1:00 PM
Small hands, easily distracted, and indeed, I do not know much Tchaikovsky

: )

in fact my ability to play seems to have diminished.
I can't seem to press the right keys.

That sounds like a case of not enough practice...

Actually, I've been practicing only one relatively simple piece for the last few weeks and I still can't play it right...

I can relate to that.
Which reminds me: going to practice now, bbl : )

1:13 PM
I have no problem playing one octave by one hand, e.g. as in the beginning of Mendelssohn's Wedding March: i.stack.imgur.com/qvBLa.png
But I doubt I have a chance to get to the level you're speaking about (playing Rachmaninoff). Especially considering that I hardly play once in a month now...

@QED It's just plain wrong. Same misconception. I added a comment.

I can span about a major 9th, but anything larger is difficult.

Major 9th means betwee C and E?

C to D

I mean c1 and e2.

1:18 PM
C to E' would be a major 10th, I think.

Don't have keyboard here to try, but I guess if there only these two notes, I would be able to do C ti D. But trying to play some notes in between by the same hand would be a problem.

Sometimes though, I wonder if there are some secrets no one ever taught me about reading music. Like this:
I'm not convinced that's meant to played exactly as written...

Well you can try music.SE to find out about musical secrets.
@ZhenLin Why do you think that?

It looks like it's meant for three or four hands!

Of course there are always things like phrasing and dynamics (strength), which every player does slightly different.
@ZhenLin Because of the jumps in the left hand?

1:22 PM
Well, the right hand seems to have two things going on at once...

@Srivatsan If A has full rank, you can invoke inertia, since you can treat the cross-product matrix as a sandwich with the identity matrix within.
I wonder if there's a MathJax equivalent for LilyPond...

Probably quite a bit harder...

It's hard to say just from the sheet music; not having an actual keyboard here. The first line seems difficult, I would guess that second and third are playable.
But you would have to ask somebody more experienced.

I imagine it's playable: I have recordings! But no video.

@JM I used pmx to write music in LaTeX, but it was long time ago. Now I don't even have it installed on my computer...

1:30 PM
Lilypond seems nice enough, but I have difficulty getting the octaves right the first time...

(Speaking of music: Yanni is so damn relaxing to listen to...)

Can we close this question, please? I'm getting tired to see it popping up, incomplete and incomprehensible as it is, while the OP has long left the building.

@tb I used "too localized" in place of MO's "no longer relevant"...

@JM thanks, that's what I had chosen before my vote withered away...

@tb I did not know that close votes expire after some time...

1:45 PM
What is the problem with the problem?

@Srivatsan Simply put, the unregistered user has abandoned the question posed.

Having a few experienced users here, do you think that could be an useful tag? I think there are a few questions concerned with the properties of limsup and liminf. Usually they're tagged limit.

@MartinSleziak If there's more than ten, I think it's justifiable.

@Srivatsan it is unclear what is being asked... Is inner or outer measure of $E$ meant by $m\ast(E)$ (then the question whether it works for non-measurable $E$ has an obvious negative answer since $E$ is measurable if and only if $m^\ast(E) = m_\ast(E)$ assuming completeness, or the question doesn't make sense). If ordinary measure is meant by $m\ast(E)$ then the question doesn't make sense. Either way: the question is incomplete and not answerable in its current form.

1:53 PM
@MartinSleziak I don't have a strong opinion. I think it might be useful but far too down the tag hierarchy.

A few questions where this tag would (in my opinion) make sense:
http://math.stackexchange.com/questions/6168/definitions-for-limsup-and-liminf
http://math.stackexchange.com/questions/8489/liminf-of-difference-of-two-sequences
http://math.stackexchange.com/questions/60873/limit-supremum-limit-of-a-product
http://math.stackexchange.com/questions/60229/limit-supremum-finite-limit-meaning
http://math.stackexchange.com/questions/73508/an-exercise-on-liminf-and-limsup

@tb One question: can you elaborate on the obvious negative answer? I'm asking because the question only says $m_{*}(F)=m*(E)=m^{*}(G)$, not $m_{*}(E)=m*(E)=m^{*}(E)$.
Duh! Sorry, got it.

@MartinSleziak I don't see why not, but maybe ask on meta to be sure?

It bugs me that $m*$ was never explained/corrected.

@DylanMoreland It's the convolution of $m$ and $(E)$.

1:57 PM
I tried to make it more readable, but for some reason this does not make a clickable link: 8489
Now it did... ?

Yes, it did.

@Srivatsan :)

@MartinSleziak funny: this link is entirely hidden behind the "flag/star/reply" tools for me.

A few questions where this tag would (in my opinion) make sense: 6168 8489 60873
Hopefully now it is ok.

That passed J.M.'s "10 test" =)

2:01 PM
I'm looking for the book "Symmetry Methods for Differential Equations: A Beginner's Guide" by Haydon. Is there some ebooks-site to which I hope my university has a subscription that has this book? ebooks.cambridge.org doesn't seem to have it.

@JM You meant a new question probably. (We do not have some long thread for introducing new tags, such as we have for merging, do we?)

Sorry to bring this up at the same time (I have to go shortly). I think a [continuity] tag will be useful. What do you think?

@MartinSleziak Oh, right. A new question... but I think the new tag is wholly defensible anyway.
@Srivatsan e.g.?

@Srivatsan Like today's question about equivalent definition of continuity?

@MartinSleziak Yes, that's one. I missed that tag for my previous question. =)
@MartinSleziak The two that you mention -- they would be an ideal fit. =)

2:05 PM
@JonasTeuwen So, not this one?

@JM Well, if that's the opinion of the "chat comittee" than perhaps I could just introduce the tag. If someone will disagree, he will probably post his objections at meta.

@JM Holy cow. I just entered the title in the search and it didn't give me anything!
Too bad I can only see the contents pdf :(.

@MartinSleziak Yes, I think so. :)

@MartinSleziak There are loads of question about "uniform continuity". May be that should be a different tag? Not sure.

@JonasTeuwen Invariably, I've found that built-in search boxes on most sites are less than optimal compared to a suitably-restricted Google search.

2:07 PM
@Srivatsan Well I agree that seems useful. IIRC there were questions about relation of continuity and sequential continuity, which would fit this tag.

@JM Thanks. The website recognizes my IP but it tells me I have access to nothing.

Not sure about uniform continuity questions, but I think they should go under a different tag. I would expect most of "continuity" question be in and "uniform continuity" in .

@JonasTeuwen Aw. :( Maybe you can bug the library to get it for you...

@MartinSleziak OK, I have to go now. But I will make a better case study when I am free.

The library has it but doesn't have it available in their catalogue because it needs to be transfered to the main library :-/.

2:09 PM
Here's a challenge for your Google skills... can you locate an online copy of: Walter Rudin, Lebesgue’s first theorem (in L. Nachbin (Ed.), Mathematical Analysis and Applications, Part B, in Advances in Mathematics Supplementary Studies, Vol. 7B, Academic Press, New York, 1981, pp. 741–747)?
2

@MartinSleziak In fact, something like that went through my mind as I wrote that comment. Hence the addition "Maybe that should be different tag? Not sure." =)

Jonas: Then I don't see any other way than using some warez website ;-)

What I'm really curious to see is the "very easy example" mentioned by Brian in his answer here

Martin, This is my feeling: [continuity] would be slightly less useful than [limit] in calculus questions, but very useful in analysis and topology. I wonder why it's not around already.
OK, I'm off. Bye!

Bye Srivatsan!

2:13 PM
Bye Sri!

Bye

@tb Gah, all I could find was this. It doesn't seem to be in SD...

@JM Been there, done that :) Thanks!

Well gee, I thought you had the answer and was posing it as a puzzle... :)
If there's a scan of it somewhere, it seems to be pretty well-hidden.

2:25 PM
No, it was an honest challenge which I myself failed to meet (hence my "what I'm really curious to see..." post). I agree. If it is scanned somewhere it definitely isn't OCR'ed or so new that Google hasn't stumbled over it, yet.

Speaking of tags, is there a difference between and ?

@MartinSleziak Okay, that I think can be posed to that long thread...

Can someone explain to me how the substitution by Will answers anything here?
(I must be missing something)

@JM Ok, I've posted this in the long thread...

2:45 PM
@tb second it

Maybe the point being made is simply that the value is $\sum_{k=1}^n \frac{2^k}{k} - H_n$. After all, it gives a different and just as easy expression of the integral as the one given by Mike

hmm kk
would like 2 see a proof of that though

The two expressions for $H_n$? It is given here, for example.

thanks

This one needs another vote.

2:58 PM
This one needs two more.

@tb I'm not quite sure myself; Mike's and Will's expressions seem to have the same complexity.

@JM Yes, however the identity $\sum_{k=1}^n \frac{1}{k} \binom{n}{k} = \sum_{k=1}^n \frac{2^k}{k} - \sum_{k=1}^n \frac{1}{k}$ doesn't seem to be obvious as such, is it?

Yeah, some massaging is definitely needed to go from one to the other.

3:15 PM
@JM Could you take care of this, please?

Nuked.
Now that I think about , isn't there a more generic tag encompassing both lim sup and lim inf?

@JM You mean that we already have one?
I think that most of those questions that I listed as examples of question suitable for limsup tag are tagged limit: chat.stackexchange.com/transcript/message/2885007#2885007

I don't think we already have one, but I was wondering if there's something that can refer to both lim sup and lim inf.
More specific than "limit", but less than either of lim sup or lim inf.

Well, limsup was intended for question about both, as I explained in tag-wiki.
I am not sure, but I think limsup and liminf are sometimes called extremal limit points.
I do not know about another term that would encompass both of them.

3:31 PM
@MartinSleziak Yes, a term like that would be a much better name. For now, I guess we should be happy with the current name.

Well but extremal-limit-points is kind of long and I do not think many people know the term.
I am not 100%-sure it's correct.
It seems that some people use the name extreme limits: "extreme limits" "lim sup"
Perhaps this could be worth even asking on the main - about the terminology which would include both liminf and limsup.

Hmm, makes sense; "extremum" is the generic version of "supremum" and "infimum", no?

@JM If I think of "extremum" I think of "maximum or minimum", not of "supremum or infimum"

Oh, right. Hmm...

Why not simply (liminf-limsup)?

3:42 PM
Well, the tag has only two questions, so it would be easy to retag, if you think that's a better name.
I would like better adding liminf as a synonym, if we want to have liminf somewhere in tags; but you certainly have more experience with tags.

I was thinking it might feel somewhat weird for the prospective tagger to use when his question is entirely formulated in terms of lim inf...

@MartinSleziak I don't think so :) I'm not very good at coming up with new tags. I just think there is little sense to prefer one of liminf/limsup over the other and every term encompassing both would most likely lead to us having to do the tagging ourselves since beginners won't be familiar with it.

But are there in fact many questions concerning limit inferior only?
I guess that mostly results on limsup/liminf are either concerning both of them; or they are formulated and proven for limsup, and liminf is mentioned as dual.

Now gmail has changed looks and I have to scroll : (

Anyway, my opinion is this: I did what I considered the best way: I've created [tag:limsup] and mentioned liminf in tag-wiki.
Feel free to create new tag and retag the two questions if you have better name. I do not plan on adding other questions to that tag until tommorrow.

3:49 PM
@Matt Google seems to have gone through quite some makeover during the holidays. I don't like the new look and feel of plain search (but I hated it since they had this instant preview anyway).

Sometimes I feel that people are just adding Ajax to their pages now just for giggles...

But I'll ask about name encompassing both liminf and limsup on the main; it seems interesting to me independently of this tagging discussion. (It would be the third question having this tag...)

@MartinSleziak Yes please; I'd upvote it...

@tb I don't like that either.
But that was easier to ignore than the changes in gmail.

4:07 PM
it's our own fault for using web interfaces rather than software that interactrs via some protocol
but that's the (bad) direction software is going in general so it can't be helped

Ajax is a fine piece of technology. The trouble, as we've seen with SE and now with Google, is that it now seems gratuitous at a certain point...

I don't mean ajax specifically, just the whole idea of having a web interface
doesn't matter, someone will answer it anyway

People are upvoting this ...
well
it's clear it was only upvoted because I downvoted it

My favourite proof of Cayley–Hamilton!

4:19 PM
@QED I didn't upvote, but it'd have been nice to explain why you downvoted an arithmetic question...

Does @downvoter work?

no
Isn't this question just totally rubbish

Why?

Well I don't see how it has anything to do with mathematics, and it is answered fully by looking at the first hit on google for "percent"

I don't see how an arithmetic query could be rubbish myself.

4:25 PM
This is a guy who has spent a year at least programming C++

How can he not answer a primary school level question by himself

What does that have to do with the question?

it concerns the question directly
I thought he site for mathematical questions

You should judge the question on itself, not on the one asking it.
2

4:27 PM
@QED To my own chagrin, I've found that there are people who can program and yet be less than stellar with arithmetic...

@JonasTeuwen, I am
Yes there is a sad phenomenon of hobbyist programmers with no mathematical ability

and arithmetic questions, even in the guise of a word problem, are still mathematical questions.

arithmetic means to me things like prime numbers
I didn't count this question as arithmetic

certainly there are numbers involved but..

4:32 PM
The border between arithmetic and number theory is a tad fuzzier for you than most people, I take it...

@DylanMoreland "I am a PhD student and I study mathematical physics."

well apparently this is a good, acceptable question. That's a real surprise to me. I think it's awful.
I really hate this "You last voted on this question 26 mins ago Your vote is now locked in"
It's got more upvotes than the majority of my questions.

@tb Oh, I mostly thought the answer was funny.

@DylanMoreland The whole thread reminds me of Dalí... Answerer can't access the ArXiV and the question and comments, oh my...

is arxiv banned in some countries?

4:41 PM
How do I show that $d\eta = 0$? You should show that $d\eta = 0$.

really banned in some countries?

@DylanMoreland Logic bomb, that...

Math EVISCERATED by simple experiment.

I think he's trolling
he's made a simple mistake and instead of correcting his work, thought it'd be funny to post it as a joke online

@QED I said something similar a while back, minus the "I think" portion...

4:45 PM
ah I missed that

Don't worry, it was in relation to that infamous thread... so quite a long time ago.
I'm not sure why this place was picked to take the piss on...

Doesn't that OP conflate conditional probability and conjunction of events? Why has none of the answers explained that?

That's how I would have answered, but I didn't take the question seriously.

@Srivatsan That certainly is the more fundamental gap, yes.

4:54 PM
Hmm

@Srivatsan, I downvoted this math.stackexchange.com/questions/96372/… - but I guess I retract that because apparently it's a good, acceptable question
I don't get it but I'm fine to just accept that

@QED You do not have to accept anything. I am not saying it is a good question; but that doesn't mean it's not acceptable either. The site's policy/vision is to be open towards "math of all levels". It seems hypocritical to me to declare this if we downvote a question simply because it is elementary.

It's not because it's trivial

btw what is d long form of OP?

But perhaps you downvoted because the OP had not showed research effort; that is true. You could stand by your downvote then.

4:59 PM
that I thought it was a bad question

If I did down voting that would be a candidate.

@Matt Basically, the a priori probability (the true probability) is different from the a posteriori probability after part (or whole) of the sample point is revealed. I think that is a legitimate answer.

you don't down vote anything?

care to answer a trivial and nomenclature-related question guys?

@Matt You don't want Critic badge?

5:02 PM
@NikhilBellarykar What guarantee do we have that it's trivial? :)

coz I know :)
btw what is d long form of OP?
that is d question

d?

d=>the

@NikhilBellarykar Original poster. See this list of acronyms at meta.
2

@Martin thanks

5:03 PM
or "original post"; it depends.

ew

@JM I see
thanks
kk
I happened to read a VERY good math joke
why do motorcycle gang members use motorcycles to go for work?
because members of cyclical groups commute

@QED I've edited the question, so I guess it should be possible for you to change your vote.
I wasn't quite sure about adding the tag, but we have a few other questions about percent tagged algebra-precalculus, so I guess I did not much harm. math.stackexchange.com/search?q=[algebra-precalculus]+percent

I don't think it's algebra.

@QED Well, the tag can be removed (if someone decides to do so). Main purpose of the edit was that you can retract you downvote. It's not a good reason for editing, but I think we've seen worse edits...

5:18 PM
I really should be asleep now, so: see you guys later.

goodnight

bye J.M.

@JM Good night!
@Srivatsan I think as it is it's not suitable as an answer on SE.
Duty calls. I'll see you later!

I wish I knew how ot link to a comment
> the manipulations of the quantities dy and dx that occur e.g. in the theory of differential equations have a meaning
can anyone show me that?
I would like to learn about it

5:32 PM
very nice thank you

I did not know we had a meta question on that.

5:53 PM
@tb and @Jonas, would you look at my comments to Didier's post to see if I am making sense. I might need to add my comments there to my answer.

Good day robjohn

@QED howdy! how are things today?

@robjohn Okay :-).

@tb and @Jonas: good day by the way :-)

well I had a nasty fall but I'm fine now

5:55 PM
Good day!

@QED did you break or sprain anything?

no I just tore my trousers

@QED that is not good, but in the grand scheme of things, better than breaking something.

yeah
I was able to warn the others not to slip too

@QED that was good, for them at least.
Did this fall involve ice?

5:58 PM
no it's just really rainy
yesterday there were amazing winds, many trees uprooted and apparently a whole apartment got blown down
some vans smashed into each other and injured people

@QED Ah. Once, when it was snowing at Princeton, I was heading toward the main door to the math department, about 30 feet away, and I saw the secretary coming out of the door. Next thing I knew, I saw the secretary looking down at me asking if I was all right.

wow!!
That's scary

The snow under the building had turned to black ice.
couldn't see it, but if you were a little off balance, it would take you down.

Ah, it is the same kalle guy that did the recent math-crushed question. I knew the 0.999...98 thing was familiar.

What's up?

6:09 PM
Depends on your frame of reference. (I never tire of that response.)

It's a proper class.

Where is that LaTeX in chat meta question? Or the bookmark?
ah, found it

21

OK, so chat is now available... but; it has been suggested that for Mathematics we should have TeX support. The current TeX processing has some non-trivial client impact. Before I even attempt trying to hack this in, is this something that the community would want / use? (this would only apply ...

@yoda I have never seen that before. I don't really have a grasp on its significance yet.
@anon You can always look in my profile

@robjohn I'll do that, but in about 6 hours when I really have time to think about it.

6:13 PM
@robjohn: thanks

@tb No rush, I appreciate whatever you can do :-)

So in between doing phone surveys for CNN yesterday I had an interesting thought. For $p$ an odd prime, define the truncation map $$t_{p^r}:\mathbb{Z}_p\to\mathbb{Z}/p^r\mathbb{Z}:\sum_{l=0}^\infty a_lp^l\mapsto\sum_{l=0}^{r-1}a_lp^l.$$ Then primitive roots lift to $$W_p=\{w\in\mathbb{Z}_p:\langle t_{p^r}(w)\rangle=(\mathbb{Z}/p^r\mathbb{Z})^\times\}.$$ Does $\langle W_p\rangle\subset\mathbb{Z}_p$ have a name or any formal study?

@anon What is $\mathbb{Z}_p$ in this context?
Are you talking $p$-adics?

@robjohn: Numbers of the form $a_0+a_1p+a_2p^2+\cdots$ represent the $p$-adic integers, yes.

Ah, okay. I saw $\mathbb{Z}_p$ and thought $\mathbb{Z}/p\mathbb{Z}$
I will now shut up, since I have not studied $p$-adics.

6:21 PM

@anon I can ask one of my office-mates. He does a lot of $p$-adic stuff.

@robjohn I have something else to do as well, but I will check it!

obviously not MSE, basically I need to find out what to do if I don't get a math class

I basically never went to any classes.

@QED You mean general life, or 18+ kind of things?

6:22 PM
It just didn't work for me and I could study it all by myself anyway.

lol

er I am 23 years old

@JonasTeuwen Same thing, no rush. Thanks for whatever you can do :-)

I am not talking about nudity or violence though

Running around naked can be very liberating.

6:22 PM
that's true...

@JonasTeuwen The incarceration afterwards is not so liberating...

It can also be painful...

@AsafKaragila very painful :-p

Depending on your gender, I suppose.

@anon that just determines the latitude of pain

6:24 PM
I suppose Jonas would know what he's talking about, though.

@yoda Or the longitude.

@AsafKaragila In some cases, the longitude is not unique.
@AsafKaragila Those are the cases that bear closer scrutiny :-)

The metaphors here are getting crazy.

@anon Yes.

@anon So is Jonas, if he wants to run around naked in the cold.

6:26 PM
@Asaf: Yes to the metaphors getting crazy or yes to the $p$-adic question?

> I agree with @Matt E, as almost always. But I think it is true that a standard (pun not originally intended) freshman calculus does not provide any mathematically useful information or insight about infinitesimals, so thinking about freshman calculus in terms of infinitesimals is likely to be unrewarding. – Pete L. Clark 4 mins ago
funny

@anon Yes. (<-- Reference to the joke that a mathematician is a guy that when asked "Do you prefer X or Y?" answers "Yes.")

#$*%& I need to find an income source and figure out other things all these years of school taught me essentially nothing useful @QED Sell your body... I'm sure your kidney is worth some money. 6:31 PM @QED money.SE ? it's not really money specifically @Asaf, I do not regenerate kidneys in a fast/renewable way that will not work @QED You have two, and some liver. By then you can get some kids and sell them for parts too. 6:45 PM @Asaf: Did your mate happen to say anything about the$W_p\$, like a name?

@anon Not that I recall.

Hi, everybody.

@Matt, why doesn't hiragana have la li lu le lo?
Hi Daniil

@QED It does. It's called ra ri ru re ro : )
l = r in Japanese.

6:56 PM
aha

Are "Could somebody check my proof?"-type questions allowed on the main site?

so it's just like monty python
@Daniil, yes that's fine but be sure to point out what ares trouble you specifically
I don't know what the heck thisd is...
I was wondering about that anyway ty
actually I can't read what that says, it might say something terrible

Is there a term for a poset in which every two elements are incomparable?

@Daniil antichain
In mathematics, in the area of order theory, an antichain is a subset of a partially ordered set such that any two elements in the subset are incomparable. (Some authors use the term "antichain" to mean strong antichain, a subset such that there is no element of the poset smaller than 2 distinct elements of the antichain.) Let S be a partially ordered set. We say two elements a and b of a partially ordered set are comparable if a ≤ b or b ≤ a. If two elements are not comparable, we say they are incomparable; that is, x and y are incomparable if neither x ≤ y nor y ≤ x. A chain in S is a...

Thanks.

7:05 PM
Maybe discrete poset too.
Google says that some people use it: "discrete poset" and and discrete poset.

my post seems to generate a lot of discussion, math.stackexchange.com/a/96377/16697
not really what I wanted

@QED What? You removed your message.

@Matt, oh it was just something repeating the letters over and over again

OK : )

I'd like to know about "the manipulations of the quantities dy and dx that occur e.g. in the theory of differential equations have a meaning"

7:25 PM
@Martin: Thanks for the explanation in the nets-thread.

@tb I guess Micheal might add more things, but this one I did not find in any other book.

I wish I could turn off that "Another answer has been posted!"

@tb In fact I learned about this material when I discussed problems with various definitions of subnet on Wikipedia en.wikipedia.org/wiki/Talk:Subnet_%28mathematics%29
BTW that is also the reason why Schechter's book was mentioned in the comments to this question: Do we need net refinements not induced by preorder morphisms?

Next time when there is an AC question, ping me :-)

@MartinSleziak Yes, I almost expected the subnets-debate. I was always happy with the order-preserving+cofinal definition and never felt the need for the other one. I haven't thought about Alexei's question really.

7:38 PM
When I look at the comments in Norbert's question it seems that the comments together give a sufficient answer to his first question already - and they came very quickly. Nobody said anything about his second question. Wouldn't it be better to divide it into two separate questions? What do you think t.b.?
@tb About Alexei's questions, I spent some time on it. My guess was that it doesn't hold but I wasn't able to find a counterexample. I hope to get back to that question. (But there is already too many questions which I would like get back to...)

@MartinSleziak I think the second question is rather simple: on first sight there is no issue or Norbert should clarify what he wants to know.

Well, I don't work with sums over arbitrary index set too often; so I was not sure what can be said.

@MartinSleziak I deleted part of my comment since I figured out that I never actually proved that in detail but I'm sure it should work. I needed a bit of summability in topological vector spaces but it's really no problem at all. It's just a special case of nets written differently (as series are a special case of sequences).

@tb You mean considering the series as a net on the set of all finite subsets directed by inclusion?

7:48 PM
Exactly.

I guess I have seen that somewhere already. I wish I had better memory.

No upvotes from me there, so I guess not.
Thanks!

@QED So how do you get the ID number of a comment if you want to link to it?

I like Bill. He deleted his answer because the post is a dup.

7:59 PM
there's a script to do it