@JM burn it with fire

Sure, I don't want a rash of people suddenly asking about 2+5/3 or that "unanswerable question" nonsense...

@JM I didn't resist to also answer him (

@Gortaur ;P

@JM though it was closed quite quickly

12:45 PM
only 'cause Willie's there...

@JM i don't think it's a bad question. off topic, sure, but isn't bad

i especially liked the one about blowing up points on the plane

@AlexeiAverchenko which one?

1:08 PM

@JM Done! That felt good.

@JonasTeuwen I know, right? :)

1:31 PM
Hmm, apparently there is now a Tintin movie coming soon...

@JM Yes.

hi @all : I need a formula for discrete Riesz transform in terms of Fourier multiplier...plz help
in 2 dimensions
basically i need to compute a Riesz transform for an image ( a 2-d array of pixels)

Please ask this on the main site! This is more like the "social room" of MSE to me.

"Pub" is shorter to say, Jonas... ;)

1:40 PM
@JM Then where are the drinks? :D.

Asaf has drunk them all... :D

drank !

All the presents that I've got yesterday involve alcohol. Does that mean something? Oh, I've also got an automatic pencil sharpener!

What kind of gift is a pencil sharpener? :D

a good pencil sharpener is hard to find, i say!

1:50 PM
So... Are there any simple examples of the n roots of unity in the context of ring theory?
For I know that 1) my professor is fond of roots of unity, and 2) I have a test on ring theory in 40 minutes!

Best of Luck !

:)

I only use pencils to write.

Oh, you don't like ink?

I push way too hard plus I'm left-handed. It gives a mess.

2:04 PM
"push way too hard" - But you don't break pencil lead?

Yeah, I have found very good pencils. The lead doesn't break!

At least you're now circling "Staff" instead of "Student"... :)

Yes!
I can see that it is not approved yet.

It is quite impressive that a mathematician can influence you so much that you are unable to spell his name right...

yeah it should be galwah not galois

2:18 PM
@TheChaz Good luck The Chaz! Unfortunately my knowledge does not extend beyond first and second roots of unity, I'm afraid...

Huh... the funny thing is, I'm told that Viets are usually pretty good with French...

@tb Wait. It is Évariste Galois right? Just as it is written there?

^_^ thanks! I'd better sign off

Oh. CW. Nevermind.

@JonasTeuwen Yep, I already corrected it.

2:30 PM
Good one: 100€ real life bounty for an MO answer :)
2

At least I understand the question :-).
100 EUR should do the trick I think :-).

Has there ever been a day where all the questions on MO's front page could all be understood by at least one mathematician? :)

@JM Today it doesn't seem that much of a challenge. I would say that I understand all but 5 of the first 30 right now.

My life fades... the vision dims... all that remains are memories.

Meaning: I understand the questions, understanding their motivation is another issue...

2:41 PM
math.stackexchange.com/questions/83379 is a duplicate, but not of that question you suggested JM.

It is a duplicate of that other one with the "paradox -1=1"

@Asaf: sorry, went to the FAQ thread and just picked the principal roots question. Please vote with that better duplicate.

I cannot find it, though :\

@JM I think I found it and Zev has closed the question.

2:46 PM
All those tags are useless sometimes.

Maybe we need a tag `awesome`?

For stuff that we will later close duplicates of? More like or ...

@t.b. : thanks for the edit.

Hmm, that's nice as well (how do you do the thing with tags in the chat?).

`[tag:blablabla]`

I hate when i ping someone and don't get a response

@JM Does he have a further account? I remember this one and flagged for merging.

@JM Heh.

@Rajesh: you're welcome

Yeah, I remember asking that rearrangement question and poof, there's Stan Wagon...

2:53 PM
Did we remove or did Victor just tired himself out of using it?

Porton?

Oops, I mean it's Candlejack, not Crackerjack...

:D.

@AsafKaragila Looks like it was burninated (as Jeff would put it). I'm pretty sure that this question was tagged this way and the revision history doesn't show any edit removing the tag.
@JonasTeuwen Who else?

@tb Trogdor, The Burninator!!

2:58 PM
@JM I thought you meant he was on crack since he checked all of those graphs.

Oh, no. I meant he shows up some time after I mention his name...

3:19 PM
For the question on compactness characterization for metric spaces, can someone help me formalise/bust my idea?

@Srivatsan what idea?

What's the idea? You can find this theorem in many textbooks on metric spaces...

I thought of something and want to know if it works.
(As the OP notes, proving the theorem is not the issue. S/he wants to show 5=>4 and some other implication directly.)

Oops, I've just skimmed the question :-).

Given a cover A. Roughly, I want to set up a partially ordered set of subcovers of A ordered by inclusion.

3:22 PM
I would go indirect assuming not 4 for both implications OP asks about.

Ok, let's go that route.

What is a point to put a part of my answer an hour after as a separate answer?

So, there is a cover A of X containing finite subcover. (thinking aloud)

But I haven't really thought about it. I can show not 4 implies not 3 (easy) and I don't really care bout 5.

@Gortaur No clue. Yours is better anyway.

3:25 PM
@tb Me neither; this is the first time I am seeing 5. =)
Is it useful?

@Srivatsan I don't remember having seen it in use.

@JonasTeuwen just surprised by a situation: usually two questions either very close but appear almost in the same time, or the latter one mentions the first one and adds something more )
@Jonas: how are you? how is the 1st day of the defended PhD student? and thanks for upvoting btw

@TheChaz How did it go? Did you find your roots?

Not smoothly.
R[x] is a PID <=> R is a field
Ring of formal power series of a field is a PID
R[x]/I[x] isomorphic to (R/I)[x] for ideal I of ring R
Plus a few things that I WAS able to do...
No roots of unity or Euclidean domains.

@Gortaur Defended MSc student :-). The PhD is for in four years!
Roots, bloody roots.

3:36 PM
@JonasTeuwen you're defended, but you're PhD student. After you defend your PhD you're not a student anymore

@TheChaz Looks like you should start reading your professor a bit better :)

@Gortaur Complex ;-).

Seriously! He said there wouldn't be any computation, yet I spent most of my studying on norms and division algorithms.
Now I'm in a lecture on Jensens inequality, then ultimate frisbee. I'll return later. Ciao

sounds like interesting problems
what is I[x]?

@TheChaz have fun! see you later

3:41 PM
is it it just (I,x)?
no it can't be

@AlexeiAverchenko Hi, almost from there :)

4:00 PM

"Then I have a line from x to the height of 1 on y and join these points. " - can you tell what the OP means?

@Srivatsan I like the "taking screenshots in mac" tab.

@tb I can never seem to remember it =)

I think its better to suggest a textbook on co-ordinate geometry.

4:04 PM
@J.M. he must be really struggling if he thinks there's enough information in that for someone to be able to understand it

@Srivatsan I don't know, but one certainly doesn't draw a slope...
@Srivatsan Can you check again?

@Srivatsan I don't know if this still exists in Lion, but I'd assume so. For a long time there's been shift-command-4 which gives you a cross-hair with which you can select the region you want to take a shot of.

@tb Yes, I think it does. But this was kind of faster.
Any issues with taking the scrshot of the whole screen [other than the privacy concerns]?
@JM Well, I interpreted it as how to visualise the slope; that makes some sense.
@JM That works.

@JM In the first line after "we have" the closing parenthesis still is too far to the right for me
Maybe 3-4 mm or so.

tb might be right. I can't tell where the math is supposed to end.

4:11 PM
Any suggestions from you guys? Anything smaller than `\small` is too small methinks...

@JM It looks like square brackets would do the trick for me.

@JM footnotesize =)

@Srivatsan :P

Perfect for large involved calculations such as this. =)

On the other hand, the preview reveals that the closing parenthesis is more or less tangent to the right hand border of the display, so I'd probably just leave it.

4:15 PM
@JM You asked the OP not to post that question there. Where is there? Just curious.

I went with brackets anyway... thanks, you guys.

Looks much better this way, yes.

@robjohn I was echoing Gortaur in that thread. :)
@Sri, it seems you introduced an error in the rencontres thread...

@JM It's interesting that the OP asks for tips to be a "social homosapien" in a math forum. =)

4:20 PM
@JM There's one thing I don't understand: shouldn't you round up?

@JM One second. Let me check.

@Gortaur: in your comment to this question, you ask the OP not to ask the question there. Where is there?
@JM So there :-p

@robjohn good morning. I gave one guy a reference to MO thread since he asked about cool formulas.

Ah, so don't post to MO. Good advice.

and since this guy didn't seem reliable I asked him not to post on MO
@JM where?

4:22 PM
there ;-)

@tb Nope, it's round to nearest. The formulation in CM is in fact \lfloor (stuff) +1/2 \rfloor.

@JM "where the ratio is rounded up for even n and rounded down for odd n. For n ≥ 1, this gives the nearest integer." - nonstandard notation and the OP somehow picked only the math leaving the explanation
Er, =/. Another blunder @JM. I rolled back to revision 3 without realising your edit

@robjohn :-p

(I wonder if we'll ever get standard notation for the rounding function)

now i know where to send love letters to 8)

4:23 PM
@JM [x] = floor(x), isn't it?

Nah, in some contexts, since \lfloor x \rfloor is already used, that frees brackets for either Iverson or rounding...

@Gortaur Hey, at least I provided a link :-)

@JM I still don't get it: say that !n is an integer and you know that !n > n!/e and the error is smaller than an integer. So ceil should do the job, no?

anyone understood Chaz' earlier question? what's I[x] in R[x]/I[x]
is that notation used often?
(I've never seen it)

Is there a way to get a link to a comment (like this) other than looking at the source of a page?
2

4:26 PM
@tb Oh... you're right. I guess I can use the ceiling. :)

@robjohn brutal methods you use )

Though round and ceiling actually do the same thing in this case, using the ceiling is more logical. I'll edit.

@JM I usually use floor(x+1/2)

@robjohn That's what Knuth et al. had in CM... :D

@Gortaur that's why I was asking if there is a gentler method.
@JM Then I take solace that I am in good company :-)

4:28 PM
@robjohn but if you use rounding very often in your paper you may want to denote it as a single symbol

@Gortaur True. I have never seen a symbol for it. I think because in CS there are so many flavors of rounding.

Round to the nearest integer comes up less often than I would expect it to.

@JM I'd really avoid the square brackets for nearest integer. Gaußklammern still are pretty commonly used by the Iverson-unenlightened.

Oh, some people use \lfloor x \rceil. How about trying this, @JM?
Although I find it asymmetric and hard on my eyes.

In one flavor round(3.5) = 4 = round(4.5) and round(5.5) = 6 = round(6.5)

4:33 PM
@tb Wait... for odd n, the ceiling looks to be off by 1 from the sum representation. Rounding works, however

@robjohn I think it's called the the banker's algorithm?

@Srivatsan ...and that's why I don't like it. :)

@Srivatsan I don't know the name, but if the number is exacly half way between, round to the even number.

@JM Agreed. I wouldn't push someone to use it any day.

It fixes the up or down grading of \$.005 in most cases.

4:35 PM
Banker's algorithm is something else.

@Srivatsan Cool compendium of rounding methods.

@robjohn Thank the wiki-god. =)

@Srivatsan I pay homage every day.

@JM Ceil(Integer x minus something smaller than 1) = x for me. I'm confused.
Ah, I see, you seem to have dropped a sign

!n is not always greater than n!/e

4:39 PM
@robjohn Yes, I just looked at the last displayed equation before the horizontal line. There's a (-1)^{n+1} missing there.

@robjohn [adding to robjohn's comment] In fact, since 1/e = 1/0! - 1/1! + ... is an alternating series, the partial sums alternate above and below 1/e.

QED, I is an ideal of ring R.
I[x] is the polynomial ring with coefficients in I.
(R/I)[x] is the polynomial ring with coefficients being cosets (I think! - keep in mind that 60 is a generous upper bound estimate of my grade...)

I'm shaky too, then -- I had to look up what the hell sec is.

@Srivatsan Well, I don't know how to handle sec/csc either. Never seen any use in them

4:44 PM
@tb Really. I thought sec comes up everywhere. // Forget cosec. That's useless; I agree.

I write 1/cos

Everywhere in trig identities!

I wouldn't say "everywhere"... but it's pretty convenient with Mercator...

@tb That's new to me.

(so-called)

4:45 PM
@Srivatsan We only learn sin/cos/tan in school.
(amply enough for everything)

@JM I was exaggerating a bit, but yes, it does come up everywhere. =)
@tb I thinking of a compelling case for sec. The main thing I can think of is that sec^2 is the derivative of tan. But you could of course, remember it as 1/cos^2...

Well, as I said, secant is pretty intertwined with the Mercator projection. Otherwise, I don't know any other reason to consider sec except convenience...

(Oh, and versine is numerically sound, I maintain.)

@HenningMakholm tan is just sin/cos. =) So why is that tan gets a special place?
[Serious question.]

4:51 PM
@Srivatsan That's what I always do. In fact, I was thinking about asking a question on the main site: "why do people here like to use sec/csc?" (I decided against it for being subj/arg. They seem like they only produce an overflow of trig identities for nothing. If I remember correctly dropping the other functions was a decision taken by the pedagogues sometime back in the early 20th century in Switzerland.

@Srivatsan My best guess is that the tangent is particularly important because it connects "angle" and "slope".

@Srivatsan tan really arises often enough, for example slopes...

If we take the inverse function viewpoint, I like arctangent more than the other inverse functions...

@JM Yes. Arctangent is particularly nice.

Computers agree with that -- they usually have arctangent as a primitive, but not other inverse trig functions.

4:53 PM
So, if I wanted "extreme trigonometry", I'd only retain sine and arctangent...

I still think that sec is a primitive. To think otherwise... I don't even know what that means. =)

@Srivatsan Like I said, the importance is with the mapmakers...

@JM And, another question: why place sine ahead of cosine? For some reason, I like cosine better. // It's reciprocal is this other nice function called "sec" =)

@robjohn The SE modifications script does that (so you can just right click on the time stamp and and copy the link). Jack said some time ago that it is easy to make a bookmarklet out of the relevant part.

2 arctan(y/(x+sqrt(x^2+y^2))

4:55 PM
@robjohn What is this?

@Srivatsan I think we'll have to go all the way back to Babylon for that...
@Srivatsan How to fake two-argument arctangent...

@Srivatsan Gives you the angle from x and y. No quadrant chasing. What JM said.

@robjohn Ok, thanks.

@JM I like tan(x/2), you can get all the other trig funcs from it pretty easily.

Speaking of which: I'd estimate that about half the time the arctangent is being used, it'd be more appropriate to recast in terms of the two-argument form...

4:58 PM
And it's a useful trig sub

two argument?

@QED Some languages call it `atan2()`.

@JM I also like cos for another reason. It's usually nicer to keep the denominator clean and push the mess to the numerator. So, I like to think of tan as sqrt(1-cos^2)/cos, rather than as sin/sqrt(1-sin^2).

@robjohn I agree that Weierstrass is totally neat.

What tags are appropriate for questions on differentiationg under integral sign?
According to tag wiki (integral) does not belong there: math.stackexchange.com/tags/integral/info
But many of them seems to be tagged (integral) - and to me it seems quite reasonable. math.stackexchange.com/search?q=integral+differentiation math.stackexchange.com/search?q=integral+derivative

4:59 PM
@JM So basically my world contains cosine, cocosine, tangent and secant. =)

@MartinSleziak apart from ? Hmm...

Right.

Hehe, "cocos"...

Legendary beginning of an answer: HINT: first of all I think that your substitution isn't correct. :D
2

5:01 PM
@tb :D

Oh Bill... what have thee wrought?

@JM I did not like real-analysis as the only tag here: math.stackexchange.com/posts/35625/revisions So I retagged - and I did not notice that I included (integral) tag, which Henning delete just a few minutes before.

Hah, we were discussing "calculus" versus "real analysis" only a few hours ago... :D

@MartinSleziak My main business was to remove (differential), which I'm currently exterminating.

@HenningMakholm I agree with this, though I wonder if we should have a separate tag for all those "derivative of blabla" questions...

5:06 PM
That's a good but separate question. I think at least half of the (differential) questions are just there because someone typed "differential calculus" into the tag field. Very few of them are about actual differentials.
But I would be very happy if at the bottom of the (differential) pile I find that it all started with a question that subsequently migrated to mechanical-engineering.SE.

Yep.

Well, it seems to be rather unclear what should go under real-analysis and what under calculus.

Probably the only thing agreed on is that real analysis is the superset...
@Henning: "quotienting" might not be a real word, but I think I might try it out sometime... :D

What on earth is this question about?
@JM "To quotient out" appears to be a respectable verb in algebra. Why whouldn't it have a gerund?

5:22 PM
@HenningMakholm Work in Gödel-Bernays and take the group axioms but replace sets with proper classes.

Oh, right, there was a definition in the first line. Didn't notice that among all the shouting :-)

Hmm, apparently group theory does use "quotiented"...
I learned something today! :)

It continues to amaze me that questions such as this get upvoted.

Does anybody know how to change the user name?
I don't want to be confused with robjohn

5:32 PM
"Please frame your answer not in a high-technical manner, but in the way a beginner can understand, but please answer me in a detailed manner. " - sorta kinda oxymoronic, no?

@JM I continue to be confused by your rencontres answer. Isn't there a sign missing in the formula between "and since" and "along with knowing"

@JM Yes, exactly. The "please tell me exactly what the the author of this-and-this particular enigmatic remark intended" theme is bad enough in itself, but this...

@tb Tsk, right. Thanks for catching.

@JM That's where the whole ceiling/rounding confusion came from, as far as I'm concerned :)

Sorry about that. I misinterpreted a sentence in CM. I added an absolute value, which apparently was implicit in the sentence I misunderstood.
(and thanks again for debugging!)

5:42 PM
No problem, and the argument afterwards is very easy to follow even if it looks scary... But the prize of the scariest formulas of the week go to the other answer here (the Dirichlet thing)

What does it take to think like a pure mathematician?

My queation is what is the major difference between the way a pure mathematician thinks and the rest of us and what brought about that difference? Thank you.

@HenningMakholm Yes it was closed before I got a good answer Sir
Obviously, what brought about the change was an inborn ability to abstract but what are some others?

Why don't you give it a rest?

6:10 PM
@Matt I apologize if I have offended you or anybody else here ... I will "give it a rest" Sir

6:45 PM
Was I too rude there?

I might have been more abrasive myself, so I can't answer that... :)
Apparently the harmonic series is not in the FAQ. Would this be a good candidate (after a bit of editing)?
Or this?

7:01 PM
@JM I vote for the second one. And I agree that it's a good candidate for FAQ.

@Sri: could you do the honors? :)

@JM - what should I do?

On that note: the words "harmonic" and "Oresme" only show up in the comments. Google will pick that up, but the built-in search engine won't...

Hilarious: OP's question starts with: A proof of the quadratic reciprocity by Zolotareff has recently been found.. Qiaochu: I don't mean to be rude, but 1872 is recent? OP: @QiaochuYuan: I mean recently found by me, sorry for the inconvenience...
3

Oh, English... :D

7:14 PM
I'm finding Eisenbud/Harris's Geometry of Schemes to be a wonderful book. It should be recommended more often!

@JM done/done/done.
I added the name "harmonic" to the post. Oresme - is that too relevant?
It's of historic interest, sure. But I don't think users will search for that keyword.

I decided to append it to the top answer.
Off to bed for me. Later.

Good night, @JM.

Good night!

Goodnight!

7:29 PM
@Zhen: If by Sym(V) you just mean any permutation of V, then there is a class-ful of permutations there.

Indeed. That's the point.

If you mean elementary embeddings... then V has only the identity.

Which is why I didn't write Aut(V), which would have been ambiguous.
Anyway... I thought the universe could have non-trivial automorphisms?

@ZhenLin The axiom of choice implies that no. It is still open whether or not ZF is fine with nontrivial automorphisms.

Ah.
One of Forster's students here recently thought he had a proof that ZF couldn't have automorphisms. I think. I don't quite remember.

7:38 PM
Interesting. Do let me know if you remember anything.

@Zhen: only assuming that inaccessibles exist, but as is well known, they don't :)

There were some conditions attached... something like, non-decreasing on ordinals.

I don't see how it can be decreasing on ordinals and still be elementary embedding.

shrug

8:03 PM
Glendronach is good stuff.

Send me the bottle. It is your sworn duty to your Koenig.

@Asaf: if you give me your address you can have all my (empty) bottles, if you wish.

I'm good, thanks :-)

What's all this about free bottles?!?

Free empty bottles.

8:09 PM
@JonasTeuwen If you're interested in adding some joyous flavor by being the executioner, try here, here or here

@tb Nice. Damn Asaf and Sr. closed the last two.

Muhaha.

Guys, why do you think I addressed this to Jonas, that you eejits close it? It was supposed to be a gift for his master!

Yes, quite lame of you @AsafKaragila.

He has whiskey. I have nothing.

8:12 PM
You're lying.

Seems he didn't get to write up the low-hanging fruit question either.

It feels quite strange to not take the mathematics home.

"The master forbids it" - from the MO thread on anecdotes/urban legends

Okay, fine. I have some stuff. He got whiskey though.

No, I've got whisky.
Don't you dare call Glendronach whiskey!

8:13 PM
Minor distinction that eludes the König, I s'pose

I've found worms in LHFruit before, so I approach with caution

Nah. I know the difference.

(hmm. Accessing the chat room in "mobile view" enhances my usual sensation that I am talking with myself!)

Irish vs. Scotch...

@Srivatsan: you could make those two \$X\$ and \$Y\$ lowercase while you're at it.
Thanks!

8:16 PM
(done)

@tb I was wondering myself =)

Isn't he suspended from MO?

I think a few weeks more, yes.

8:29 PM
Why exactly was he suspended? // Any particular trigger?

For being... himself.

=).

He was at the feet of all the professors.

Ok, got to run. Have a talk right now.

Good luck.

8:32 PM
Huh? Do two irrational numbers have a rational sum if and only if they are two irrational numbers that sum to a rational number?

Two irrational numbers a,b have a rational sum if and only if a-b is rational.

Really? So since a=4-pi and b=pi have a rational sum, it follows that a-b=4-2pi is rational?

I meant a+b.
I'm tired and all that.

Okay.

@tb Maybe the 100 EUR question has been answered :-).

8:39 PM
@Jonas By you?

@AsafKaragila No :(.

@JonasTeuwen No surprise that people went for a counterexample (everything else would have been). Let's see what happens.

@tb @Jonas Functional analysis question: on a finite measure space, which way around are the L^p containments?

@ZhenLin If a function is bounded then it will be integrable. You have a chain of inclusions :-).

May I ask your scholarly opinions on a pdf file I found?

8:49 PM
Yes, but it goes one way for finite measure spaces and the other way around for counting measure...

Yes, but you can quickly figure out with Cauchy Schwarz or by L^infty in L^1.
The rest is the same.
Yes, for the counting measure it is the other way around, but that is no finite measure space usually.

@ZhenLin As Jonas put it the infinity case is the key mnemonic: (power) summable sequences must tend to zero, so must be bounded, so the little l^p spaces grow with p. The finite measure case was mentioned by him.

Ah, thanks!