look at $$ h=\frac{1}{f(z)-x} $$

it will be holomorphic and bounded

@DominicMichaelis but why entire?

f(z)-x is nowwhere 0 hence 1/ is complex differentialbe everywhere

so you are assuming that there is a unique element not in the image?

sorry liovilly implies that the set is $\mathbb{C}$ minus some closed sets which only open subsets are the empty set

there can be more than one element not in the image

@DominicMichaelis I am not following your argument

wait i need to do something give me 5 minutes

ohh, right, I see it now

so Liouville shows that if x is not in the image, then unless the function is constant, there will not be any open ball around x not in the image

so the set of elements not in the image is discrete

well lines could be not in the image too

made a mistake in my thinking

but at least no open balls

@DominicMichaelis ahh, right

otherwise, we are not sure that the function is bounded

jupp

well i guess we can disprove the lines with some fancy connectness proof

@DominicMichaelis or we could look up a proof of Picard of course

mh yeah i guess that works too :)

why to hell is my answer is not right -.-

hi

I have been studying this matrix by the method of prolonged staring for more than year. The only things I have learned are that one can calculate the von Mangoldt function and the Moebius function from it, and that the diagonal is the Dirichlet inverse of the Euler totient. And also the most negative eigenvalue appears to be close to a prime number.

Damn, I need a pen!

Is my comment out of order?

@GitGud I would say very much so

for what you need an easy solution when you have a complicated one

we want to encourage answers that provide extra details and shows how this fits into the more advanced theory

i always prove that there are infinite many primes with goldbachs conjecture ;)

@DominicMichaelis That's my point, I doubt his intention is anything other than to show off.

@GitGud it is still a really rude remark

@TobiasKildetoft I had the impression it might be, hence me being here asking people about it. I already deleted it.

good

I find that post very entertaining. Even better, being the date it is.

LOL

@Expert Hi dude.

Wait, what the hell. That "Expert" is just a user fooling us. Argh

In this case, he is.

@JasperLoy I guessed so.

@JasperLoy Haha, amen!

By the way, what happened to that guy called usersomething who was studying group theory?

@GitGud he was called caveman for a while

he left recently

nope he means user5861 or something like that

Might be. I don't know. Can you find a link to his profile?

Dominic is correct.

@JasperLoy “her”?

user58512, right?

@pen Yeah, probably. I don't know the number by heart, but it is familiar.

Wait, 58512 was the username of caveman. I don't know the new number.

Chat Etiquette Guidelines | $\LaTeX$ support for chat?

was caveman all the time caveman ?

@JasperLoy I LHF'd.

The shame

@JasperLoy Where, where?

@PeterTamaroff could you please not answer such questions until the asker has had a chance to clarify where he is stuck and how he has had those functions defined?

@JasperLoy whether it is helpful to the OP depends on those things

@JasperLoy I disagree. For the first period of time, the answers should be aimed at the OP

To help Tobias' point, I don't even know what $P$ is supposed to be.

@JasperLoy yes, but = does not depend heavily on context

for me, a capital P in the context of combinatorics will usually mean some kind of partition

@JasperLoy The thing is, assuming I'm not a complete ignorant to this matters, if it's elementary enough and I don't know it, maybe there's something wrong with the question? And look, not even julien knew what it was.

@TobiasKildetoft Well, $C(n,k)$ is standard notation. $P(n,k)$ too. It is the number of subsets (respecting order) among subsets of size $k$ of a $n$ size set.

For example, if we take $n=3$, $k=2$

@PeterTamaroff yes, but there are two ways of defining those functions

We have $a,b,c$ and

and depending on which way they have been defined, a different answer will be more useful

we get ab,ac,ba,bc,cb,ca

@TobiasKildetoft I was certain of the notation.

also, since it should be an easy exercise, it might be good to know precisely why the OP is not able to do it

@PeterTamaroff I do not mean they have more than one meaning

@TobiasKildetoft Utter lazyness, I say.

they have more than one way to define the same meaning

and if they had been defined the algebraic way, your answer is not useful in the slightest

@TobiasKildetoft In the algebraic way?

by the formula

Like $P(n,k)=n(n-1)\cdots (n-k+1)$?

right

I cannot see why someone would ask that, but well...

@κρανίοπεριπολία do you wanna see? };)

@jayesh ?

I wonder if there's a human hand behind the expert.

I mean, I was looking at a question and that guy was suggesting different methods.

adviza.stackexchange.com/transcript/lZIx83wTaEKN

> Expert: I once tried to guarantee an integer lattice point centroid, it worked remarkably well.

Is the bot a simple redirector?

facebook.com/…

$\uparrow$ My first thought

@PeterTamaroff I don't agree with it. Why not both?

@JayeshBadwaik My thoughts exactly.

Thanks for answering @jayesh

@JayeshBadwaik The transcript @pen linked to looks like it's an Eliza script coupled to a Markov model for generating answer-like sentences -- probably seeded by high-voted actual answers.

@HenningMakholm Or probably sourced from most popular user chat messages.

No, I mean, I was looking at a question related to lattice points.

@Expert

What's a trivial kernel? @Expert

@Raindrop $\{e\}$

@Raindrop The "trivial" group is usually said to be the group of one element, comprised only of the identity.

I guess you're reading "a homomoprhism is a monomorphism iff it has trivial kernel"?

I don't understand .

I'm referring to point 4 of the answer at math.stackexchange.com/questions/228971/…

Please comment there,I guess it 's more productive that way

@Raindrop Do you know what a kernel is?

nope

btw how to bold single alphabets in latex?

$a_1 \bf{v_1}+a_2 v_2 + ... + a_n \bf v_n =\bf 0$ isn't working well for me

\text{$a_1 \bf{v_1}+a_2 v_2 + ... + a_n \bf v_n =\bf 0$}

$\text{$a_1 \bf{v_1}+a_2 v_2 + ... + a_n \bf v_n =\bf 0$}$

$a_1 \mathbf{v}_1 + a_2 \mathbf{v}_2} etc

@Raindrop For a linear map $f:A \to B$, the kernel of $f$ is the set of elements of $A$ that map to $0$ in $B$. The kernel is trivial if it contains only the single element $0$ (which must map to $0$ in $B$ by linearity).

In linear algebra is it fine to just mix up using $\vec x$ with $\mathbf {x}$? Like, using arrows and boldface to indicate vectors.

@Raindrop I guess either one is enough

@Raindrop it is a bad idea to mix those

@peter how wasGOF?

but either one is fine

@Raindrop Usually when we get to linear algebra, we're running out of different typefaces to indicate which kind of thing we're speaking about, so may authors just give up and use plain undecorated letters for elements of vector spaces.

also, not using anything special to denote vectors is also fine, as long as you remember to note that letters denote vectors

If you do want decoration, though, you should at least be consistent about which decoration you use.

Darn! I capped.

Peter capped himse-elf! Peter capped himse-elf!

@HenningMakholm It wasn't me, it was the upvoters!

I was like "Dafuq! I'm getting upvoted, but my rep isn't going up!"

This tells how long it was since I really got upvoted. I even forgot about capping.

Can someone help with this experiment on meta: meta.math.stackexchange.com/questions/8961/…

@PeterTamaroff you're welcome

@TobiasKildetoft It's at +1-1 now.

@HenningMakholm ok. It is still on my unanswered tab

but it might just not be updating correctly

didn't get to check at 0 total score though

could someone give it an upvote so we can check when the total score is 0?

By the way, do people think I should rather have kept quiet here?

@HenningMakholm nah

@HenningMakholm I find the tone a bit harsh, but then, so was the tone of the OP

hello guys

anyone wants to see another annoying question from me ? :p

@TobiasKildetoft Yeah, well, if the question hadn't been closed, somebody could have stepped in to play the good cop now and attempt to explain patiently why the community norms are as they are ...

@mick If it's all the same to you I think we'd prefer to see a non-annoying one from you.

i think my rep should go up with 150k , just because it is april the first.

@HenningMakholm i dont have such :)

but it did not get any downvotes either ... if i wait long enough i might get tumbleweed badge :)

@Charlie hi

I posted the question of yesterday on main @Charlie

Good @mick

going to eat later ...

@HenningMakholm This guy looks like an offended Shakespearean!

lol i capeed with 220 reputation how can that be ?

@DominicMichaelis hmm, not sure about the last 5

but accepted answers do not count towards the cap

are you sure you capped?

i got 37 reputation from 4 upvotes

and got 2 accepts so the cap should be 230

@DominicMichaelis but you also lost 12, which might not subtract from the cap

I mean might not be subtracted from the rep you gained towards the cap

this still leaves the question of those 2 rep points

mh but why should an unupvote lowers the cap?

@DominicMichaelis It must be the unupvote on 347279, if it was an upvote from yesterday that was retracted.

Today I have set a new personal record on my capping. 260 so far.

@henning on what ?

@DominicMichaelis It doesn't lower the cap as much as the cap applies before unupvotes are deducted. Just like the cap applies before rep from accepts is added.

i find this kind of strange to be honest

@DominicMichaelis Question 347279.

yeah thats where the unupvote happened

The first answer here is absolutely hilarious

Gi

Hi

i am asked one question in below page : stats.stackexchange.com/questions/54861/… . but any person doesn't answered it .

@henning shouldn't the reputation from yesterday be lowered? i am pretty sure i got more upvotes than 20 yesterday so in fact i lost reputation by this

@hadisanji Be patient.

@Charlie A little busy.

@HenningMakholm I think it is OK. The guy was way over his head.

@DominicMichaelis That looks strange to me too. It's still logically possible that your daily total for yesterday stayed the same during the unupvote because one other capped upvote was implicitly promoted to a counting one. This would mean that your actual reputation isn't really the sum of the displayed daily reputation-change totals over all days you have been registered, but that wouldn't surprise (from a software development viewpoint).

@JayeshBadwaik you always are

@PeterTamaroff I don't think there's any dispute about that. But there were 5 close-voters who apparently thought responding in answer form would be the wrong way to deal with him ...

@HenningMakholm Yeah, I think it is good to answer. But closing it is OK too, after having answered.

The guy went hysterical over some good correction Mariano made. sigh

Hello @Charlie !

@Henning I am thinking about to make a meta post for that one

@DominicMichaelis Have you tried seeing how it looks at math.stackexchange.com/reputation ? That''s usually a more reliable indicator of the actual rep computation than the nicely-styled daily deltas on the profile page.

there i have 8862 reputation and today 230

@DominicMichaelis And yesterday?

but yesterday only 210 instead of 215

That's probably worth a meta post, then.

Springtime is here, and the Red Sox are putting a beatdown on the Yankees. Life is good.

@arkamis hi Eddie

mh position 20 for this year (the first quarter) lets see what i get in this one

@expert hi anon

@arka 3.bp.blogspot.com/-BcR5sDYHk3s/TVXQujBziII/AAAAAAAADCo/…

@Charlie Sweet :D

@Arkamis Eddie the head

Gorcenski the head

Im back

.......helloooo.....

my rep is only 1253 is that a joke ?

Yes

So much fagness, imho

nope when I ask someone wher the question comes from, I want an indication on which level the answer should be

@DominicMichaelis watch the profile and you know his level

@Charlie fagness ? are you joking ?

@mick nope this normally doesn't give a clue in most cases

@mick no

@DominicMichaelis well neither does the book , because anyone can read any book , even above his level.

@Charlie is my comment fagness or theirs ?

@mick Clarifying where a problem is from can often give an idea of the level if not precisely pinpoint the level

especially if the OP can at the same time be persuaded to say something about why he is stuck

@TobiasKildetoft and if it has no good source ? or the OP came up with it ?

Then the thought process about why he came up with will be much appreciated. Sometimes, it is even possible that the OP is looking at the wrong question.

@mick then that is also a good piece of information which should preferably have been included in the question in the first place

lol the chat with an expert lady is here too :) woot

@mick theirs.... Everyone's lately

@Charlie tnx :)

@TobiasKildetoft what is the question is from numerical simulations / experimental math ?

@mick again, good information to know for anyone wanting to answer it

: /

i feel like its asking , where does this " creativity " come from. which cannot be answered if it is original.

@TobiasKildetoft How does it make a difference ? I mean if someone asked me about an integral and i asked how he got it and he said with a numerical method. I do not feel helped or would not give a different answer.

@mick well, if you just wrote up some random stuff and made a random conjecture based on computations, that is good to know

@mick knowing where a question comes from helps to unterstand the notation and so one

@DominicMichaelis if the notation is well defined , there is no such need.

On

@mick since that means I will look at the question differently (I will spend at least a little time also looking for counter examples to the conjecture)

@Charlie Off

and knowing why the OP thinks the conjecture is true will give me an idea of where to look for counter examples

@jasper :)

@TobiasKildetoft hmm yes but that might be hard , meaning that if the process is not understood theoretically , then neither is the numerical precision ... well often

@JasperLoy :D

Marilia ?

Jasper is a dark person

@mick easy example, someone posts a question like the limit of $$\sum_{i=1}^\infty (-1)^i $$

:)

@mick also, if the problem has been made up randomly by the OP, I am less inclined to spend time on it, as it becomes a lot less interesting

@TobiasKildetoft I disagree with that. I quote Hilbert , " if it would be false , nobody would have had the imagination to find it " about the work of ramanujan. (!!!)

@mick why is that quote relevant here?

there are 2 cases, the first one the person is interested in something like cesaro summability which gives the sum to evaluate to $-\frac{1}{2}$ or the other case is that he is a freshman quoting his homeworkquestions wrong

@mick what?

@TobiasKildetoft because he did not have a reputation yet , nor a degree and the results seemed to amazing to be true !!! but they were.

@mick I still fail to see the relevance

@Charlie why are you called that ?

That's my secret identity

@DominicMichaelis homework question are easy to spot.

@Charlie not anymore !

@mick nope they arent

im off for 15 min ...

@mick screw it...

hi! Does anyone know the identity of 5pm / PavelM who was a recent mat.SE contribution ?

@mick don't tell me you are really suprised. You tag it with dynamical-systems, and I guess only god know how this one is related to dynamical systems. You define 3 functions without any motivation from where they come or why it is interessting to look at them. You don't even give an heuristic why $g(n)$ is well defined (as you have an infinite sum, you should really mention why it converges). To continue your question has a poor formatting in my opinion (you write $arcsinh$

Not that I am condoning mick, but the stuff he mentions can come from bifurcation diagrams.

Instead of $\operatorname{arcsinh}$, you use to little parenthesis). After all you give us an conejctured inequality to prove without a motivation how you got it, or at least showing your self it is right for some special cases. To continue you don't even say us if $A\in \mathbb{N}$ or $A\in \mathbb{R}$. You can be lucky that you got no downvotes till now, but thats not enough, you got the balls to come to chat and discuss about how pissed you are of that comment that Did makes, which only