Mathematics

Zhen Lin

1:00 PM

Small hands, easily distracted, and indeed, I do not know much Tchaikovsky

Matt

: )

Zhen Lin

in fact my ability to play seems to have diminished.

I can't seem to press the right keys.

Matt

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

Zhen Lin

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

Matt

I can relate to that.

Which reminds me: going to practice now, bbl : )

Martin Sleziak

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...

t.b.

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

Zhen Lin

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

Martin Sleziak

Major 9th means betwee C and E?

Zhen Lin

C to D

Martin Sleziak

I mean c1 and e2.

Zhen Lin

1:18 PM

C to E' would be a major 10th, I think.

Martin Sleziak

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.

Zhen Lin

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...

Martin Sleziak

Well you can try music.SE to find out about musical secrets.

@ZhenLin Why do you think that?

Zhen Lin

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

Martin Sleziak

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?

Zhen Lin

1:22 PM

Well, the right hand seems to have two things going on at once...

J. M.

@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...

Zhen Lin

Probably quite a bit harder...

Martin Sleziak

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.

Zhen Lin

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

Martin Sleziak

@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...

Zhen Lin

1:30 PM

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

J. M.

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

t.b.

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.

J. M.

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

t.b.

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

Martin Sleziak

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

Srivatsan

1:45 PM

What is the problem with the problem?

J. M.

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

t.b.

@MartinSleziak Close votes age away harmlessly after 4 days if the threshold is not reached. Each new close vote resets the timer, and close votes only start expiring if the question has had 100 views.

Martin Sleziak

Having a few experienced users here, do you think that limsup 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.

J. M.

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

t.b.

@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.

Srivatsan

1:53 PM

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

Martin Sleziak

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
http://math.stackexchange.com/questions/85498/limit-of-sequence-of-sets-some-paradoxical-facts

Srivatsan

@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.

J. M.

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

Dylan Moreland

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

Srivatsan

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

Martin Sleziak

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... ?

Srivatsan

Yes, it did.

Dylan Moreland

@Srivatsan :)

t.b.

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

Martin Sleziak

A few questions where this tag would (in my opinion) make sense: 6168 8489 60873

60229 73508 85498 84727

84526 85120 84601

Hopefully now it is ok.

Srivatsan

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

Jonas Teuwen

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.

Martin Sleziak

@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?)

Srivatsan

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?

J. M.

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

@Srivatsan e.g.?

Martin Sleziak

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

I meant What's wrong with this definition of continuity?

Srivatsan

@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. =)

J. M.

2:05 PM

@JonasTeuwen So, not this one?

Martin Sleziak

@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.

Jonas Teuwen

@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 :(.

J. M.

@MartinSleziak Yes, I think so. :)

Srivatsan

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

J. M.

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

Martin Sleziak

2:07 PM

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

Jonas Teuwen

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

Martin Sleziak

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 general-topology and "uniform continuity" in real-analysis.

J. M.

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

Srivatsan

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

Jonas Teuwen

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

t.b.

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

Srivatsan

@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." =)

Martin Sleziak

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

t.b.

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

Srivatsan

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!

t.b.

Bye Srivatsan!

J. M.

2:13 PM

Bye Sri!

Martin Sleziak

Bye

Jonas Teuwen

Bye

J. M.

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

t.b.

@JM Been there, done that :) Thanks!

J. M.

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.

t.b.

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.

Martin Sleziak

Speaking of tags, is there a difference between propositional-logic and propositional-calculus?

J. M.

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

t.b.

Can someone explain to me how the substitution by Will answers anything here?

(I must be missing something)

Martin Sleziak

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

Nikhil Bellarykar

2:45 PM

@tb second it

t.b.

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

Nikhil Bellarykar

hmm kk

would like 2 see a proof of that though

t.b.

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

Nikhil Bellarykar

thanks

Matt

This one needs another vote.

t.b.

2:58 PM

This one needs two more.

J. M.

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

t.b.

@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?

J. M.

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

t.b.

3:15 PM

@JM Could you take care of this, please?

J. M.

Nuked.

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

Martin Sleziak

@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

J. M.

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.

Martin Sleziak

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.

J. M.

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.

Martin Sleziak

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.

J. M.

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

t.b.

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

J. M.

Oh, right. Hmm...

t.b.

Why not simply (liminf-limsup)?

Martin Sleziak

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.

J. M.

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

t.b.

@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.

Martin Sleziak

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.

Matt

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

Martin Sleziak

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.

t.b.

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).

J. M.

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

Martin Sleziak

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...)

J. M.

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

Matt

@tb I don't like that either.

But that was easier to ignore than the changes in gmail.

Transcript for

$Mathematics$ Mathematics