which changes dynamically based on whether her expectations are met or not, but I've never had a change to look into this problem formally

quite a monologue of myself :)

@Ilya So what you do involes some kind of probability logic? I have seen some stuff by Keisler and Hoover, who used model theoretic methods to develop an equivalent to the finite dimensional distributions for adapted processes.

@Michael: I have to leave right now, sorry

No prob. I should go to sleep anyways. Bye, Ilya!

Good night, folks!

I'm having some trouble getting some Mathematica code to run. I'm guessing it has to do with variable scope. Here is a code example:

i = 2; k1 = 2; k2 = 1;
For[k3 = 0, k1 + 2 k2 + 3 k3 <= i + 5, k3++,
 If[k1 + 2 k2 + 3 k3 = i + 5,
  cur = cur + i!/(k1! k2! k3!)
  ]
 ]
cur

I get numerous errors along the lines of Set::write : Tag Plus in 0+2+2 is Protected.

Does anyone have any idea what I'm doing wrong?

Oh, let cur=0; go at the top of that snippet.

I will just leave this open parenthesis here, hope I am not annoying anyone

(

Er, ok, figured that one out. Just needed == instead of = in the If. But I'm still producing another error with my code. I'll have to try to create another short example for it.

@AntonioVargas There is a Mathematica SE and attendant chat room.

@DylanMoreland Yes, but it was a simple question and the chatroom isn't active right now.

@DylanMoreland But thank you :)

@N3buchadnezzar Why would you do such a heinous thing?

Someone dastardly may close the parentheses at any time and therefore relegate all of the interim discussion to tangential parenthetical commentary.

)

What about...

}

now we need a time traveler or a hacker to fix the stability of the chatroom

or I could flag you, and get the offending symbol removed..

])]]}]

Muahahaha!

This

Gerry has a way with words, that he does

I've just spent an hour typing up a solution to a question only to finally reread the question and realize my answer is completely irrelevant.

@AntonioVargas Link?

possible duplicate :)

@Antonio, that hurts the soul.

@Limitless your question somewhat reminded me of this question. Maybe you want to have look at the answers given there to practice re-indexing.

@tb Gee, I wonder why! :-)

@BrianMScott Comme c'est bizarre! Que c'est curieux! et quelle coïncidence! (Ionesco)

Wonderfully appropriate.

...I anxiously await the day where I don't have to explain Iverson brackets anymore...

@JM I do and I don't, loved your magic on Limitless's question.

@tb Was that the manipulation of summations?

Heh. :)

@tb Thanks.

@BrianMScott yes, this one

I'm glad I could make a good question.

@Limitless Got some good answers, too.

Definitely. You and the others make it look so easy o_o

@Limitless ...and it was nice to try figuring things out yourself as well.

@Limitless I especially like the fact that you posted your own solution. I wish more people did that.

@tb This was an interesting non mathematical question.

@Limitless It just takes practice... :)

@t.b. I was worried it was inappropriate. I'm glad you all approve.

Seems to me it was a combination of mathematics and cognitive neuroscience. (The depth perception question, that is.)

@Limitless No, it's not. That's the point of the "Self-Learner" badge they offer here...

@anon Right. But it didn't fit anyways. Had to put it down.

@J.M. I had struggled with it for a day or so, on and off. I had finally figured it out tonight. My issue was the inequalities. I didn't follow all the implicit reasoning, so I had to work out every little piece.

@anon Reminds me of that optical illusion question where Willie managed to post a mathematically-flavored answer...

@Limitless That’s where practice makes all the difference in the world: the manipulations become increasingly automatic. (Especially after you’ve taught this material out of this very book!)

@Brian I'm casually trying to learn the chapter on summation as a whole. It's so rich. I hope I can master it enough to do all the problems in the chapter.

@Limitless The book is quite densely packed in each chapter, I would say. :)

I'm getting increasingly tired of Pete posting comments as answers only linking to some of his notes...

(or saying thank you for reading my notes)

@tb Wait, what? Just links, no math?

@Limitless My recollection is that they’re definitely doable up through the homework problems and probably through the exam problems.

@J.M. Definitely. I'm terrified that if I could get through just half of the book, I'd have an awesome grasp beyond what I thought possible. :P

like, this one of PLC recently, I guess

not like I can really complain much...

@JM this and that for example.

@Brian What is the typical time frame for a chapter in that book? 2 weeks? Or one?

@tb Ech, not even a quick summary of what's in the notes... :(

@Limitless Probably more than that, unless you’re very quick.

If I could seriously dedicate myself, I think I could do it. My life is currently hectic, so I am doing it in my spare time and as a way of relaxing.

@Limitless then by all means take your time! There's no point in hurrying without understanding properly.

@tb I don’t mind the second one: it was a response to a question about the notes, and the gap had been filled in by others already. I am a little miffed that he never acknowledged or corrected another gap found by the same person, though I sent him an e-mail about it with a link to the question.

@t.b. I suppose you're right. I just like to cover things very quickly; I'm not used to the speed you cover a college book as compared to a highschool book.

@Limitless You have the luxury of savoring it; I suggest you exploit that. :)

You're right. I am thinking I should take my friend's advice, "Slow down and smell the flowers." With respect to mathematics, anyway. :)

@Limitless When I taught a one-semester course using the book, we covered Chapters 1 and 2, much of 3, the first four sections of 5, the first three sections of 7 plus the basics of convolutions, and some bits and pieces from 6 or 8. And most students had a pretty rough time with it even at that pace, though I didn’t ask them to be able to do any of the moderately difficult (or harder) problems.

I bet it was extremely difficult on you as a teacher. There is so much to be confused by and such subtlety that it escapes you easily. I can't imagine trying to explain it to students.

It was one of my favorite courses to teach, but that’s because I liked the material a lot; it certainly wasn’t one of the easiest to teach.

It really inspires me in a way. I suppose the ultimate test of understanding is whether you can share it with others.

Hi

@Limitless I agree with that. If you're at the point when you can explain it clearly to somebody else, then likely your grasp is more than adequate.

(math.SE is a good place for that.)

Hello Raj.

@Limitless I actually learned quite a bit of math over the years from teaching it; a couple of times I volunteered to teach a course specifically to make myself learn (or review) the content.

Life sucks

It is great talking with you all. But, a girl has been waiting on me. So, I hope we can talk again another time.

@Limitless By all means don’t keep her waiting!

Also, Rajesh, I hope you feel better.

never mind, its not about feeling

@RajeshD No; gravity sucks :-)

@robjohn I thought it was air pressure... :D

@JM Air pressure blows...

i'll remove it

@robjohn Gravity is no joke.

It's strange how "it sucks" and "it blows" got to have the same meaning...

@JM ‘Thar she ... sucks?!’

Now I'm forcibly trying to pull my head out of the gutter...

@JM Waste of energy. :-)

Frankly speaking What is your opinion on Indian mathematicians and Indian scientists (not those who have flocked to US or abroad), I mean the Indians who live in India?

I don't know enough people there to have a very informed opinion but I think there's a very broad range from absolutely outstanding to, well, terribly bad. But that's an observation that applies to most countries...

Mornin.

'Ello. Thumbs up!

hey

@tb : Not about their competence in research, we all know it varies and no problem with that. But the beurocracy and politics and they mean more to them, not research. Thats why we never hear anything special from indian researchers.

never mind

"I throw you out of the university", "I'll kick you out", "I don't want you to do research" , "Why don't you just leave? you are a pain to me", "I am sure you won't get job anywhere", these were the exact abuses i used to recieve from my advisor all my three years with him and now i am out of it.

@RajeshD Doesn't sound healthy. Good thing you got out.

When I approached another prof at some other reputed university, He simply said that he had good relations with my prev. guide and he doesn't want to spoin that. My guide is a big daddy in this are in the entire country, nothing move without his knowledge and influence and he is hell bent on ruining me. Its like i have a no way out or in.

It is very hard to reply anything reasonable to that since we only know your side of the story. It saddens me that you feel this way and that apparently your "guide" has failed miserably when it comes to guiding you. Be that as it may, feel free to decompress here but I don't think we can do much in terms of constructive encouragement.

never mind @tb : i am just hoping that good things come my way while i try looking for opportunities in other directions. There are some many things we encounter which we have no clue how to explain

test

heh, works.

Oh, for going to a specific page?

@JM yes, that's the intent. Doesn't it work for you? You should land on page 374/375

Anyway, it was only this waste of time

@tb It does; it's just that my connection's slow... :)

Hey

hey

@JM I don’t want to hear about it! :-)

how are you theo

@JM thanks for confirming

@BenjaminLim busy and sleepless.

thus not productive.

I know when one is tired and not enough sleep one is restless and like no inspiration

some idiot yesterday made toast at 4am and left it for too long in the toaster

fire alarm went off

had to go outside -4 degrees celcius in pyjamas

FOOL WHO LEFT TOAST FOR SO LONG IN THE TOASTER IMMA CHOKE YOU

that sucks...

yeah

@BrianMScott :D I know, I know...

@tb Have you worked much with Noetherian spaces?

Not that much. What about them?

oh. I was just wondering if whenever we have a cover of a noetherian space we can extract a countable one.

Aren't Noetherian spaces compact by definition?

well that's what I am trying to prove now :D :D

What's your definition of Noetherian?

@tb Every ascending chain of open sets eventually stabilises

@tb Yesterday I solved this problem with an AK - 47. My friend then solved it with a pea shooter.....

So, what's the trouble?

Some proof is given at this blog. Among the first Google results for noetherian space compact.

well my proof assumes that if we have a cover that has no finite subcover

then I can get a countable subcover out of that that does not cover the whole space

@MartinSleziak math.kth.se/~laksov/courses/algebradr01/notes/topology4.pdf

Remark 4.24 is about the same as my proof.

Except that

Can't you just cover your space and take finite unions of your cover. Then you have a maximal element which must be everything...

yeah ok that's probably more elegant

but theo

suppose you do it using the ACC

Hello

how come if I have a cover $\{V_a\}$

then in the proof above

I can assume that there is a countable collection out of that that does not cover the whole space?

@DanielMontealegre hi

why are you so focused on countable?

Because then my proof goes through :D :D

By ACC you mean countable choice?

I have a quick question. If K/F is finite Galois and cyclic, with generator sigma, I have to prove that if x\in K, then Tr(x)=0 if and only if \exists y\in K^\times such that x=y-\sigma(y).

@MartinSleziak Ascending Chain Condition

'Doh; I should have figured that out.

I already prove <== this

@DanielMontealegre If the problem did not involve traces I could probably help

unfortunately we have not done traces yet in class

@Daniel: if you press the up-arrow key, you can fix typos in your post.

If it didn't involve fields I could probably help.

unfortunately we have not done fields yet in class

@tb LOLOLOL

@MartinSleziak Suppose we have a cover $\{V_a\}$ of $X$

sorry just trolling.

Ben I still don't understand what you're trying to achieve.

I'm trying to make my proof go through.....

Maybe I'll just abandon it.

@Benjamin : Are you from KTH?

KTH?

the link you just gave is from KTH

@Benjamin So you're question is whether we are able to get from arbitrary cover (without finite subcover) get a countable one (with the same property)?

@MartinSleziak yea

Or is it something different you have trouble with?

it's that

because you see

suppose we have a cover that has no finite subcover

I want to that that cover reduces to a countable one

and then do some stuff.

@RajeshD No I am not from there.

ok

What about $X$ being uncountable discrete space and cover consisting of singletons.

yes

then.....

yes

we cannot extract out a countable subcover

Ok, that's not Noetherian space, so this is not a counterample... :-(

My mistake, I was too hasty.

If you see here: math.kth.se/~laksov/courses/algebradr01/notes/topology4.pdf

Remark 4.24

Well my approach is something like that .....

@MartinSleziak My approach does not work, abandon it

ok

@DylanMoreland hi

Hi Benjamin.

How is life after politics?

@dylan after politics?

@tb I hope you don't mind if I ask this. You mentioned review of Vermessung der Welt in chat. Now I noticed that some Herr Bühler is mentioned there.

@BenjaminLim mod elections, he means

@DylanMoreland It's ok well it's prob good that I did not get elected.

probably will be pretty busy soon

@MartinSleziak Must be someone else and completely unrelated. It's a very common name. Not quite like Smith but close.

@tb Once I called my lecturer Fraulein (her surname)

Don't do that...

why?

Is that not miss or something

(unless that's her preference)

Ok. It just struck me as an interesting coincidence. (I did not know to which extent that surname is common.)

@MartinSleziak Bühl = Hill and there are many hills around here...

@BenjaminLim I know of no unmarried woman younger than 50 who likes to be addressed this way and of very few younger than 80.

Why is “Fräulein” considered offensive, as opposed to “Frau”? at german.SE

OMG OMG OMG...........

@tb Is Bühl some kind of Swiss Deutsch? Or is it standard German and I should now the word?

My dictionary did not find it.

@MartinSleziak It's not even used in Swiss German anymore I think. It has only survived names of ... hills and mountains.

Wiktionary article for Hügel mentions it as Süddeutsch dialect. I'll take your word for the fact that it is also some kind of veraltet form and I'll try to start doing something more useful than this.

@MartinSleziak Duden lists it under Bühel: süddeutsch und österreichisch in geographischen Namen für Hügel.

Yes, use Hügel.

But thanks for that, I've learned something new.

You may know Kitzbühel.

oh, of course

@MartinSleziak "The abolishment also had a lot to do with people calling unmarried mothers with children "Fräulein" in public to draw attention to their amorality." - didn't know this. Very sad... :(

@tb From the identical MHD bühel.

MHD = Mittelhochdeutsch?

Yes.

@JM Moreover it has the distinct ring of alte Jungfer.

BTW, since election results are known, should we expect something like inaugural speech from the newly-elected mods?

Has that ever happened?

I was already puzzled last year that no official announcement was made. They could at least have installed a banner for a day or two.

The banner would be SE equivalent of inaugural ceremony.

Exactly.

@Dylan It was my attempt to make a lame joke, but I wasn't around during the last election, so I do not know what usually happens after elections.

Apparently the assumption is that we'd be dutiful enough to check the election page when it's all over...

@tb Reminds me of a joke: "Shall we call you 'Professor' or 'Mrs.'?" "Call me 'Mrs.'; I worked harder for it."

Heh :)

Why can't we vote to migrate this to the main site?

(the close dialog doesn't provide the option).

That's odd.

Last year there was this question on meta concerning the elections.

@JM 2n+1?

@tb The close dialog doesn't provide Mathematica.SE either.

I asked a meta question and Asaf pointed out that there was already a question about that. I bumped it since the last bump was a month ago.

@robjohn But I index at $n=1$... :D

@JM but you're odd, so I'm not surprised :-p

your gravatar went all Yves Klein, @ClarkKent

@tb Hey

I've ditched my old approach, but the new one is not working out either.....

@MarianoSuárezAlvarez What is that for....

you reminded me of that

with your «I've ditched my old approach»

ah ok

:)

Naah I'm just trying to prove compactness of a noetherian space using a different approach

haha

The usual one is people say let $\Sigma$ be the collection of all finite covers of $X$

that follows from the intersection property at once, no?

@MarianoSuárezAlvarez Mmm, Kipling.

intersection property?

compactness can be expressed using closed sets instead of open ones

ah ok

But I am trying a different approach now

Would you like to see where it fails?

if it is not too long :)

ok

Let $\{V_a\}$ be a cover for $X$

By the Noetherian condition we get a maximal element $V_1$ out of this collection

We then get a maximal element out of $\{V_a\} - V_1$

and so on

and we get an ascending chain

$V_1 \subset V_1 \cup V_2 \ldots$ that must eventually stabilise

Say there is $n$ such that $V_1 \cup \ldots \cup V_n = V_1 \cup \ldots \cup V_{n+1}$

I claim that $V_1 \cup \ldots \cup V_n$ is a cover for $X$.

yes

If not, then there exists $x \in X$ such that $x \notin V_1 \cup \ldots V_n$

Now Mariano the problem comes in getting the contradiction out of this

Which I am failing now

@Mariano Somehow I want to use the fact that my $V_i's$ were all maximal elements of $\{V_a\} - V_1 - \ldots - V_i$

well, it would be best if you stopped the construction at the point where for no $V_{n+1}$ you get a bigger union

which is....

because otherwise you might get bad luck in the way Zorn picks the maximal opens

You mean say that $V_1\cup \ldots \cup V_{n+1}$ is my cover

no

ok

I mean: keep adding V_n's until you cannot add another element which increases the union

ok

didn't I do that already when I stopped at $V_1 \cup \ldots \cup V_n$?

well, you simply stopped when a maximal element fif not increase the union

I think that's what he did, Mariano. See what he writes here.

you might be unlucky in that a maximal element of the set of opens that you are left with at some point is actually contained in the union you have so far

hmmmmm

oh, ok, now I see the difference

I'm not getting the difference....

You might find that your $V_{n+1}$ doesn’t add anything new, but another maximal element does.

ok

so you're all saying

instead of looking at where the ascending chain stabilises

look at where the union does not add anything new.

Yes. Because the chain might stabilize temporarily, because of a bad choice at one stage.

Holy monkey.

in fact, you do not really need to pick a maximal element: it is enough to pick any open set which enlargens the union

@BrianMScott But this process could go on forever right? I mean to say, it is possible that everytime I throw in another $V_n$ I get something new...