edit (18.Dec.2011 Taiyuan China) Amusing: How does anyone (but him) know or care that he is in China? =)

Am I missing something?

I stay away from Lies. =)

@Srivatsan $\sum_k a_k b_k\le C\|a\|_{\text{sup partial sums}}\|b\|_{\text{total variation}}$

@robjohn - what is total variation?

$\sum_k|b_k-b_{k+1}|$

@robjohn I see. [Yes, that definition makes sense to me.]

@robjohn The proof is not that hard, I suppose.

Write $b_{k+1} = b_{k} + c_k$, and then group terms appropriately? We are given that $\sum |c_k| \lt \infty$.

@Srivatsan Yes, it is the Cauchy convergence test

perhaps I am naming it wrong...

@robjohn They are all the same. What's in the name? =)

Dirichlet convergence test...

@Srivatsan Does this look ok, @tb?

[Click the arrow...]

@robjohn Cool. I didn't know this one before. Haven't used it before either.

@Srivatsan Dirichlet convergence test with painfully detailed proof

@Srivatsan Except on the Wiki page, they use monotonic for the other sequence, but any sequence of bounded variation is the difference of two monotonic sequences

@Srivatsan yes it looks okay.

@tb bad link?

@tb Your link is pointing to MSE questions page.

@Srivatsan I have a proof of a generalized version here

Yes, fixed. I'm having some trouble with copying links in Firefox. Somehow it doesn't do what I want it to...

Um, I will take a look at it a bit later. Thanks for the link, tb.

And this Abel summation has successfully remained a mystery to me till now =)

@robjohn Did you produce your ASCII art manually or how did you have some sort of tool?

@tb It is all manual.

The summation sign is kind-of cute.

This was long before MathJax. I might update the pages to use MathJax

@robjohn wow!

@robjohn No! please don't do that! That's a sin on a similar level as LaTeX'ing books written by typewriters. You destroy works of art and you have to fear to burn in tb's hell for that. :)

@tb Okay :-)

Less work for me :-)

@tb At last count, I was already burning in a number of hells. =)

@robjohn Or if you do it, please preserve links to the old pages for nostalgically inclined people like me. :)

@tb Oh, I would never remove those pages, I would just have new LaTeX pages in addition.

@tb Out of curiosity, have you preserved your notes from way back? =)

I did so many ASCII-art proofs for sci.math that I can do them pretty fast.

You should post one such proof here. I have a feeling you'll get at least one upvote (from tb) =)

@Srivatsan I don't think we can force a monospaced font here, can we?

@robjohn four blank spaces at the beginning of each new line

(this gives a code block)

@tb perhaps I'll try one sometime :-)

@robjohn If you really do it, I will upvote it at least for the effort.

I wonder how many downvotes it will generate, though?

@robjohn Not too many but one can never know :)

I did some ASCII art when I was too lazy to do it using xypic, e.g. here

@tb That looks every bit as readable to me :-)

I think it's *ok*-readable, and I wouldn't complain if I have to read occasional answers like that...

@robjohn I think so, too. Here I over- or underdid it a bit. Somehow the brown blobs spilled over the white background don't look that good.

BTW why Neumann series, and not von Neumann series? This name is standard, I suppose.

@Srivatsan It's Carl Neumann

@tb Ok =)

I thank myself for not "correcting" the posts "appropriately" =)

@tb I am not seeing blobs.

@tb why are you using the the code-block style in the main text as well? Diagrams, I understand.

@Srivatsan Because I didn't want to mix the fonts.

@robjohn By blobs I meant the code blocks I used inline.

@tb Ah, I see. It's no worse than when TeX output is pasted as an image with the wrong background for the page.

test fail: $\texttt{However, we can get...}$

use \mathtt

@Srivatsan \texttt only works outside of math mode

(robjohn taught me)

@robjohn It'll be hilarious if you simulate a monospace font inside TeX and use ascii art =)

@Srivatsan It has to be done!

It is now a moral imperative!

@robjohn Well, do that and I bow to thee.

@Srivatsan I preserved a few of those notes that I took carefully during the first years of study. I threw most of my notes from high school in to the thrash can when I moved the third or fourth time because I figured: since I've never looked at them I won't look at them within the next, say 20 years. From elementary school I don't know. Maybe my mother has one or two notebooks somewhere.

It'll be on the level of using $\dfrac{\bar{\Xi}}{\Xi}$

@tb Nice. I am pretty certain I don't have any of my notebooks.

JM pointed that out in his aha in the starred comments.

That was too painful. I don't think I can produce ascii art using TeX.

How was the burger?

Decent+

That's not ascii art. :-)

That's a dirty limerick, what's your point?

That was mainly a bad limerick... :)

Indeed.

I always feel bad when Andreas Blass replies to stuff I write on MO.

Why?

He makes me feel like most of what I'm saying is wrong, or not the sort of thing a mathematician should care for.

Can I ask you something "forcy"?

Sure, just be quick about it.

How is $\bigcup G$ a function?

When?

\mathtt is not monospace; dashes are very long.

@AsafKaragila Always? I don't know. I'm not even sure. To me it's just a set but I think I read somewhere that it's a function.

@robjohn Wrong ping?

It is not a function is the conditions are tuples of functions and sets and whatever.

@Matt Sorry, I didn't see the address at the beginning of my text input pane

@AsafKaragila It's not a function if it's a set of tuples of functions or tuples of sets?

@robjohn I guess dashes are actually minuses

The generic filter "generates" new sets, it also generates a new function. If your conditions are functions and the extension involves set inclusion (i.e. $p\le q$ means $p\subseteq q$ and ...) then the result is a function.

@tb But monospace should treat minuses like hyphens, right?

Simply note that two conditions are compatible if they agree on the intersection of their domains. It means, in particular that $p\cup q$ is also a condition.

@AsafKaragila Thanks.

From this it is easy to see that $\bigcup G$ is a function.

Anything further?

@AsafKaragila No further questions.

@Matt Very well.

Goodnight folks.

'Night, Asaf.

Good night Asaf!

Good night.

Hmm. I hope to cap out nicely tomorrow. It would carry me over to the 20k

Whoever got some great AC questions should keep them until I'm awake tomorrow :-)

So long! :-)

Looks like the cats are quite pleased that the puppy has gone.

And how exactly is the puppy gone?

@Matt Not just the cats... =)

@Srivatsan Indeed. : )

@Srivatsan We had puppy stew for dinner.

@Matt Is this for real?

Seriously: we managed to flog her to someone else : )

@Matt what does flog her to someone else mean?

@Srivatsan Talked someone into buying her off us.

Although, that's a bit of an exaggeration. They totally fell for her the minute they saw her.

@Matt A'right.

Now I'm cured from thinking that I wanted a dog.

@robjohn Did you see the latest bounty question? Looks doable.

I wonder how the troll question about pi got 84 up votes. Must be the fact that it contains a picture...

@Matt Yes, beyond a point, votes are just a joke.

@tb Looks like a homework problem, too

@robjohn yes, but it was asked 3 months ago, so I don't think it'll do harm answering it. Beni's a nice guy and he asks for help in the bounty banner.

@Srivatsan How's Byron's present doing?

(I see 4 -nuos and 2 -nous)

@tb In that case, I will look at it in a bit. Right now, I have to see if the firewood place is open and get some firewood if they are.

@robjohn They don't do central heating there, do they.

@Matt they certainly do, but it is nice to have a fire in the fireplace on a cold night.

@Matt This should be fancy fire...

That was an attempt at humour. Never mind : )

@tb yes, but they are darn long unless I put them in \text{...} but that elides all spacing to one space. So I need to do spacing outside the \text{...} and escaped with \ . Ick!!!

@robjohn oy, then I'd go for a code block.

It looks like this is now obsolete given this

Heh, I just looked at the OP of this question, and he hasn't been here since he said that he had answered the problem. I don't think I have to worry about being accepted on that problem ;-)

There's one "discontinues" and one "discontinuos" left.

Nor do I think this question will draw much more attention.

Off to get firewood. BBL

Off to get some sleep. Hopefully there will be more snow. bbl