@robjohn People upvote less seems so.

Well ...

This one we discussed on channel in the past

Nice approach (+1)

@Chris'ssistheartist It has seemed harder recently to get upvotes. I don't know if that is in general, or if it is related to having a high rep.

@Chris'ssistheartist that one is not very sharp. Using Gautschi's inequality, we can see that the terms are $O(1/\sqrt{n})$

@robjohn Yeah, but it is useful for the objective in the problem.

@Chris'ssistheartist indeed, and it is dead simple

@robjohn Yeap.

If there is one person upvoting a large number of my (or anyone's) posts (I just got 7 upvotes in about 5 minutes), beware that upvoting a large number of answers by one user might be reversed as targeted voting (just as downvoting a large number of posts might).

I don't think there is any harm, but your votes may be automatically reversed during the night by the targeted voting script.

well I know it isn't all by one person since one answer got a couple of votes :-)

See, your answers are just that good :-)

Thank you for being apart of this site @robjohn

@skillpatrol I just verified one of my answers by writing a simulation, and it matches quite nicely :-)

@robjohn cool

I wrote a question on stats.SE and after a bit more digging I find it fits better on math.SE. I attempted to post the question on math.SE only to be told it does not fit quality reqs. Is this because it is posted on a different site? Is it proper protocol to have it migrated? thanks for your time.

This question? @UhlBelk

Yes indeed.

@robjohn Morning. I just woke up.

You should ask a math mod to look into it @UhlBelk :-)

Thank you for the advice. Do you recommend anyone in particular? Or should I just pick one at random.

I would recommend you post your question in the math mods' office. @UhlBelk

Thank you again :)

np pal :)

Morning @MikeMiller.

Quote: "sex is like math: you add the bed, subtract the clothes, divide the legs and pray you dont multiply!" Source: ud

What does "ud" stand for @StanShunpike?

Source: "ud"

@skillpatrol urban dictionary

Thanks @StanShunpike I should have guessed :(

this room did really turn into a joke (wonder who said that before)

Are you saying there is no place for jokes in math?

@skillpatrol are you saying that qualifies as a joke?

If so could you not say "in math" because it shames us all

in math

in life

is that better @AlecTeal? :D

...and no I'm not saying what qualities a "joke" has pal

@user I'm just saying can't we all just be pals?

@skillpatrol there s difference between something to be a joke, and to joke in something, nothing wrong to be lighthearted unless you are heart hurting

True, the intension behind the context is the most important issue :-)

@JasperLoy I hope your day is going well.

@Agawa001 It's just a chat room like so many others. It just happens to have people interested in math, who are, in the end, just people in a chat room.

As the good Professor would say:

:D

@skillpatrol You know, when you miss one stop sign, it seems as if you miss them all...

Well said @robjohn

....?

@robjohn i doubt you heard of something called "fairness" cuz i was been suspended for things infinitely trivial comparing to what is been highlighted in starboard

anyways im not here to complain or whine about anything, sometimes i just wonder how do people think like

@Agawa001 You mean from Code Review?

Welcome to the club @Agawa001 yours truly is the current only active member for this room who has been suspended the most, under the name of skullpatrol. "Fairness" by definition always has context attached to it. May I suggest you not "doubt" what people have or have not heard about; but instead forget about what people think like and just be yourself and of course be nice while you're having fun :-)

@Agawa001 I got a 30 day ban from SO before, and a week day and my alt account deleted because of Codereview

I called someone a tard and told them to RTFM - which is a common phrase for "read the manual" and for code-review I gave pseudo code and a 15 year old moderator didn't approve of that for a Java question, saying it might not help the OP. I was like "can the OP read?"

FUCK THE POLICE! Am I rite?

Also genuinely a 15 year old.

@skillpatrol You misspelled intention.

@AlecTeal Not nice to call people tard, even though a large part of this world is stupid and evil.

@JasperLoy I did wonder why he didn't see it as a complement...

@AlecTeal You misspelled compliment.

Bitch is gonna go down....

@AlecTeal why?

inten s ion

intention

@JasperLoy

:-)

@skillpatrol i have always been myself, Im just not indulgent with people being rude to me, i do never make the first offense, I do never take offense while keeping a stupid smile and being such a tammed dog

good to know pal

@AlecTeal yes, someone flagged me there for asking a reasonable explanation why m I being downvoted, flagged line was taken offensive, then mod asked me to delete my "inappropriate" answers, the unique fault of my poor answers they were too mathy than necessary, tbh, I cant do nothing for people who underestimate mathematics

ontopic questions are smothing down in less rate than a month before, it explains that beach time came where examinations period gone

@skillpatrol the sky isnt blue, even the sea isnt blue, the human vision lies to you

@Agawa001 Sometimes, the sea really is blue

(but that is due to algae)

blue-green algae

oh, i thought its the jellyfish, cursed fish it bites me all the time

i saw someone of the size of my head (truly)

Careful pal they can be poisonous...

that if the vision didnt betrayed me again

because they look smaller than they are under the wate

@skillpatrol has someone died because of them (i dont speak about massive jellyfish attack)

I'm sure they have...

...perhaps children.

en.wikipedia.org/?title=Jellyfish#Toxicity

In 2006 the Spanish Red Cross treated 19,000 stung swimmers along the Costa Brava.[91]

mediterranean sea ? i thought these kinds of deadly jellies live in oceans (where the pacific in australian borders

which means im in scope of danger

can you avoid em without wearing diver's suit ?

dunno, sorry

I would avoid them by not going in the water :D

@Agawa001 Even with a diver's suit, I doubt you can avoid them (I mean, those usually leave several places exposed anyway)

especially if it is for diving in areas with jellyfish as those are generally where the water is quite warm (so a fully covering suit would be very uncomfortable)

@TobiasKildetoft yes i see them in calm sea depth shining from distance, it gives a stunning sight

whoow , i never thought they can be this big

Hello

Hi pal

@Agawa001 :O amazing!!!

neither did I.

hi @iwriteonbananas

hi @BalarkaSen, hows it going?

not well, struggling with schoolwork.

yikes

me too sort of

I see the (not-so-high-quality) answer I posted got an upvote.

beginning to prepare for exams now

Hello@Balarka Same here struggling with school work.. I wasnt able to even do maths yesterday :(

you're referring to your most recent answer?

@iwriteonbananas you're an undegrad, right?

yeah, @iwriteonbananas

@BalarkaSen yeah

which year?

2nd

cool

you're a 14 year old school kid, right?

:P

no

are you enrolled at university?

no

ok, i wont push any further, i'm under the impression you dont particularly want to talk about it

i said no because that 14 should have been 15

:P

i dont believe you that you're 15

i think your answer is pretty cool by the way

@iwriteonbananas hmm? why not?

@iwriteonbananas it's really a rough sketch, not a rigorous answer to anything

but you can translate that in rigorous mathematics, sure. that's what Jim Belk does, more or less

what kind of 15 year old studies algebraic topology? :P

a pretty weirdo one, i assure you

@BalarkaSen yeah, it provides nice intuition however. heck, i'll upvote it

i drew that thing with my favorite technique of drawing higher dimensional things.

what's your drawing technique for higher dim things?

didn't you see the sketch there?

oh that's what you mean

it's a simplistic method, but actually pretty useful

you can visualize hopf fibration using that drawing techinque, for example :)

*technique

i learned that from the symplectic topologist fellow who sits right in front of me in prof's office.

hello

I have developed an AI

@BalarkaSen im confused again. what are you actually referring to?

that can understand the world

just as a human can

the 1st sphere on your sketch?

@iwriteonbananas represent higher dim things by lower dim things

but I have a problem

oh yeah

the AI learns but does nothing

it actually works pretty well

how can I program emotions into the AI so that it has motivation to use its intelligence?

i pretty much do that too

yeah. i guess it's pretty common out there.

@BalarkaSen what is a sympletic topologist?

on the other hand, one can draw $S^3$ as a sequence of disjoint copies of $S^2$ first expanding, and then shrinking.

that works well too.

@iwriteonbananas um. one who works with symplectic topology?

@BalarkaSen true, i've never considered that

@BalarkaSen i guess i should've asked what symplectic topology is about

it's actually a simplistic version of the genus 0 heegaard decomposition of S^3, i.e., pasting two $3$-balls via the boundary sphere using the identity homeomorphism

@iwriteonbananas i really don't know.

@BalarkaSen interesting. i didnt know that yields $S^3$. i only knew that taking two solid tori and identifying longitudinal circles in one w/ latitudial circles in the other gives $S^3$

@Rememberme boundary of A is the set of things which both intersects the interior of A and the complement of A

@iwriteonbananas I only think I have seen the term symplectic geometry

@iwriteonbananas both yields S^3

Okay thats how it goes...

(I don't think a topology is enough to speak of symplectic things)

@BalarkaSen how can i see that pasting two 3-balls via identity homeomorphism gives $S^3$?

in particular, pasting two solid $g$-genus surfaces along the boundary which glues longitudal circles of one to meridianal circles of the other.

@iwriteonbananas take a 3-ball in R^3. take complement. R^3 then is your 3-ball \cup the complement.

one pt cptfy. the cptfication of the complement is also a 3-ball

since one-pt cptifcation of R^3 is S^3, you're done

@BalarkaSen why is the cptficiation of the complement also a 3-ball?

well, prove it. just a point-set topology exercise.

ok

pretty nifty argument

nods

on the other hand, you can just directly prove it as follows : a 3-ball is the same as cone over a sphere. pasting two cones by the base (by the identity homeo) is the same as taking a suspension. so the space is just suspension over a sphere.

this is precisely S^3.

another really cool argument. i gotta remember that

Man, removing one little assumption (which turned out to almost never hold unfortunately) means I go from a formula that is just a product of two terms to one that is a sum over two variables of products of three terms

@Tobias drawbacks of being an algebraist :P

/joke.

hey B

ello.

barite?

yes

@BalarkaSen Heh, yeah

soham, how old are you? :P

Hello,S

@BalarkaSen It even took me a little while to figure out how the assumption gave the nice result by plugging it into the general formula

That Hausdorff exercise was really nice... :)

@Remember you never really completed the exercise

your argument was flawed, as I pointed out, but you left.

well, almost flawed.

Due to quantifiers right?@Balarka

almost

Yes I did put the quantifiers later

But I got to extend it to finite sets

But till now the proof was really nice

the gist of the proof for singletons is that any point outside can have nbhd not intersecting the singleton (hausdorffness), thus implying that the complement is open

but I think you wrote that up in a contrived and without-quantifiers way

I used closures and showed that the closure equals the set.. Hence proving that singleton set was closed

when you've done it for finite set, try figuring out why the same with infinite sets doesn't work.

Why doesnt it work

that's for you to figure out

@Rememberme yes, that's a valid proof.

I just got to extend it ... How am I suppose to do that

so what?

Are finite sets

So if one point sets are closed then the union of closed sets is also closed

and hence finite sets are closed

ok, good.

now think about infinite sets.

@Balarka We can think about the interval (0,1) that is also the union of closed sets (infinite union) but it is not closed.. This can be an example to say that infinite sets are not closed

@Hippalectryon did you know this series has a very nice closed form?

fair enough. what about countably infinite sets? :)

all of these have easy answers, but it's good to know them.

Countable makes me remember of co countable topology though:p @Balarka

not particularly relevant.

@Remember ps : d'you know of an example of a topological space $X$ which isn't metrizable, i.e., there is no metric on $X$ which induces the topology on $X$?

Induces means its the basis for the topology right?@Balarka

@robjohn see above :-) It has a nice closed form.

@Chris'ssistheartist which one ?

@Hippalectryon The one above.

Will a point set work @Balarka

@Chris'ssistheartist Interesting series. If the closed form is simple, it is even more interesting.

@robjohn Yes, it is.

I mean, is there a topological space $(X, \tau)$ such that there is no metric $d : X \times X \to \Bbb R$ such that the topology generated by the basis of open balls $\{x \in X : d(x, x_0) \leq r\}$ is $\tau$?

@Rememberme what's a point set?

@robjohn I add it to my book.

A one point set..... though I havent thought about it much

$\{x\}$?

with what topology?

Yes ... thats what I am thinking about the topology

any topology on it must be the discrete topology

so just consider the discrete metric.

Okay that's gone

@Remember you can't whip one up all by yourself. here's a hint :

can you prove that every metric space $(X, d)$ is Hausdorff?

That seems to be a nice exercise

Okay lemme see

@Balarla Sorry But I cant do your question now.. I am completing a proof about boundary point and interior of a set .. Do you mind checking it I feel the proof is fine...

sorry, I'm a bit busy right now.

seeing a lecture.

Oh okay .. I also need a break.. Bye for the moment :)

I feel amazing now!

Oh, what a feeling...

Anyway, I can handle with that.

@skillpatrol I think in mathematics anyone should excel on his own creations. What do you think about that?

Agreed.

i have many creations, never thought about a book

@Agawa001 Well, writing a book is hard work

@Chris'ssistheartist Feynman once said "what I cannot create, I do not understand"

@TobiasKildetoft i have papers though

@Agawa001 Well, it's not easy writing a book. I see that almost every day trying to publish my own book.

@skillpatrol Deep and true.

@Agawa001 Those do tend to count more in the eyes of the academic community anyway (as books tend to contain less original research)

@Agawa001 What area have you published papers in?

AI

and cryptography

My aim is to reach up to 500 problems in integrals, series and limits. Well, the mathematical part is not hard, but the way you send the message to the readers, since this might make the big difference between a good and a bad book (although I wouldn't use bad word for describing books).

they r in the library of the university i have been in

written in french, not english

@Agawa001 Ahh (but still neat)

Why write them in French though?

well its standard common language used in scientific and academic papers

here

@Agawa001 But not internationally (any longer. I guess it used to be)

no, french is still commonly used here

generally in all north africa

@Agawa001 Right, but it is no longer considered "normal" to publish solely in French, since too few mathematicians can then read the papers.

and France :-)

morning chat

hi pal

my academic knowledge and scientific terminology is limited in english

@Chris'ssistheartist will your future book be locally spread or all over the world ?

@TobiasKildetoft i think i should post translated version of my papers in academia.eu once i have time

@Agawa001 Why there rather than arXiv?

I think it's hard to find in my country many passionates about such problems, and that's probably true in general.

first time i hear of it :/

@Chris'ssistheartist lol do you live in europe, you say ?

@Agawa001 In Romania, yes.

wierd

@Agawa001 Hear of what?

I'm out for a while to buy some food for my pets.

@TobiasKildetoft this website

@Agawa001 You mean arXiv? It is pretty much the only place I use to keep up to date on new papers

@Chris'ssistheartist i dont thin any people are so plugged into football and stuff more than mathematics or any other science beside africans

@TobiasKildetoft is it CC BY-SA ?

@Agawa001 As I recall, one can choose a couple of different licences when uploading

Pretty much all math papers are put on arXiv before being published in peer-reviewed journals these days

some journals even allow one to submit via the arXiv ID

@TobiasKildetoft interesting

that guarantees published rights atleast.

@Agawa001 It also means that I will be able to see people's new results when they are done rather than a few years later when the paper has finally been through the long process of peer-review and publication

I'm really enthusiastic to publish my AI paper , it has average 100 pages, and need to be translated to english

@Agawa001 Wow, that is a long paper (longer than all my current papers combined)

@TobiasKildetoft graphs and figures, lol

@Agawa001 Ahh, yeah, none of mine contain such (yet).

I am turning my dissertation into two papers, and those will have some Young diagrams

@Chris'ssistheartist if i define $\zeta^{(n)}(s)=\sum_{k=n+1}^\infty \frac{1}{k^s}$ (i.e. $\zeta(s)$ less the first $n$ terms) then that has the tidy representation $$\sum_{n=1}^\infty H_n \, \zeta^{(n)}(2)\, \zeta^{(n)}(3)$$

it's a matter of taste, of course, but i rather like that it that way :)

@Semiclassical Back. Nice, indeed. :-)

@Semiclassical It has a very nice closed form. I plan to add it to my book, still I won't be able to publish it somewhere (as a paper) because it's based upon multipel results, and each one must be proved separately and take a lot to write. :-)

though the thing which i'd want to know for purposes of being sure it converges: how fast does $\zeta^{(n)}(s)$ converge to zero ($s>1$)?

@Chris'ssistheartist Why does the amount of writing prevent it from being publishable as a paper?

also, what kind of 'nice' closed form does it have?

@TobiasKildetoft i assume it is one-topic writing

@TobiasKildetoft Well, maybe it's not necessarily the amount of writing, but the fact that it uses multiple results that might be published separately.

Publishing all in a single paper is too much I think. Just my opinion.

@Chris'ssistheartist I am not sure I follow. If those results could be published separately, that would just mea publishing several papers

i mean a study on different sides of a problem is worth to be concretized as a book even it is small

@TobiasKildetoft Exactly, that is the point, publishing more papers.

if it was too much for one paper, you could do it as part 1, part 2, etc.

now you've got me trying to think how on earth one would find a closed form for that :)

Glad to read that. :-)

best i can think of right now: find integral representations for those zeta-type summations, and hope that something nice happens

the first part is plausible, i think, but the second is probably wishful thinking

It might work.

huh, interesting

This one.

the presence of $e^{-i x}$ in there would tend to make me want to turn it into a contour integral

Yeap, it would be a good idea. :-)