Mathematics - 2013-02-22 (page 1 of 5)

amWhy

00:16

@user58512 Me too!! (Maybe we should "lock" the comment to avoid "me too!" responses!)

@user58512 Just upvoted the question. I'll look for a modified answer, given all of @anon's help!

I missed it earlier today!

@OrangeHarvester hello!

@anon anon, what's your favorite abstract algebra text?

anon

if I had a nickel for every time I've been asked that I'd have enough money to actually buy one

I don't really have a favorite, I bounce from pdf to pdf too much to have a birds-eye view of what I cover.

amWhy

@anon That makes sense...Sorry to ask the same old, same old ;-)

Jonas Teuwen

00:32

Holy guacamole!

I have made quite some decent LaTeX -> HTML (for Wordpress) translator.

Including references and all, you know.

Well, actually it is just HTML, but I use it on my bloggie.

kan

@JonasTeuwen Wow!

BTW, do you know there is such a thing extant, I can guess yours might be better... can you point me to your code if you have them online?

@JonasTeuwen You write a blog? News to me. \heads to google.

Jonas Teuwen

@kan Yes. Here it is.

kan

@JonasTeuwen http:// :)

Jonas Teuwen

Argh.

kan

[](http://)

There we go. :)

Jonas Teuwen

00:40

Yes, I've tried all the options and then figured the problem.

I will publish the code when I figure out the best settings.

As I am not really satisfied with the markup.

Not at all, actually. But at least it parses.

kan

@JonasTeuwen Sure. :)

@Jonas Why not try something like Jekyll instead of breaking heads with WP?

Jonas Teuwen

I have many of such tools already (have a couple of big software projects).

But Wordpress has many advantages: you can link it to the others.

Alexander Gruber

l

Jonas Teuwen

Otherwise I'd have to break my head on how to connect all those tools while all I want is like a central place to make things work.

For my 'professional' things I have a subdomain called 'dashboard' and there all crap comes in. Notifications, server metrics etc.

Khromonkey

what is the difference between wordpress and blogger

kan

00:45

Hah! I see.

Jonas Teuwen

Reworking the latter to include more things like e-mail and calendar.

Yes - I had to boot up a new server to run WP as I did not want filthy PHP on my precious cloud...

That reminds me to choke it in a jail.

kan

@JonasTeuwen So if all goes well, you're writing a software for a modern mathematician... :)

Jonas Teuwen

Yes.

I want to make some software tools for academics.

kan

Great!

Jonas Teuwen

One to reduce headaches, not add.

I started it some time ago, but I will now shift to mobile platform immediately.

kan

00:47

Well, those that add won't survive the test of time. :)

Jonas Teuwen

Windows did 8-(.

kan

Oh, but, Windows attracts more users but more users who are OK with computer dictating terms. Not so many who'd like their computer do what THEY want use Windows.

Jonas Teuwen

I need to find a slick way to have an interface for the 'Eisenhower importance scheme' in the TODO app.

It should be a bit like on paper, the 'TODO list', but then actually easier to use.

user19161

Windows 8 is good.

Jonas Teuwen

It is so horrible.

kan

00:49

@JonasTeuwen True that.

Jonas Teuwen

Where is the bloody terminal?

kan

@JonasTeuwen He is talking about the windows on his house's walls, I'd preseume. ;-)

Jonas Teuwen

Actually it should work like a piece of paper but give you metrics FOR FREE!

Windows 8 is quite funny, but my desktop is not a tablet 8-(.

kan

@JacobBlack It sucks. I saw it. The Central Computer Center here has a couple of Windoze machines.

Khromonkey

@JacobBlack apply ice to the burned area

jking

user19161

00:51

@kan Yes, and 8 refers to my glasses.

Jonas Teuwen

Alright, my todo-list does not have all items marked and it is almost 2AM. For instance 'clean up room' from 2 weeks ago and 'throw out thrash' of two days ago is still there!

kan

Oops. Lazy you! ;P

Jonas Teuwen

I've been like constantly busy since 8AM 8-(.

Tim

thrash' -> trash?

Jonas Teuwen

Yes.

kan

00:53

@JonasTeuwen I know, I was just joking.

Tim

Busy man

Jonas Teuwen

I am so busy because I have such a low qualified job.

Tim

what job is it?

Jonas Teuwen

Lecturer.

Tim

Prof Jonas?

Jonas Teuwen

00:54

Professor is only used for full professors here.

And I do not have a PhD (yet).

That is why I am so busy, I need to speed up the process.

skullpatrol

Why is it "low" qualified?

Jonas Teuwen

Because almost all other positions are higher qualified.

And I do not feel less qualified than most of the people that have one of those jobs.

Tim

I always think you are very smart

Jonas Teuwen

Is that... good or bad?

Tim

Dont worry, jonas

good

Jonas Teuwen

00:56

In that case: thanks.

Tim

I am your admirer and fan

Jonas Teuwen

Hah, nice.

skullpatrol

I think of a good lecturer as a highly qualified job and I believe most students do to.

Tim

I admire people who are good at mathematics, and especially in functional analysis and stochastic processes and probability, because I am always troubled with all those questions.

Jonas Teuwen

It is very cute.

skullpatrol

00:59

Hi @Charlie

Argon

Hi @Charlie

skullpatrol

@Charlie Hi

amWhy

@JonasTeuwen What do you lecture?

what classes, I mean...

Argon

@Charlie Hi

Tim

functional analysis?

skullpatrol

01:01

@Charlie hi @Charlie

Tim

Charlie, please say hi back to them!

Argon

@Charlie hi @Charlie

Jonas Teuwen

Depends... now: nothing. Previous semester: differential equations.

Tim

PDE is hard

Jonas Teuwen

Now I supervise theses :-).

skullpatrol

01:02

$\Huge\text{Hi}$ @Charlie

Jonas Teuwen

One of them is in wave front sets in (quantum) optics - cool stuff.

Argon

@Charlie

Tim

What books in stochastic processes and probability and functional analysis do you recommend, Jonas?

skullpatrol

$\frac{Hi}{@Charlie}$

Tim

Do you maintain a list of courses and books or notes?

Argon

01:06

$\text{Hi}^{\text{@Charlie}}$

anon

hmm, is there notation for the $\pi(T)$-adic completion of a function field ${\bf F}(T)$? and its ring ${\bf F}[T]$ (or ${\bf F}[T^{-1}]$)

Tim

What is T?

anon

formal variable

Tim

ranging in which set?

anon

"ranging"?

Tim

01:07

I mean taking value from which set?

or "formal" means "formal"

Forgive my ignorance

Jonas Teuwen

I should have never put on the Mozart Violin Concertos - Now I will never be able to sleep before light comes again 8-((((.

Tim

maybe drinking a little will help your sleep?

anon

it doesn't take values, it's a formal variable, and $\bf F$ is a finite field. see polynomial ring and rational function field. (note that the adjective "function" is highly misleading)

Tim

Thanks

Charlie

@skull @argon hi boysssssssssss! How cute!

Tim

01:12

Dear lord

Charlie speaks!

Charlie

@Tim yes I dooooooooo!

Tim

Hope you are doing well

skullpatrol

@Charlie Hi

h

o

w

a

r

e

y

o

u

?

anon

:/

Charlie

@skullpatrol I'm good, skull

Jonas Teuwen

01:19

HOLY GUACAMOLE! What the heck are you doing?!

user19161

@JonasTeuwen Are you talking to your guacamole?

Charlie

@skullpatrol how are you ?

skullpatrol

@Charlie Fine thanks.

Charlie

@JacobBlack hi Jasper

Jonas Teuwen

@JacobBlack Yes.

Charlie

01:24

@skullpatrol good

Hello @jonas

skullpatrol

@Charlie Do you like expresso?

Jonas Teuwen

Hi.

I just threw out some old paper. Like 2000 pages 8-(.

Charlie

@skullpatrol no, I don't drink coffee

Jonas Teuwen

Still plenty left.

Charlie

@JonasTeuwen oh noes!

skullpatrol

01:27

@Charlie I brought you a cup

kan

@JonasTeuwen I have so much of papers to throw too. I haven't gotten around to it. :)

Bye folks.

skullpatrol

later

Charlie

@skullpatrol how cute :)

Jonas Teuwen

@kan Start writing correct things then! I keep trying, but still plenty of crap coming in... 8-(.

Good night guys.

skullpatrol

later

Charlie

01:29

Good night @jonas

user19161

@Charlie Hi M.

Argon

@JacobBlack Hi JB

Charlie

@JacobBlack :D

user19161

Geezis, I made a terrible miscalculation, luckily no downvote before I edited, phew!

Khromonkey

@JacobBlack I'd need some scotch to calm myself down after that

@JacobBlack is combinatorics more math or compsci?

user19161

01:43

@Khromonkey I don't know about comp sci, but it is definitely a major branch of math.

Khromonkey

@JacobBlack but comp sci majors seem to learn more of it

user19161

@Khromonkey Well, depends on what courses are offered. This varies greatly from uni to uni.

math101

Heyyy

amWhy

@math101 hey! hay...heigh...!

math101

@amWhy Hi

Ethan

02:05

If $\psi_0(q)$ is the digamma function, $$\sum_{\substack{\gcd(a,r)=1\\1\leq r\leq a}}\psi_0(\frac{r}{a})=-\gamma\phi(a)$$

skullpatrol

Hi @OrangeHarvester

amWhy

02:33

@Orange Yoo-hoo!? (You Who?) Yahoo!

@skullpatrol How'd you come up with your user?

Orange Harvester

@amWhy Me Orange!!!! Yahooooooooo....

@skullpatrol hi!

amWhy

@OrangeHarvester :-D

Orange Harvester

@amWhy Howz it going?

amWhy

@OrangeHarvester okay...could be better, could be worse. So, I'll take comfort knowing thing could be worse! Optimistic, hey?

@skullpatrol Is that a riddle? Maybe I'll call myself a "Cheesehead"

Orange Harvester

@amWhy Yes. I hope things are better with you soon. Optimistic is the right way to go.

amWhy

02:37

@skullpatrol Is that related to a fan of a particular team, or of a particular sport.

skullpatrol

@amWhy here

amWhy

@OrangeHarvester Yes, one always has hope...and I've got the essentials, and am better off that most folks in the world: I have a roof over my head, food to eat, a warm place to sleep, and passion and compassion...so I should answer that I'm doing well.

2

skullpatrol

@amWhy How'd you come up with "amWhy"?

amWhy

@skullpatrol I love the word "why" for one. But phonetically, it is identical to a letter in the alphabet...hint hint...

@skullpatrol I'll convert you yet: Green and Gold all the way. Go Pack! ;-)

Orange Harvester

@amWhy Yes. :-)

amWhy

02:42

@OrangeHarvester how 'bout you? Aside from as yet being deprived of an email from me ;-)

How 'goes it?

@skullpatrol naww...I won't try and convert. It's good to be dedicated, as you clearly are to your Raiders. I wouldn't want to deprive them of a loyal fan.

Orange Harvester

Well considering that that is the worst thing that can happen to me... :-(
But I am good, finally understanding the basic things in mathematics, so now can more forward.

skullpatrol

@amWhy I give up ... what letter is it?

m

amWhy

@skullpatrol "why" sounds like "y"

Now add that to "a...m...+

skullpatrol

:(

amWhy

@OrangeHarvester Great! What you moving on to?

@skullpatrol a+m+y = Amy

Orange Harvester

02:47

@amWhy Measure Theory.

skullpatrol

:D

amWhy

@OrangeHarvester Wow! Good for you. You can teach me what you learn ;-)

Orange Harvester

@amWhy Yes. :-)

amWhy

@skullpatrol I just don't want my name to be too obvious, to casual onlookers. Gender can be a liability in the field of mathematics.

@skullpatrol I have been playing around for over a month trying to construct a new user...to use...I'm rather attached to amWhy, but variety is good, and I need change to get out of my stagnant rut of a life.

skullpatrol

@amWhy Stagnation is never good ;-)

amWhy

02:54

@skullpatrol You're right about that. My biggest dread, as an adolescent (which still lives inside me) was living a stagnant life. So I'm committing to "shaking things up a bit."

Ethan

stagnant?

amWhy

@anorton You did a really nice job with this. Do you have "logicly" or some similar circuit construction software?

I see, you used LabView...I have logically. Your pictures are prettier.

user62753

If I have a double summation (two variables with bounds) what is the correction notation for showing that the variables gcd must be 1?

(sum i = 1 to x)(sum j=1 to y) yada yada
gcd(i,j)=1

peoplepower

You can use iverson brackets in the summand.

Link

Hi

skullpatrol

03:01

@amWhy The Raiders have always been committed to "shaking things up a bit." But we just hide it and call it "Commitment to excellence" ... it helps put an end to stagnation :-)

Link

Quick physics thing.

Say i have this image

peoplepower

I.e. $\sum_i\sum_j [\rm{gcd}(i,j)=1]\dots$

Link

And I make the raidus smaller

is work done negative?

user62753

@peoplepower but then what about the actual thing being summed

skullpatrol

@Link Yes, if pulling down on the string is considered negative work.

peoplepower

03:04

@user62753 What do you mean? You just multiply the bracket with the "yada yada".

user62753

for some reason that command [\rm{gcd}(i,j)=1] is throwing off the rest of the expression

peoplepower

Are you talking about latex?

user62753

yes

peoplepower

It is not clear what "throwing off the rest of the expression" means.

user62753

whatever \rm is it wants to apply to the rest of the expression

i have sum sum [\rm{gcd}(i,j)=1] rest of expression

peoplepower

03:08

Ah, in mathjax, I just use \rm, but you should use \gcd in a real latex document.

Link

@skullpatrol, thank you.

user62753

what is the proper way?

peoplepower

I am not the one to ask for proper latex usage in general, but here one should use [\gcd(i,j)=1].

user62753

fantastic; thank you!

peoplepower

There are other ways, that I will mention, one is to stack conditions under a single summation. I.e. you can have one row be i=1,j=1 and the row under it be \gcd(i,j)=1.

Khromonkey

03:27

what are the things I should study before doing an undergrad?

I really like math but I am sort of stupid

guys?

I need to take a bath good night

or goodbye depending where you live

MJD

04:31

data.stackexchange.com/mathematics/query/99148/…

3

In case anyone here would like to search for questions in which their answers might have been plagiarized.

skullpatrol

Thanks

+1

Orange Harvester

05:03

@MJD Would it be reasonable to post that link in the gnometorule's thread . So, as to allow more visibility to your query?

MJD

You may if you like.

I find se.math's rules about what is reasonable to post in meta to be inscrutable.

Orange Harvester

Hehe. Okay.

anon

se.math?

Orange Harvester

anon, anon, anon... when will you learn to commute? ;-)

MJD

math.se is confusing because it looks like a Sweden domain name.

user19161

05:09

@MJD I just saw your comment. I was rather shocked too.

MJD

On the bright side, I'm having fun composing queries.

Deleted posts are really not queryable.

I can search post histories for deletions, but I only find them for posts that were deleted and subsequently undeleted.

Orange Harvester

There is a sentiment on that meta thread, that the issue should have been dealt with privately by moderators, but considering that the issue was hidden for so long, I am not sure how not making it public would have helped the cause of finding the plagiarism in so many other posts.

@MJD Probably moderator can query deleted posts?

MJD

Surprisingly, no.

Orange Harvester

Ohh.

user19161

Sometimes I do post an answer, think of some improvement, and log in to find that others have answered, in which case I still go ahead with the edit.

anon

05:16

Hmm, I just rechecked the thread and am also shocked. Tsk tsk, amwhy.

user19161

Sometimes, I may have naturally used some phrasing of words to describe something because I have read an article 9000 times and sort of remembered it.

skullpatrol

...students a taught to read their notes 9000 times, no?

user19161

Yeah. So I am just raising some peripheral issues here for one to consider before trying to classifiy something as plagiarism or not, just general comments.

skullpatrol

So am I pal.

Plagiarism

Plagiarism is the "wrongful appropriation" and "purloining and publication" of another author's "language, thoughts, ideas, or expressions," and the representation of them as one's own original work. The idea remains problematic with unclear definitions and unclear rules. The modern concept of plagiarism as immoral and originality as an ideal emerged in Europe only in the 18th century, particularly with the Romantic movement. Plagiarism is considered academic dishonesty and a breach of journalistic ethics. It is subject to sanctions like expulsion. Plagiarism is not a crime per se but ...

user19161

@skullpatrol Most things in life are unclear...

skullpatrol

05:22

@JacobBlack ...maybe.

user19161

However, to copy something from X and accuse X of copying him, or to then lie to X that no copying was done, makes it a clear cut case of plagiarism.

MJD

Yes.

It also makes me a schmuck for letting it go.

user19161

So there is wrongful plagiarism, wrongful accusation and wrongful falsehood.

Orange Harvester

I agree with your sentiment, and believe me I am firm proponent of Everything is a remix but the fact that the following statement was copied and similar other statements were copying fails to strike me anything but willful.

"Amazingly, the answer that was left was the correct answer (he was working on finding roots of polynomials, I think). "

skullpatrol

...and wrongful wrong

QED

user19161

05:28

QED

anon

hmm, the only paper specifically covering eigenfunctions of the p-adic fourier transform I can find ... is in russian

Ben W.

Welp, time to learn russian.

user19161

Also, wrongful insult of people saying they have inflated egos for pointing out.

skullpatrol

What has been inflated can also be deflated, no?

(removed)

Ethan

@Sanchez do you think, $$\lim_{s\to 1}\frac{1}{\zeta(s)}\sum_{n=0}^\infty\frac{\mu(an+b)}{(an+b)^s}=0, \text{ for all coprime a,b, b<a}$$ is as strong a statement as, $$\lim_{s\to 1}\frac{1}{\ln(\zeta(s))}\sum_{p\equiv b\text{ mod a}}\frac{1}{p^s}=\frac{1}{\phi(a)}, \text{for all coprime a,b, b<a}$$

minopret

05:40

Hi from Philly area. Would someone mind to critique my question that is unanswered after 13 hours? Maybe it's just too long. math.stackexchange.com/questions/310306/…

Ethan

way to long

Sanchez

hi

minopret

I suppose I could chop off lots of it and possibly bring it back in another form some other day.

Ethan

@Sanchez do you think it would be any easyier to prove the first result, then the 2nd one?

Sanchez

what first and second?

Ethan

05:42

The limit involving the mobius function is the first

and the other the second

skullpatrol

@minopret +1 for effort :)

Sanchez

I don't know what you are talking about

Ethan

how can I refrence a previous comment?

in chat

minopret

@skullpatrol Thanks!

skullpatrol

@Ethan Drag it down to the message box

Ethan

05:44

5 mins ago, by Ethan

@Sanchez do you think, $$\lim_{s\to 1}\frac{1}{\zeta(s)}\sum_{n=0}^\infty\frac{\mu(an+b)}{(an+b)^s}=0, \text{ for all coprime a,b, b<a}$$ is as strong a statement as, $$\lim_{s\to 1}\frac{1}{\ln(\zeta(s))}\sum_{p\equiv b\text{ mod a}}\frac{1}{p^s}=\frac{1}{\phi(a)}, \text{for all coprime a,b, b<a}$$

skullpatrol

(removed)

awllower

:8220692

Orange Harvester

@minopret Your question is very vague. Kepler's equation is transcendental in the sense that is involves sine function which is transcendental itself, and hence, does originate from the fact that it is impossible to square a circle. But the focus of kepler's equation is not to prove such an impossibility. It already assumes that. Its focus is to express a relation between two quantities as a way to calculate stuff.

awllower

@minopret Hm.

I was just trying to refer to a previous comment in chat, not to you.
Sorry if this seems ofensive.

Having trouble understanding how to refer to comments...

@OrangeHarvester :)

Ethan

@anon can u give me some advice

anon

05:47

just paste the url of the permalink; chat will automatically turn it into a quote

probably not ...

awllower

:-)

Ethan

do you think it would be easyier to prove the first statement I wrote

as apposed to the second one?

anon

dunno

Ethan

:(

user19161

When the great anon doesn't know something, we can all go home.

anon

05:49

actually my guess is on the second

Ethan

really?

anon

yes, it's in the PLC notes I have linked to you, as J would put it, over 9000 times

minopret

@OrangeHarvester OK, that makes sense.

Ethan

Im pretty sure the first sum is $O(1/\zeta(s))$, so it would be $lim_{s\to 1} o(1/\zeta(s)^2)$

Orange Harvester

@minopret Also, I feel Kepler's Law does not depend on squaring the circle. That is, impossibility to square a circle is not the key point of proof in kepler's law.

@awllower Yo!

awllower

05:52

yo!

http://www.youtube.com/watch?v=mIydlgER51o
Call me danger...

If a group hs quite small order, then its irreducible representations have to be one-dimensional... Am I on the right track?

For examlpe.

hs=>has

minopret

@OrangeHarvester So practically every transcendental equation is as near to (and as far from) the topic of squaring the circle as Kepler's equation. And presumably transcendental numbers were considered (although not in terms of the quadratic closure of the rationals) long before Kepler. I suppose there's something there but it's not really special to Kepler's equation.

Sanchez

@awllower, what you said is wrong when over nonalgebraically closed field.

awllower

I would like to know why.

It only uses a dimensional argument, right?

minopret

whoops strike "(although not... rationals)" which was a very confused thought.

Sanchez

@awllower, the sum of squares statement is wrong.

awllower

05:59

Oh!
So what arguments still remain valid?

Sanchez

Em, I'm not sure what you can do in general.

awllower

But we still can decompose the representation into irreducible ones, right?

Sanchez

But for descent to $\mathbb{R}$, there're things you can say - start with an irrep $V/\mathbb{R}$, then the behaviour of $V \otimes_{\mathbb{R}} \mathbb{C}$ is known

Yes, semisimple part is still true.

awllower

Is that suggesting us to study the twisted forms of $V /R$?

43 secs ago, by awllower

Is that suggesting us to study the twisted forms of $V /R$?

Oh I know now. Thanks.

I mean I know now how to refer to previous comments, not that I know how to answer that question.

skullpatrol

27 mins ago, by skullpatrol

@Ethan Drag it down to the message box

Sanchez

06:12

I'm not sure what you mean by twisted forms. I don't know these well to be honest, but my impression is that if you start with an irrep $V/\mathbb{R}$, then $V \otimes_{\mathbb{R}} \mathbb{C}$ is either an irrep/$\mathbb{C}$, or irrep + its conjugate. So if you know what happens for all irrep over $\mathbb{C}$, you can use this to find all the irrep over $\mathbb{R}$ @awllower

awllower

@Oh It works like that, I was thinking about Galois descent techniques...

@Sanchez

Sanchez

I don't know what Galois descent is.

awllower

@skullpatrol Thanks for telling me that: it is very useful!!

An introduction!
http://www.math.uconn.edu/~kconrad/blurbs/galoistheory/galoisdescent.pdf

skullpatrol

@awllower Thanks for the video link :)

awllower

But I know it only through studying central simple algebras ...

skullpatrol

06:15

22 mins ago, by awllower

http://www.youtube.com/watch?v=mIydlgER51o
Call me danger...

awllower

What video? FOC?

Oh. NP:)

That series helped me a lot in learning English: I do not know why, but it was through my attempts to listen to their songs that I developped my English skills to some extent.

@Sanchez Might I suppose that you are a specialist in representation theory?

skullpatrol

Listen to as much as you can and back it up with reading the lyrics.

awllower

Indeed. :)
Those lyrics are oft quite funny!

Sanchez

@awllower, not at all.

I can try to answer your questions if I happen to know the answer.

awllower

@Sanchez Sorry for this misunderstanding then.
It just sounded that you know a lot on the subject. ^^

Sanchez

06:21

oh, not really - otherwise i could probably answer your question.

The relationship between irrep over $\mathbb{R}$ and $\mathbb{C}$ should be well known, but I can't work it out right now.

awllower

That is fine!
Looking forward to your solutions then. Hope I would work out it at that time.:D

skullpatrol

@awllower Here is another one :-D

awllower

:)

Very interesting!
Thanks for sharing!!

skullpatrol

np

:)

awllower

:)

Frank Science

06:47

I'm reading the proof of Lebesgue's monotone convergence theorem on Baby Rudin.

Nimza

Hi!)

awllower

hi

Nimza

Hm, anybody who heard about morphology of binary images, is there some topological description of binary image in this relation?

o, nice, it's a digital topology

robjohn

07:18

@Nimza what makes a topology "digital"?

Frank Science

@robjohn Suppose $\mathfrak M$ is a $\sigma$-ring and $\mu$ is a nonnegative measure on $\mathfrak M$. Put $\mu^*(A)=\inf\{\mu(E)\,\vert\,E\in\mathfrak M\land E\supset A\}$ and $\mu_*(A)=\sup\{\mu(E)\,\vert\,E\in\mathfrak M\land E\subset A\}$. Are $\mu^*$ and $\mu_*$ so called outer measure and inner measure?

robjohn

I was looking at Digital Topology

@FrankScience As I remember, that is correct.

Nimza

@robjohn I think it is called digital because it is used in computer science, but I'm not sure :) What do you think?

robjohn

@Nimza according to that article, that is right

Frank Science

What about $A_1\supset A_2\supset\dotsb$ and $\bigcap_{n=1}^\infty A_n=\emptyset$ implying $\mu^*(A_n)\to0$?

robjohn

07:39

@FrankScience countable additivity

Frank Science

@robjohn $A_n$ aren't necessarily measurable.

What does that mean?

user19161

07:59

@robjohn Never heard of that term.

Transcript for

$Mathematics$ Mathematics