12:00 AM
@ClarkKent yes (and the answer's yes)

user19161
@tb Shh...

It ain't no secret.

user19161
OK I only just figured it out, I am 9000 years behind the times.

@ClarkKent No.

I just got a little fed up with lots and lots of unsolicited mail, so I decided to hide it to the casual users.

12:01 AM
Good night!

good night.

user19161
@JonasTeuwen Ding ding ding!

@ClarkKent Yes!
Bai.

baba

goodnight

user19161
12:02 AM
If anyone knows where I can preview Folland's Advanced Calculus let me know.

user19161

user19161
I tried google books, amazon of course.

I was very tempted answer V. this to his query on the most complicated formula:

user19161
Another book I would like to preview is Kodaira's complex analysis.

user19161
12:04 AM
These publishers won't even let people see a few pages, sigh...

user19161
At least let people take a look before they decide whether to get it or not.

@tb What is that theorem?

user19161
And also I hope they get Ahlfor's Riemann Surfaces back into print. And also Beardon's Complex Analysis.

@PeterTamaroff dunno. I was more interested in the picture :) (and the Petit Nicolas story)

@PeterTamaroff I think he meant it in Jest.

12:09 AM
@PeterTamaroff you did see this, right?

user19161
@tb I remember how you once chided Strongart. I sort of chuckled.

@ClarkKent Oh, geometric measure theory?

user19161
@tb I can't remember the question, but you commented on his saying some nasty things in his profile.

But I also answered a few of his questions. They aren't bad if you manage to parse them.
@ClarkKent Are you having this comment by Alex B. in mind?

user19161
@tb Yes, I got the wrong person, haha!

12:14 AM
@ClarkKent Well, I wasn't nicer here (but Alex B. is another user whose name disappeared).

user19161
Haha, the comment is still there after so long.

And I believe the one with Alex's comment was the very first question I answered here.

Does anyone remember offhand whether a (non-diagonal) Jordan block necessarily has infinite order in GL_n(C)?

what if the diagonal is zero?

in GL_c they're invertible, so that's not allowed
pardon, GL_n(C)

12:19 AM
Oh, sorry, I misread. It's getting late :)

I suppose I should have said the group GL_n(C)

No, your question was fine :)

The min poly is $(x-\lambda)^{m-1}$ for an mxm block...

So I guess only roots of unity could do bad things, right?

yeah.

user19161
12:21 AM
@Bean Well, it already is a group.

that was a very subtle hint.
I think.
Just running some rough examples it doesn't look like the inverse can be obtained by powers, but I don't have a proof of this.

@tb There is a summer school in Number Theory at the Georgia Augusta this july right?

@FortuonPaendrag very possible. I left from there more than three years ago.

Oh, I see. A friend of mine was thinking about attending.

@FortuonPaendrag this, I assume.

12:33 AM
They seem to be advertising the same thing however

Yes, definitely.

@tb I measure people's worth by how they spell definitely.

@PeterTamaroff where did that come from? :)

@tb Just a fun fact.

I happen to be rather careful about it, myself, and I don't understand how it can be difficult nowadays... Every computer has a reasonable spell-checker.

12:41 AM
i judge people's self worth by their measure of others' self worth
2

@EricGregor I forgot to add use of punctuation, too, and how they spell "succinctiness". JK
Any cool foreign word I can learn?

Anyone else try and trick people with large vocabulary?

@PeterTamaroff paralelepípedo

Try Jugendtraum @PeterTamaroff

means cobblestone in portuguese

12:43 AM
Sending texts to numbers with "And don't worry, your looks definitely don't detract from your lovely personality".

@DannyRancher Just fooling around. You know, right?

No man, I'm for real.

@EricGregor Spanish is my mothertounge. Maybe a cool French word.

@PeterTamaroff I once spent an evening memorizing and learning how spell and pronounce Muvaffakiyetsizleştiricileştiriveremeyebileceklerimizdenmişsinizcesine. Needless to say that I didn't succeed.

@tb What is that!?!?!?

12:45 AM
"Hey, where's your smile gone?! I've done nothing but garland you with florid adulation since we met."

@PeterTamaroff the new longest Turkish word. Formerly it was, well, follow the link.

@tb Yeah, just read it. And I thought German had long words.
@DannyRancher Where's the trickery there?

@PeterTamaroff Ahh no trickery on the second one.

@PeterTamaroff yes, but we can't construct that complicated things. How about: Donaudampfschiffskapitänsmütze?

"You're the definition of pulchritude." is funny.

12:48 AM

@BrianMScott, I am understanding the answer at this exact moment! Thank you for your help.

You're very welcome.

@DannyRancher It sounds like it is a negative connotation! In Spanish the word "Pulcritud" is not really used. What would be the adjective, as in "you are ___________" (In Spanish we use "Pulcro")
@tb I only get the Captain part, if it isn't anything else.

Yes, its especially exciting when they think they have been insulted.
I guess it does share the same sounds as sepulchre (tomb).

stillicide is a good word

12:52 AM
@tb Google split it in two: Donaudampfschiff Kapitänsmütze

@PeterTamaroff 'cap of the captain of a steamship on the Donau'

Right.
When will THC start?

@PeterTamaroff If you load a question, it now displays a message claiming that the THC is going on right now, with a link to it. My clock says that it's actually about 6 minutes away yet.

@PeterTamaroff I believe the adjective is pulchritudinous.

@PeterTamaroff It might be that they now allow splitting those words into pieces. I grew up with the old version of the orthography, and I won't ever be able really learn the new one.

12:54 AM
@DannyRancher LOL

@DannyRancher Yep.

@PeterTamaroff Yes dripping with irony.

I invite everyone here to THC, starting right now.

### Math Town Hall Chat

I'm giving it a miss; I'd rather read the transcript.

I wonder where Gigili's gone..

1:05 AM
@FortuonPaendrag Town Hall Chat, I assume.

No, she isnt there either @Brian.

Well, I think that she did say at one point that it would be a bad time for her.

@BillDubuque THC STARTED
@robjohn THC STARTED

ah, that would explain it.

@FortuonPaendrag Let me think; she's 7.5 hours ahead of me, so it's 0430 her time.
And robjohn might be late getting back from his birthday dinner.

1:07 AM
oh, wow. its only 3 AM here in Budapest.

Gigili's UTC+0330.

I always thought she was from somewhere in South America, for some reason.

In her candidacy she mentioned being able to cover Asian time fairly well.

Ha. I should pay more attention to details, then.

@FortuonPaendrag I was in Budapest for about 10 days once, back around 1980 or so. Big topology conference.

1:12 AM
Its a beautiful city, is it not?

I thought so.
Though there were still some pretty grim reminders of unpleasantness in a few places.

Right. That was still back in the day..

Yep. Different world then.

The hour grows late. I wish you a good night, Brian! I will retire to bed now, for I have class early tomorrow!

Good night!
(I always hated early classes.)

1:16 AM
Also, you asked me to remind you of the sequence problem, which i just remembered myself.
Haha, same feelings here!

I've a feeling that that's going to be hard to repair, but I'll give it a bit more thought.

Thank you :)

I just figured out why I was rather unhappy about answering here lately. Of my last 10 answers only 2 were accepted and most of the others had absolutely no feed-back from the OPs whatsoever. The accepts are basically the only thing that really counts.
Since I'm often the only answerer of a question this always leaves me wondering what's wrong...

@tb :(

user19161
@tb Maybe the questions and answers are too difficult for the general population?

1:24 AM
I don't so much have this problem, since the questions I answer are usually easy, but the site has lost some charm.

user19161
@tb This is a sign that you should forget about the site and do more real math!

@ClarkKent I'm not complaining about lack of votes, I got quite enough (though for the wrong answers, as usual, I believe). It's the lack of feedback of the askers that I find really strange.

Does anyone else think that the town hall chat would be the ideal place for Jordan to complain about his academic life?

@ClarkKent maybe.

user19161
@DavidK Sorry, but no.

1:27 AM
@DavidK I'd rather love to see this :)

That would be awesome!

user19161
@tb I chuckled when I saw that question too.

user19161
@DavidK He invented the canonical form after all.

;)

Okay, I think I'll go have a peek into the "town hall"...

1:32 AM
come on over ;p

user19161
I'll come too.

Since f is linear, it is an injection.
Can the inverse be used to show a function is not an injection.
Since f is non-linear, it is not an injection.

What

it seems like some non-s moved where they shouldn't have and some conclusions are just wrong.

The lack of context is heroic, but certainly not all linear maps are injective.
2

1:37 AM
So, is this answer incorrect? math.stackexchange.com/a/140285/30011

user19161
@DannyRancher You need to look at an answer in the context of the question. You cannot just ask out of the blue "since f is linear it is an injection".

@DannyRancher Bill is correct as always, but also terse as always.
You could ask for clarification there. But it is a general pattern that any map $f\colon \mathbf R \to \mathbf R$ of the form $f(x) = mx + b$, with $m \neq 0$, is injective.
If you restrict such a thing to a subset such as the domain in your problem, it's still injective.
Does that make sense?
I'm really surprised that "The Chaz" is not participating in this.

Can someone help me with yet another Galois Theory question?

@DavidK I'm always up for Galois theory. Did you ever sort out that last one?

user19161
@DavidK It might be better to post on the main site to get more exposure.

1:45 AM
No. Not entirely.
@DylanMoreland I haven't yet determined if that Galois group of $$\Bbb{F}_{2}(x^{3})\subseteq\Bbb{F}_{2}(x)\subseteq\Bbb{F}_{2^{3}}(x)$$ is $C_{3}\times C_{3}$ or if it's $C_{9}$.
Where $C_{N}$ is the cyclic group with $N$ elements.

Well, again, I don't see a way to believe that it's $C_9$ if you believe that it has two distinct subfields of degree $3$. I'll try to set aside some time for it.
It is pretty shameful to be constructing $\ell$-adic Galois representations and yet not be able to nail something like that down.

I agree that it isn't $C_{9}$.
Yes. Shameful indeed.

And those are the only two groups of order $9$.

Ok. Suppose that I have the set of distinct roots $\alpha_{1},\ldots,\alpha_{\ell}$ of the monic irreducible polynomial $f$ over $\Bbb{Q}[x]$.
Then form the product $g_{n}(x)=\prod_{i}^{\ell}(x-\alpha_{i}^{n})$.
I'm trying to show that $g_{n}$ is a positive integer power of an irreducible poly over $\Bbb{Q}$.
Oh and $f$ is not cyclotomic.
I feel confident that I can show that $g_{n}$ has coefficients in $\Bbb{Q}[x]$ using Newton's formulas for symmetric polynomials. But I can't figure out how to show that $g_{n}$ is a positive integer power of an irreducible poly.
I tried it out using a CAS and some example irreducibles, and it seems that $g_{n}$ is always either a polynomial to the power 1, or to the power $\deg\{f\}$.

One way to go about this would be show that the $\alpha_i^n$ are all conjugate in some Galois extension of $\mathbf Q$.

1:57 AM
what a bummer this THC...

Right? I think that works. You really just want to show that the roots of that polynomial are roots of a single irreducible polynomial, and that happens iff you can find some automorphism over $\mathbf Q$ taking any given one to any other.
And from that perspective it seems clear. Look at the splitting field of $f$. The Galois group acts transitively on the $\alpha_i$, hence on the $\alpha_i^n$.

Hmm... Yes indeed. I hadn't thought of it quite like that.
But honestly I've been having trouble seeing the forest for the trees on this one.
@DylanMoreland Is this because for $\sigma\in\operatorname{Gal}(K/\Bbb{Q})$, $\sigma(\alpha_{i}^{n})=\sigma(\alpha_{i})^{n}$ ?

Exactly.

The townhall is ending, and the candidates are likely to come over here.

we're being kicked out :-)

2:03 AM
Was it just as short last year?

I think I see a bit of a way forward now. But I have another question on this problem. Suppose that I have $g_{m}$ and $g_{n}$ with $m<n$. Is it always the case that $g_{m}$ and $g_{n}$ have no common zeroes?

Now, I have to take Lilly out for a bit. I will return.

yes, just one hour last year too

I have to study for a midterm, but feel free to ask me anything. I'm around.

I liked Rob john's suggestion towards homework. I quote "I think that hints should first be given to help provoke thought. If they show interest in working the problem, then more of the answer can be shown in an answer. After a time, say a week or so (to give the assignment to be due), a complete answer could be given for completeness of the site."
This makes sense and in fact that is what I prefer. It would be great if that is made the policy and posted on the meta discouraging people from posting solutions.

2:06 AM
"After a time, say a week or so" - assuming good memory, that is...

Those contesting for mods can you kindly take the steps to make this as a policy?

At the current rate questions are coming in, it's easy to entomb a nice question...

@JM Then make a grammar and a spelling mistake in the title.
@JM Yes, s%·t just got real.

@PeterTamaroff Devious... :)

@Marvis This is my belief as well. I try to follow exactly this (but sometimes I break my own rule).

2:08 AM
@PeterTamaroff ...but things have always been complex here...

@JM Just fooling around. Maybe we can wait for tomorrow and try get the most users to see it. When do we have the peak hour in math.SE?

@Marvis I strictly object to making any simple-minded and rather obvious rules-of-thumb policies

@tb And I agree with this too.

There should always be things that manifestly don't have to be spelled out...

@Marvis The "gaming" nature of the SE platform spoils any hope of that kind of teaching succeeding. Some folks can't resist giving the complete answer to gain the rep. That spoils the teaching dialogue.

2:11 AM
@PeterTamaroff Nowadays I don't know. Maybe there's a query for that in the data explorer, but I haven't tried.

@BillDubuque I insist however, that if the OP asks for a full solution, and someone chooses to do so, he/she shouldn't be condemned.

I think Bill nailed the primary antagonist towards a cohesive homework policy.

@PeterTamaroff There's room for both. Let the OP choose what they desire.

@BillDubuque That's my point.

@mixedmath It is the nature of the beast.

2:17 AM
What do folks think are the biggest issues we face nowadays on MSE?

Imbalance of power and resources.
Oh, on MSE?

@AntonioVargas That's a different can of worms. :)

My main concern is the ever-increasing influx-rate of questions, mostly on the lower end of any scale I can think of.

@tb Any ideas on how to deal with that?

On that note: it is likely that there are questions languishing for lack of a better answer, or an answer, period. Only because the right people haven't seen them...

2:24 AM
@BillDubuque I don't know, but I'm getting less and less enthusiastic about the "question improvement" by over-zealous editing. Let the bad questions stand as bad as they are, ask the OPs to make them comprehensible by commenting. I'm not saying we shouldn't lend a hand when it comes to formatting, but we should not do even the "asking part" of asking a question.

@tb Indeed, editing cannot supply missing context. Perhaps we should strongly encourage folks to say something about their knowledge level in their profile, e.g. by having a standard form they could quickly fill out saying how far they have progressed in their studies. It certainly would be useful to know what courses they have completed and are studying, so e.g. one would know if one can mention ideals or not when answering questions in number theory.

@BillDubuque That is a good idea. But yes, what about people like me?
I think the OP should make it explicit what context he/she is solving the question in.

@PeterTamaroff "I ran into this problem when I was looking at exercise bla-dee-dah from book Y..."
(sadly most people don't bother with sentences like that.)

@JM Right. Or simply "I'm studying X and I can't solve this problem Y".
Maybe we can create a templete people can read before making a questions. Like those "Did you know?" when you get a new program.

2:32 AM
I mean, there's a reason why "what have you tried?" is an exceedingly common comment.

I don't mind having to ask a question or two in the comments; the response or lack thereof usually gives me a good idea of how I want to proceed (or not) with an answer.

Did you know?: You will get much better answers if you provide some context to your question. Where is this problem for? What have you tried to solve it?

@PeterTamaroff Yes, context is crucial. I didn't mean to imply that those courses need have been in a university. They could have been self-study. Is that your case? Anything that serves to efficiently convey one's level of knowledge suffices.

@Marvis: I have created a question along those lines

Remember: Always make a reference if you retrieved this problem from a book. Example:"This problem is from Rudin's Analysis, Chapter X, Section Y".

2:34 AM
whoops

@BrianMScott It's a nice diagnostic aid, I agree...

Thanks t.b.
I see the discussion here is about the same topic

@mixedmath Maybe I can add what we're discussing (the auto hints).
But some people might not like it. I'm not sure yet.

you could certainly air the idea. Write an answer about the possibility, and see what the world has to say

@BillDubuque I like this idea and I think it should be encouraged in both departments: askers and answerers (or students and teachers): provide info in your profile if you only have a few questions, or look at the profiles before answering, respectively.

2:50 AM
Is the proof of the Marcinkiewicz Interpolation Theorem worth remembering? If you do know it, how do you remember the proof? That is, how would you state the ingrediants/recipe for it in simple words?
I will post this question on the main site, I just want to make sure it's not a poor question

Riesz-Thorin, Black Magic

lol
it's such a long proof. i was told by a professor that i should know it

Have I missed THC? I fell asleep

@Gigili It's over, yes. They'll post the transcript though.

you run an unconventional campaign @gigili
2

2:54 AM
@Gigili You did miss it!

@EricGregor I don't think you should strive for knowing it by heart directly, but I think it is a good theorem to spend a lot of time with because of the fact that nothing that enters is really boring, on the contrary: every technique has proved useful. There are various takes on it, but the essence is always the same, as far as I seem to remember.

@Gigili: If I were you, I would go ahead and answer all the questions on the THC. I think you'll still be included on the digest

I think that I saw her leave right after J.M. answered her question.

thanks @tb, i'll take a look at it tomorrow then

3:12 AM
@BillDubuque Very true and I have been guilty of this as well. The only justification I have is that there is no consensus in the community on this issue.

@mixedmath Done How does it look?
@BillDubuque See the link above. It probably concerns you.

I do not understand the moderator election. What are the duties of a moderator?

@MarkDominus Janitor+policeman, in essence.

Who are the current moderators? How long is the term?
I have never noticed any moderator actions. Have there been any lately? How would I know if someone was doing a good job?

@MarkDominus They're listed here. Apparently, they're mods as long as they can be.

3:22 AM
@MarkDominus The fact that you've noticed nothing is probably a positive indication.

Sure, but it also suggests that perhaps we don't need more moderators.

That you do not see us is good :)
2

@MarkDominus On the other hand, given the increased turnover of questions, it's nice to have a few more people patrolling...

@MarianoSuárezAlvarez Is it good if we don't even see your grin?

@Mariano Do we need more moderators?

3:24 AM
@MarkDominus Too much questions!
@MarianoSuárezAlvarez The grin should stay.

@Mark: have you ever flagged anything you saw on main, by any chance?

@MarkDominus, it'd probably help distributing the load

No, I've never seen anything that seemed to need flagging.
@Mariano Do you endorse any of the candidates?

@PeterTamaroff I like the second message, but not the first. I'd prefer that you get rid of the first and add something like Where did the problem come from to the second.

3:26 AM
I will not answer that, Mark
it would not be fair

@BrianMScott You can do that yourself. You are very welcome.

@MarkDominus Quite loaded, that one... no?

Only if the moderatorship is a prize that people covet.
If it is just a janitorial position, there should be no problem in saying who might to a good job.

@MarkDominus LOL. Wikipedia links to a Pokemon move when I hover over "covet".
@MarkDominus As I told Brian, janitor here, mathematician in former Soviet Russia.

Hey guys

3:31 AM
I need help with a title suggestion. Many people complain about titles that are purely formulas, but the body of the question makes it very hard for me t choose anything reasonable.

What's wrong with formula titles? Hard to search on?

if you remove all the formatting, the title becomes usable

what's happening with town hall chat?

@MarkDominus hard to right click in order to open it in a new tab, for example
@BenjaminLim it happens to be over

3:32 AM
@tb This is so frustrating.

oh

I think a good title would be "Is there a set $\mathfrak{S}(\mathbb{R})$, which satisfies: $\mathfrak{B}(\mathbb{R} )\subset \mathfrak{S}(\mathbb{R})\subset \mathfrak{L}(\mathbb{R})$?"

@tb Is there a $\sigma$-algebra on $\Bbb R$ strictly between the Borel and Lebesgue algebras?

Brian hit it on the nose, I think.

@BenjaminLim You can still go to the town hall chatroom and answer the questions that were asked there. Your responses should be included in the transcript published tomorrow (I think)

3:33 AM
@BrianMScott You read my mind! That's what I wanted to do, but it seemed ... intrusive, thank's I'll go for it.

thanks antonio

@BrianMScott I left because I found the answer to my question and was trying to do it before it's too late again. I don't know what you're after by saying that.

@Gigili A couple of people were leaving moderately urgent messages for you here, and I was letting them know that you might not get those messages in time. That's all.

@Gigili Yes, don't get it wrong Gig!

Hey all. Sorry I had to leave right after the THC.

3:42 AM
Ah, okay.

@robjohn Did you went to walk your dog?

@AntonioVargas I think I got them all. I looked for the comments with the large number of stars.
I should go back and look to be sure.
@PeterTamaroff yes, and then my wife and I had a small b-day celebration.

Any cake? Or was it a lie?

@robjohn Oh, apparently I haven't so: happy natal day!
@robjohn Peter was obliquely referencing this old video game... ;)

3:47 AM
@JM I thought you had, but then a lot has gone on today.

@PeterTamaroff The Greeks said that the horse was a lie...

@robjohn Hahahah, LOL

@robjohn Felicitations: you beat me by six days.

3:49 AM
@BrianMScott Well, I will try to remember, but Happy B-Day in advance :-)

Thanks! :-)

@JM Finally, you are able :-)

@JM You'll break the internets. It happened to me once.

@robjohn: I feel honored about the pinned message, thanks! :)

@tb It is interesting since I did not pin it :-)
@tb I remember you saying it, but a mod must have pinned it.

3:53 AM
ditto :)

Pah, I stayed up till 0430 AM and I only needed to wait another 30 minutes then I fell asleep. It's always like that. Pah.
Oh wait, did I say Pah twice?

@tb It was pinned by JM. I can see that :-)

You're going ballistic with Pah's

@robjohn Zounds, my nefarious scheme has been found out! :)

@JM I'm a sneaky little snit, just like Needermeyer... (from Animal House with some modification)

3:55 AM
@Gigili It 1 AM here Gigili. Is "Pah" some variant for "Bah"?

@robjohn I loved that movie...

Here is the actual quote: "Put Neidermeyer on it. He's a sneaky little shit, just like you"

I'm off to bed. Night all.

@PeterTamaroff Oboy, different time zones sucks. Yes, it's a strong form of it. Like, double bah.

The townhall was fun :)

3:57 AM
@AntonioVargas good night!

@Gigili I don't remember where you are.

@AntonioVargas See you!

@JM I feel honored, it's the second time you allot a special space for one of my ... gags?

Any one can reccommend some nice piece of music?

@tb :D

3:59 AM
@MarianoSuárezAlvarez: I've removed two of my comments already, I don't really get what you mean by less inflamed.