain. E.g. the denominator neq zero for fractions and such.

I suspect a user thingy will jump in and start insulting me right now.

unNaturhal

@Gigili Sorry, the domain of what?

Gigili

The function.

unNaturhal

I checked as first thing. I'm studying the function, an one of the things that the exercise asks for is to study discontinuity points..

Gigili

Yeah, I remember we had the same thing.

unNaturhal

Umh? :p

leo

17:56

hey

bye

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$Mathematics$ Mathematics