Mathematics - 2016-04-21 (page 1 of 2)

PVAL

12:37 AM

@BalarkaSen Let me know when you have a proof.

Jessy Cat

12:56 AM

3

Q: Mobius Transformation and Schwarz's Lemma

My goal is to find a Mobius transformation $g$ that sends $K : |z| < R$ bijectively to itself, and also sends $0$ to $a \in R$. To my knowledge, there is a theorem that says the following: For a disc $K: |z| \leq 1$ and with $f:K \rightarrow K$ being analytic on $|z| <1$, $f$ is of the following...

Not my question, but I need it answered all the same.

The guy who answered it is wrong, I'm pretty sure.

Unless there's somebody here who can show me otherwise??

anon

1:44 AM

@JessyCat it should be $g_a(z)=R\cdot f_{a/R}(z/R)$ methinks

(notice how the $a$ changes)

Jessy Cat

@anon, it's not rendering right.

anon

renders right for me

Jessy Cat

Or maybe I just don't understand your notaion.

Why do you have $g_{a(z)}$? What does that mean?

anon

Guess.

Jessy Cat

And what does $f_{a/R}$ mean?

@anon, Come on.

anon

1:46 AM

Think.

This is a good exercise. Don't $g$ and $f$ depend on something?

Jessy Cat

A little hard to do when you've slept a total of 4 hours in the past ocuple of days

anon

sigh, k

Jessy Cat

I don't have time for good exercises.

I need to gete this done so I can go home and go to sleep finally

okay, so

lemme see

anon

$g_a$ is the desired function $D_R\to D_R$ which sends $0$ to $a$, and $f_{a/R}$ is the specified function with $a/R$ instead of $a$ (it is $D_1\to D_1$ and sends $0$ to $a/R$

(where $D_r$ is the disk of radius $r$ centered at $0$)

Jessy Cat

isn't that exactgly the same thing that was there before?

anon

1:50 AM

no

Jessy Cat

I don't understand

we had $Rf(z/R)$ in the incorrect answer and now it's $Rf(z/R)$ again

it doesn't map $f(0)=a$

@anon, can you just write out exactly what $g$ is and what $f$ is explicitly?

in the comments

not here

Please

anon

done

suppose it's still off, let me fix it

Jessy Cat

yeah, what do you do to the $x$ in $f$ to yield that?

and where'd the $e^{i \alpha}$ go? I know it only takes care of rotation, but why is it gone?

anon

in your formula for $f$, what's the angle $\alpha$ represent?

Jessy Cat

I think it draws out the circle. So it's like an angle of a sector, i suppose

anon

1:58 AM

but what is it?

Jessy Cat

Re^{i \alpha} is the circle

it's arg(z)

Arg(z)

anon

then how is that a mobius function of z?

Jessy Cat

$\Arg z$

Weell, my prof seems to think it is

he put it in the notes after all

anon

are you sure alpha is arg(z)?

Jessy Cat

no

not anymore

anon

1:59 AM

where does your $f$ sends $0$?

Jessy Cat

@anon, $e^{i \alpha} * -a$

doesn't seem right

anon

mmhmm

Jessy Cat

$-1$?

anon

I think you want $\displaystyle f_a(z)=\frac{a-z}{1-\bar{a}z}$ to be the mobius transformation of the unit disk that sends $0$ to $a$ (where $|a|\le 1$)

then $g_a=Rf_{a/R}(z/R)$ is the mobius transformation of the disk of radius $R$ which sends $0$ to $a$ (where $|a|\le R$)

Jessy Cat

$|a|\|e$?

you mean $\leq$?

anon

2:04 AM

where are you talking about?

nowhere have I typed $|a|\|e$

Jessy Cat

$|a|\le 1$ rendered as that on my page

unless that's $\le$?

I'm not familiar with that tag. I either use $<$ or $\leq$

which is it?

anon

both of them render as $\le$, less-than-or-equal, in my browser

Jessy Cat

not mine

i'm using opera

anyhoo

anon

that's super weird

Jessy Cat

nothing renders for me here

anon

2:06 AM

are you using the latex bookmarklet?

nope.

why not?

is it a plug in?

see "$\LaTeX$ in chat" above the starboard in the chatroom description --------->

Jessy Cat

Never even heard of it until you just told me about it.

Ok, I will do that later.

anon

2:07 AM

you just drag/drop the link to your bookmarks bar, then click start chatjax when you're in this tab

Forever Mozart

I did it

anon

it takes 10 seconds

(ofc maybe more the first time...)

Ted Shifrin

howdy @anon, @Jessy, @ForeverMozart

Forever Mozart

hi there

Jessy Cat

@anon, Like i said. trains stop running after a while and i have to get home. time is of the essense. so later

Shahab

2:08 AM

Is there a book which covers all of the core graduate school mathematics in a dense and compact manner? This includes all core material: algebra, analysis, combinatorics and graph theory. I have found a book by Hua but it is geared towards undergraduate mathematics.

anon

hey ted

Ted Shifrin

No, @Shahab

Forever Mozart

I constructed a psychotic space for the ages

Ted Shifrin

I wouldn't include combinatorics and graph theory as "core material" for graduate school, either.

Forever Mozart

now the tedious part of writing everything down

Shahab

2:09 AM

What about just algebra, analysis

Ted Shifrin

Well, @Forever, it's only then that you find out if there are any unmendable gaps :P

And topology of various sorts ... and core applied math. No, @Shahab, I know of none.

Forever Mozart

@TedShifrin yes, I tried this before, and there was a literal gap in my construction :D

But I think I fixed it

Shahab

What would you consider core applied math?

Forever Mozart

diff eq

Ted Shifrin

@Forever: It was after I already had a job offer after grad school that I discovered a major gap in the proof of my main theorem for my Ph.D. You can imagine a week of sleepless nights.

Forever Mozart

2:11 AM

I can totally imagine that

Ted Shifrin

Numerical analysis, theory of ODE and PDE, yes.

Shahab

OK...Is number theory not considered core graduate material

Forever Mozart

When you find one thing wrong, its like suddenly the whole thing unravels

and your mind starts racing

Ted Shifrin

Not core, @Shahab, no. For example, I never took a single course in number theory.

anon

@TedShifrin hopefully your phd thesis was about things that exist

Forever Mozart

2:12 AM

like sand going through your fingers

Ted Shifrin

You referring to the famous story about the Ph.D. thesis on functions with Lipschitz exponent $>1$, @anon?

anon

:)

Ted Shifrin

Well, plenty of them exist. They just are very dull. Not worth 80 pages. :)

Forever Mozart

I hope you were able to fix it.

its the most awful feeling in the world I think

Shahab

OK. Thanks. If there was such a book would it be useful in your opinion? Specifically for teachers and those who are preparing for job interviews

Ted Shifrin

2:13 AM

Yes, but it was more subtle than I'd realized. @anon would be shocked to find out what my error was.

anon

(a+b)^2=a^2+b^2

Forever Mozart

lol

Ted Shifrin

@Shahab: You sound confused. What do teachers and those preparing for job interviews have to do with going to grad school?

Nope, @anon, not quite that stupid.

Forever Mozart

but seriously my calculus students do that, and they also cannot do fractions

ridiculous

Shahab

Suppose someone needs to to refresh all the things he/she has learnt quickly. Standard textbooks will take a lot of time

Ted Shifrin

2:15 AM

I had a group action on a space and a function (well, actually differential forms, but that doesn't matter) invariant under the action. I claimed the function had to be constant.

Grad school takes a lot of time, @Shahab. I don't get your point.

Shahab

Suppose someone has done grad school many years back (me for example). I want to revise all the stuff within a month.

Ted Shifrin

Not possible.

Forever Mozart

My life is boiling over
It's happened once before
I wish someone would open up the door

Don't you know
There's fire in the hole
And nothing left to burn

Ted Shifrin

You will realize that you've forgotten almost everything.

Forever Mozart

I'm exhausted from this proof

Shahab

2:17 AM

Ok. So the standard textbooks (written from the point of view of a first learner) are the way to go?

Ted Shifrin

If you took courses and did exercises, exams, start by reviewing all the stuff you did, yes.

Why are you trying to do this, @Shahab? What's the goal?

Forever Mozart

@TedShifrin what are the odds of someone proving the same problem at the same time, given that it's been open for around 40 years?

Shahab

the goal is to write such a book. I am wondering whether it is a useful endeavor

Forever Mozart

I feel nervous about it

Ted Shifrin

I doubt it, @Shahab.

Shahab

2:19 AM

all right. Thanks for your opinion.

Ted Shifrin

Graduate-level mathematics is a lot of deep ideas and techniques. Not something you can write a Schaum's outline for.

DogAteMy!

Shahab

yes

Simeon

If $f$ is continuous with at least one root, is it true that for any point $x$, there is a root of $f$ that is closest to $x$?

Ted Shifrin

@Forever: Honestly, the chances are probably infinitesimal. But, even if it happens, if you know nothing about the other person (and vice versa), it is still degree-worthy (if it was in the first place).

No, @Simeon.

Unless you know the set of roots is a discrete set.

Forever Mozart

that's a good way to think about it

Akiva Weinberger

2:22 AM

So I'm finally at an airport. Someone teach me about blowups?

Ted Shifrin

Airport? Huh?

anon

blowing up 8 pts on a plane joke reference

Akiva Weinberger

I'm going to Israel for the Jewish holiday of Passover

Forever Mozart

lol, what was the context behind @MikeMiller's comment on the right?

Ted Shifrin

Oh wow, safe voyage, DogAteMy.

anon

2:24 AM

@ForeverMozart US would have more money for things like education if not for throwing a lot of it at military stuff

Ted Shifrin

BTW, DogAteMy, I am (unobservantly) Jewish. I certainly know what Pesach is :P

Forever Mozart

@anon yes, and at football

Akiva Weinberger

Oh, I didn't know

Forever Mozart

the freaking coach makes 5 million a year

Ted Shifrin

Don't get me started on college athletics ...

Forever Mozart

2:27 AM

the math building is 50 years old and crumbling, but we have an indoor practice field!

hell, it's probably 60 years old

Ted Shifrin

Well, @Forever, you only have to look at the presidential/state politics to realize how screwed up this priorities in this country are.

Forever Mozart

I'd rather not go down that road, let's stay positive

Ted Shifrin

I didn't realize we'd been positive.

Forever Mozart

talkin math is positive :)

Ted Shifrin

@anon never followed up on the major gap in my proof — oh well. :P

anon

2:33 AM

heh

Forever Mozart

if it's in analysis, I probably wouldn't understand it

I only know the basics

Ted Shifrin

Well, it was really a basic notion of group actions ... Somebody invariant is only constant when the action is transitive :(

Forever Mozart

is it possible to write a PhD thesis about more than one problem?

Ted Shifrin

Sure.

Forever Mozart

I have 2 or 3 problems in topology I've been working on

and I've made decent progress on each

but no home run yet

Ted Shifrin

2:37 AM

Well, there's a question of when "decent" constitutes degree-worthy or publishable, but, sure.

Forever Mozart

my advisor thinks some of it is publishable

Ted Shifrin

Well, your adviser is ultimately the arbiter.

Forever Mozart

but I'm such a perfectionist that I'll never arrive at a draft that I'm happy enough to publish

Semiclassical

evening

Brody

Real quick... Is it possible to write $$\int_{c}^{d}\int_{a}^{b}(x^2y+2x^3y+3x^2y^2)\,\text{d}x\text{d}y$$ as a sum of three double integrals and then "split" each by $x$ and $y$?

Semiclassical

2:39 AM

the tricky thing about doing multiple problems is whether you can arrange them into one thesis

Ted Shifrin

Hi @Semiclassic

Yes, @Brody, because you're integrating over a rectangle. (Taking the sum of the integrals is never a problem.)

Forever Mozart

@Semiclassical well two of them are sort of related, but the third is not related at all

Ted Shifrin

hi @skull

skill patrol

hello Professor @TedShifrin

Brody

Thanks @TedShifrin

Forever Mozart

2:41 AM

@skillpatrol steely dan is 70s, yes :)

skill patrol

:)

pure 70s

Ted Shifrin

who's from the impure 70s?

Forever Mozart

not me, I just listen to steely dan and neil young lately

Brody

Can this can be generalized to any multiple integral of a polynomial in $x_1,\ldots,x_n$ provided the domain of integration is "rectangular"?

Ted Shifrin

I mean, Woodstock was impure, but it was 60s.

Forever Mozart

2:43 AM

69/70, who's counting

Ted Shifrin

Needn't be a polynomial, @Brody. As long as you can write a term as a product of $f_1(x_1)f_2(x_2)\dots$, you can do it for a rectangular domain.

OK, I'm heading off. Take care, all.

Brody

Gotcha @TedShifrin. It only need be a sum of terms where each is separable. Thanks again!

skill patrol

Cya later

Forever Mozart

@TedShifrin bye. glad I could be of use with the Dowker spaces

Brody

Bye TS

Forever Mozart

2:46 AM

@BalarkaSen you here?

Forever Mozart

3:02 AM

any topologists here???

Akiva Weinberger

So why is $\frac{\operatorname d}{\operatorname d\!x}\rm Istanbul$ equal to $0$?

Because the derivative of a Constantinople is zero!

Brody

What is the (perhaps geometric) intuition behind the surface integral of a scalar-valued function?

Forever Mozart

@AkivaWeinberger whaaat

Brody

Hold that question. I'm being less lazy and looking at reference sites now.

Akiva Weinberger

@ForeverMozart Constantinople

Forever Mozart

3:12 AM

oh, wow

very clever

Brody

Take 2... What is the (perhaps geometric) intuition behind the surface integral of a scalar-valued function?

Forever Mozart

it's just the "volume" of the domain times the scalar

assuming you're working with functions from $\mathbb R ^n$ to $\mathbb R$

Brody

For simplicity we'll say the scalar field is in $\mathbb{R}^3$

Forever Mozart

oh

sorry I dont do that

Brody

oh no :(

I admit my phrasing is rarely decent

Akiva Weinberger

3:17 AM

How do you make $\Bbb R^3$ a field?

anon

you don't

they're talking about scalar fields

Akiva Weinberger

What's a scalar field

Forever Mozart

I just thought about something

anon

meaning, scalar-valued functions

like a vector field, but with scalars

Forever Mozart

let's say you had to give one presentation to be king

Akiva Weinberger

3:18 AM

Ohh

Forever Mozart

to get the ultimate job or whatever

Akiva Weinberger

So, nothing to do with algebraic fields

anon

nope

Forever Mozart

could you hire a personality coach

Akiva Weinberger

Aha

@ForeverMozart Is this the setup to a joke

Forever Mozart

3:19 AM

to help you know exactly what jokes and so forth would work on the audience?

to gauge your personality and help you with delivery and so forth?

anon

you need to get a feel for what kind of personality the interviewer would like to work with, or thinks their employees would like to work with

Forever Mozart

maybe that's what I need

cause I have a killer result but people don't like me LOL

Mike Miller

I mean, there are still plenty of senses in which R^3 can be made a field...

Forever Mozart

random thoughts

Brody

Perhaps it was better to say the surface integral has an integrand $f(x,y,z)$

Forever Mozart

3:21 AM

@AkivaWeinberger not a joke, a real problem

Brody

I still don't quite understand from earlier @ForeverMozart

I believe the line integral can be thought of as drawing a "curtain" under the scalar function, giving the area. Much like an ordinary univariate def. integral

Forever Mozart

@Brody what exactly?

I should hire Sean Penn or someone in Hollywood

to help my presentation style

a professional liar

Brody

Having trouble making an analogous visualization for surface integrals of scalar functions

probably since the integrand is already in three variables so the "curtain" would (keeping in analogy) extend "through" a fourth direction

Forever Mozart

its all in your head

Brody

Right... Probably overkill anyhow. I suppose a surface integral simply sums all the scalar values along the surface like any integral of this type would.

Forever Mozart

3:27 AM

age is an issue of mind over matter. If you don't mind, it doesn't matter.

put that in your pipe and smoke it

2

Jessy Cat

It's 4/20 and everything

Forever Mozart

HAHA perfect!

@JessyCat you made my day

Jessy Cat

@ForeverMozart, I think I just made my own day

Duuude, star it! star it!

Forever Mozart

lol

i did dont worry

Jessy Cat

Muh, not that! The 4/20

Brody

3:29 AM

seems like poor practice :p

Forever Mozart

I didn't even realize today was 4/20

Jessy Cat

Cheech and Chong do analysis

Forever Mozart

all my dropout former friends are celebrating

@JessyCat analysis does make me sick

Jessy Cat

When it's taught right, it's not supposed to.

it's supposed to be fun :)

Forever Mozart

my professor was a pugilist

or a masochist

Jessy Cat

3:32 AM

interesting. one of mine did martial arts, but not boxing

Forever Mozart

he was german. very tough

classical blonde hair blue eyes 6'2''

Jessy Cat

the one i've got right now though reminds me of Mr. Mackey from South Park in the "drugs are bad, mmmkay?" episode when his head turns into a balloon and flies away

Forever Mozart

ever had a schizo professor who turned his back to you when he talked?

there's a saying

Jessy Cat

Yes, and ones who just point and gesture a lot.

And one guy who would never move so you could see what he was writing on the board

Forever Mozart

the extrovert mathematician is the one who looks at YOUR feet when talking to you

Jessy Cat

3:36 AM

First analysis prof I had was an Italian guy from Brooklyn. Best teacher ever.

Forever Mozart

I can imagine

Brody

passing question, are grad math professors better or worse than undergrad?

not precluding that some teach either

Forever Mozart

they just assume you can do more

usually very matter of fact, and if you can't understand something it's your own fault

Brody

makes sense for them to set a bar for realizing one's "mathematical maturity"

I just hope they don't use it as an excuse for lazy teaching

Forever Mozart

exactly. I had a famous real analysis professor who said I lacked mathematical maturity whenever my proofs were not as direct as possible

this guy was something else

Brody

3:40 AM

direct in what sense?

Forever Mozart

he stared off into space when talking to you

like he was in tough with higher being

touch

"you overuse proof by contradiction" and so forth

I've been lucky to meet some real characters

Brody

i can see how that critique can be justified, but he sounds like an offkey guy

Forever Mozart

very strange yes

Brody

well at least these characters made your school career more interesting

I'm heading out though. gn all

off to finish 4/20 with a bang, by listening to pascal rogé's piano and reading a book

Forever Mozart

lol, enjoy

@BalarkaSen where are you?

all you need in this life is ignorance and confidence, and then success is sure.

It is better to keep your mouth closed and let people think you are a fool than to open it and remove all doubt.

I can go all night.

all I ask of you, is make my wildest dreams come true

katy tried, I was halfway crucified

I was on my way to the other side of tomorrow

I should be a fuckin poet

skill patrol

3:58 AM

you are! a poet of logical ideas ;)

Forever Mozart

why thank you!

I needed some cafe music today, this proof is killing me

literally, I think I've aged 5 years in 4 months

Erdos is a monster

skill patrol

don't burn out :P

Forever Mozart

@skillpatrol I'm close. If there is a problem with my current proof, fuck it.

@skillpatrol you used to be skull patrol, right?

skill patrol

yup

i still have a skull army ;-D

Forever Mozart

oakland raiders?

skill patrol

4:14 AM

4life

sasha

6

Q: How to find the element of the Digit Sum sequence efficiently?

Just out of interest I tried to solve a problem from "Recent" category of Project Euler ( the link Digit Sum sequence ). But I am unable to think of a way to solve the problem efficiently. The problem is as follows ( in the original question sequence has two ones in beginning , but it does not ch...

time-complexity number-theory

Forever Mozart

sorry it's 4.20 I cant do anything

2

skill patrol

4:35 AM

@robjohn pardon me for imposing on you about the math mod office :)

i didn't realize Arthur changed his username

Forever Mozart

age is an issue of mind over matter. If you don't mind, it doesn't matter.

skill patrol

so are a lot of things

robjohn

5:20 AM

@skillpatrol impose? when?

skill patrol

@robjohn when I asked you to consider putting the math mods' office on your favourite room list.

robjohn

@skillpatrol Oh, no problem. I just ignored it ;-P

skill patrol

:-D @robjohn

datalava

5:39 AM

Someone save be from my despair; I'm grading calculus tests

skill patrol

what's the average so far?

datalava

I'm just going question by question so I'm not sure. I've been grading this class all semester though so I know it's not going to be very high lol

skill patrol

differential?

or integral

datalava

It's a class that's a watered down combo of both for non-math/science majors

skill patrol

ok

datalava

5:42 AM

So they did derivatives and this test is on very simple integrals basically

skill patrol

non-math/science majors just need the "big picture" view, no?

datalava

yeah I think that's the idea

Anyway, this was my mental break and obligatory complaint. Grading is the last thing on my end of semester crunch list. (I can do it!)

skill patrol

Have you seen this? @datalava

datalava

No. I've watched some of the OCW calc courses though. Looks like maybe the same professor

I'll watch that later -- thanks thumbs up

skill patrol

:)

Tobias Kildetoft

7:01 AM

@AlexClark Hey, I see that Peter McNamara answered an question on MO that was so old that Ben Webster (who had asked it) had forgotten why he was interested in it in the first place :)

datalava

7:26 AM

@skillpatrol this seems like a nice resource for teachers of calculus to frame the course

(wow that is not a good english sentence i.am.tired)

Agawa001

8:06 AM

what kind of professors are permitted to be taken on in your unis both of ya ?

Jessy Cat

@TobiasKildetoft, that sounds like a "yo momma" joke.

@Agawa001, I think for us, they have to be tenure-track, research professors who teach at the graduate level.

Tobias Kildetoft

@Agawa001 I am not sure what you mean by "what kind" of professor

Jessy Cat

Yo momma so old, she as old as a question Ben Webster asked about once and forgot why he asked it. Burrrrn

Agawa001

i thought they bring em from shaolin school and madhouse

Jessy Cat

I think it's also good if they've never been convicted of a felony. Although that really doesn't have a lot to do with job performance, so...

$\frac{1}{2}$

Duuuuuuude

Agawa001

8:30 AM

the only eccentric prof i had in primary school, he wore a pair of big oval glasses that made his eyes unproportionally big relatively to his face

and he talks in cryptic way, he uses mathematical symbols like overall, it exists, equivalence , induction, inclusion, deduction, all these logical notations that make his interlocutor waiting the opportun moment to give up the convo

user116211

user116211

Book - An Introduction To Algebraic Topology by Joseph J. Rotman

iwriteonbananas

Hey

@MAFIA36790 lol that's pretty good

datalava

A fellow student was talking to me today about infinitesimals today, and I guess I never really knew or considered the true definition of an infinitesimal... Is one allowed to use them practically in mathematics? I'd like to learn more about this

Tobias Kildetoft

@datalava They can be defined in precise ways, but this usually takes quite a bit of theory

How one does it also depends on what one wants to do with these

datalava

8:42 AM

Do we use them in defining integrals?

Tobias Kildetoft

@datalava They probably could if one took that route, but I have never seen it done that way

Not many people really work with them

datalava

lol apparently the concept was banned by catholic scholars in the 17th century

Tobias Kildetoft

@datalava So were most things probably (not that the concept had been made anything near precise at that time)

datalava

"that a continuous line is composed of distinct and infinitely tiny parts"

dangerous thinking, apparently

but that's hardly the actual definition of an infinitesimal

Tobias Kildetoft

@datalava Indeed, the actual definition is easy enough, it is just a matter of constructing a place where it lives ($x$ is an infinitesimal if $0< x < a$ for all positive reals $a$)

datalava

8:48 AM

and, is this related to the concept of a set of measure zero?

Tobias Kildetoft

@datalava Not really

datalava

9:00 AM

Seems like it's just more useful to define things in terms of arbitrarily small real numbers than trying to use infinitesimals, then..

Tobias Kildetoft

@datalava Well, arbitrarily small reals then need to be replaced by limits

There is a certain attraction to just being able to pick an infinitesimal and work with that (though as I said, this is not often done)

datalava

@TobiasKildetoft okay.. thanks for your comments!

g'night

Tobias Kildetoft

@datalava If you are interested in the constructions, my favorite one is of the surreals via combinatorial games

Gridley Quayle

9:22 AM

Could some give me a hint in proving that if $f$ is not continuous at $c$ then it is not necessary that $\lim_{n \rightarrow \infty}f(x_n) = f(c) $ even if $\lim_{n \rightarrow \infty}x_n =c$. I think I need to construct a counterexample and then use the definition of discontinuous but I am not too sure exactly how.

Tobias Kildetoft

@GridleyQuayle For an example, try the function that is $1$ everywhere but at $0$ where it is $0$

And pick a sequence that converges to $0$ but is strictly positive for example

Gridley Quayle

Tobias Kildetoft

9:37 AM

@GridleyQuayle The sequence $f(x_n)$ will be constant $1$ if you pick things like I said

Gridley Quayle

Oh sorry, I worked through your example and then I was trying the general case

In your example we can pick $x_n = \frac1n$.

Tobias Kildetoft

Ahh

Gridley Quayle

But I figured I could use a similar approach for any f

Valery Saharov

Anyone to help out with math.stackexchange.com/questions/1745355/… ?

Tobias Kildetoft

@GridleyQuayle Indeed, there will always be such a sequence

Gridley Quayle

9:42 AM

Thanks.

Balarka Sen

10:21 AM

@MAFIA36790 hah. HAH.

Gridley Quayle

10:44 AM

How can I go about finding two continuous, non-differentiable (at $x=0$) functions such that $f(0)=g(0)=0$ and $f(g(0))=0$ but $f(g(x))$ is differentiable at $x=0$. I feel like you'll need $f=g^{-1}$ but I haven't made any progress in finding one.

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$Mathematics$ Mathematics