@JonasTeuwen this question

@JonasTeuwen Every metrizable space is Hausdorff, correct?

@PeterTamaroff Yes trivially. Check it.

@JonasTeuwen I have already done it.

@PeterTamaroff Good.

@PeterTamaroff yes (too late)

@robjohn Cool! You are quite the syntax manipulator :-).

@JonasTeuwen syntax manipulation?

@robjohn Yep, shift with symbols. That is how I called myself as a math student. "Syntax manipulator". I shifted symbols and got a solution but I didn't have a clue how I got there. But you have mastered the manipulation.

Well, actually it became "syntax moron".

@robjohn The answers here (including yours) are also really cool.

Hi folks

@JonasTeuwen Hey, I've got something to tell you!

I know that in Euler-MacLaurin we can have diverging expansions. How do we figure out when it is starting to diverge?

@Gigili Oh. Hi.

@robjohn "How on Earth did you come up with this? :-) – joriki 9 hours ago"

LAWL

Hmm, it is actually a very cool trick, but I think I have seen it before.

@Gigili Do tell.

@JonasTeuwen I really like seeing so many answers coming from so many directions to answer a question.

@JonasTeuwen using the residues of $\frac{n/z}{z^n-1}$?

@PeterTamaroff LAWL?

@robjohn Know about this? I believe they also do that in physics, using "renormalization" 8-). They get a few digits more... then it starts to diverge. They seem to match it to experiments to claim they can make better computations.

@robjohn No, the answer of oen mentions that you can improve the estimate with E-McL, but then it starts to diverge after four digits.

@JonasTeuwen Hulio. umm I was a bit angry the other day that I called you idiot! Simply because you called me so while talking to that gut thingy. I, umm, am, umm, so, umm, rry!

@Gigili No problem. Everybody has bad moments 8-). Sorry that I've insulted you then, it was not my intention.

@Gigili Pupulon eyes

@JonasTeuwen I don't know exactly where he is coming from with that, my answer gets 24 or 25, and I could go further.

@robjohn Oh. But often you have diverging asymptotic expansions no?

@robjohn A funny inflexion of the onomatopoeia LOL

@JonasTeuwen Good, good.

@JonasTeuwen unless the function has a fourier transform that is supported in $|x|<2\pi$ (I will have to find the answer where I derive that to be sure), the EMS will diverge. So, in most cases it does diverge.

@PeterTamaroff Aren't your eyes normally like that?

@robjohn Right, so how do we figure out when the series actually starts to match "worse"?

@Gigili Not really. And I was referring to your eyes.

@PeterTamaroff It was so in the picture I saw.

Anyway, I'm off to behehed.

@Gigili I read that as beheaded.

So did I.

@HenningMakholm Twisted minds, we have. Hhm.

@JonasTeuwen Ah, there it is :-) If you normallze the Fourier transform the way I usually do, using $e^{-2\pi ix\cdot\xi}$, then if the FT is supported in $|x|<1$ the EMS series will converge.

@robjohn Oh, some good old Paley-Wiener. Then my original question! How do you know when the expansion is "good" :-)? For what $N$ is the approximation the best?

@JonasTeuwen You have to get an estimate of the error. In most cases, you look at the terms and see whether they are increasing or decreasing. Once a term starts to decrease, it usually continues to do so. Another way is to look back at the actual error term from the integration by parts that gave the EMS and estimate the error from that.

@robjohn Hmm, so a bit ad hoc?

Is that the old thing I remember that the error is always no bigger than the next term ignored (from many years ago)

@JonasTeuwen In most cases, yes. You fix the number of terms and then you find how big $n$ needs to be to make your error small enough :-)

@robjohn Ah :-).

@OldJohn When it converges (for alternating series).

I thought the same sort of thing applied for asymptotic series which were eventually divergent

@JonasTeuwen I got 25 digits since the error was about $3n^{-25/2}$ and so I chose $n=100$

@robjohn Yes, pretty cool!

@OldJohn Oh, quite possible.

@OldJohn That is just what we were discussing.

so the best approximation is pretty much at the point where you get the smallest term?

@OldJohn that is usually the way things work.

@OldJohn I try to stop a few terms earlier, just to make sure :-)

are my ancient memories not total rubbish? - please tell me if I am talking nonsense

@OldJohn about what?

about asymptotic expansions getting better up to the approximate point where the terms start increasing

@OldJohn I was trying to con firm that here

Hmm... what if you need an asymptotic expansion to find the smallest term? 8-). Would the optimal way of truncating that one be called "supersuperasymptotics"? Or "verysuperasymptotics"?

@JonasTeuwen :)

So much for genital jokes.

I should shut up - my knowledge probably goes back to Erdelyi's old book :(

@OldJohn No!

Yes! - I really am that old :(

Would it be ntarual to denote a neighborhood space as $(X,\mathfrak N)$?

Where $\mathfrak N=\{ \mathfrak N_x:x\in X\}$

@MattN. It depends on your body weight and how good your liver is at processing them, actually. So, anywhere from two days to four.

@PeterTamaroff Hmm - that notation seems to indicate there is only one neighbourhood for each $x\in X$, maybe?

@robjohn Heh, neat. I'll upvote it in an hour...

@OldJohn No $\mathfrak N_x$ is the complete system of nbhs at $x$.

@J.M. You're out of votes for today? :-)

@PeterTamaroff OK - then I am not sure whether it is best to write it as a collection, or as a union

@OldJohn Hmmm

Maybe @HenryT.Horton or @BrianMScott can weigh this.

@J.M. Hi 8-).

@robjohn I've been quickly expending my voting allowance the past few days, actually...

@JonasTeuwen Hey Jonas.

@J.M. I have slowed down recently. I haven't even had time to answer as many questions as I would like, and voting has likewise suffered.

I'd like a WBC count.

@JonasTeuwen You gotta ask a medical lab for that...

White Blood Cell?? World Boxing Council??

Yep.

@OldJohn Boxing! Chess boxing!

@JM I wonder why they have always skipped that one. Is it a very intensive (expensive) test?

I can only cope with the chess now - not the boxing

@OldJohn If you do well in the chess game, no problem if you get KO in the boxing round! 8-).

@JonasTeuwen Also messy. So, unless it was specifically asked for, it's not likely to be done.

Time I got some sleep - have fun guys

@OldJohn later!

Oh, good :-).

@OldJohn Good night!

@OldJohn See ya.

Bye

@JonasTeuwen ?

@robjohn Answer to @JM.

@JonasTeuwen Ah... When there are a lot of conversations, it is hard to associate replies with their parent.

@robjohn I will arrow it next time! 8-).

@robjohn Do you have your .txt located somewhere in like one place?

I have written a very cool tool, it is called "t" and it writes to a file "todo.txt". Really cool. t <eat pie>. It has the feature that it will avoid collisions now. The other features are lack of features as I said before (and also, no SQL!).

@JonasTeuwen .txt for what?

@robjohn Like the document about the combinatoral polynomials :-).

@JonasTeuwen I have the stuff for MSE all together in a folder, but the stuff from sci.math was over a long time, starting in the mid 1990's

@robjohn Ah, plentiful stuff.

@JonasTeuwen yeah, but there were a lot of repetitious questions there. You could refer back to earlier posts, but it was more difficult to find things. There was nothing like closing a question because it was a duplicate :-)

Did the auto-updating on the main site stop happening for anyone else?

@robjohn Hmm, pipe them to the mail client? 8-).

@DylanMoreland Did it? That's good news!!!

@JonasTeuwen I'm not completely unhappy about it :) But I did wonder whether I'd messed Safari up somehow.

@JonasTeuwen pipe to the mail client? where were you in the mid 90's? ;-)

@robjohn Messing with Slackware.

@DylanMoreland No, but if it did, I'd be bloody happy...

@JonasTeuwen really? how old were you in the mid 90's?

@robjohn 9?

(I can refresh things myself, thank you very much...)

I loved computers. At least they were not so annoying. I've got a 386SX I believe.

Like 16MHz. Kickass.

@JonasTeuwen Oh, okay. I thought you were younger for some reason.

@robjohn I am 26 as of previous Sunday :-).

I've lost some years in the process of getting a degree 8-).

@JonasTeuwen okay, I pictured your mom having to pull you away from your computer to change your diapers :-D

That would have been cool :D.

(but no interwebz!)

I've got ISDN after a while, around 1997 I believe. Was bloody fast eh... like 14kilobyte/s.

And in 1999 ASDL, like 1,1Mbps! 8-).

@JonasTeuwen yeah, email and usenet and BBS's were about it. There were rudimentary HTTP servers and clients, though

Now everybody has >= 20Mbps 8-(.

Sometimes I still miss the beeps and hums of a 56k dial-up modem...

Pieeep krrrrrgggghhh Dudududuuu...? Hmm... Should see if that is on Youtube. I feel nostalgia.

Oh yeah!

@J.M. I had a 56K modem for a few years before the DSL went in and I could go to 384 kbps (that's b not B)

I should so connect that with Squid.

I have a 100Mbps connection now and it seems like it is often slower in loading pages than in 1999 8-).

@robjohn Ah, memories...

@JonasTeuwen here's another

@JonasTeuwen Speaking of, YouTube certainly came at the right time. Imagine if they tried starting that company in 1997...

@J.M. Was there even Flash back then? 8-).

@JM Would have been youradio.com with .wav.

8 bit.

5k 'movies' with Mario Bros sounds. Would have been cool.

@JonasTeuwen Well, there was Shockwave...

How were these big black slots called...? AT 16 bit? I had a sound card for that, was so cool and so expensive.

@robjohn Yes 8-). Would there still be people using dial-up?

@JonasTeuwen There still are, I am sure.

@JonasTeuwen Brian said he was still on dial-up...

@JonasTeuwen I only have 10Mbps :-(

Oh yes, I have seen one called "budget", it was 8Mbps.

On the university the speed is limited by the network card apparently.