Mathematics - 2014-10-22 (page 4 of 4)

@robjohn let me ask this once again. I wanna show to a high-schooler that definite integrals can be evaluated without finding an antiderivative and using the FTC too

Alizter

@BalarkaSen google is your friend

The west seem to like it a lot.

UserX

So I'm searching for the perfect example

Balarka Sen

@Alizter Oh it's a movie

UserX

10:09 PM

And no, Gaussian functions aren't taught in high school

Well meh

tv series

whatevs

@Alizter tv is cheaper

Alizter

innit

mick

10:09 PM

@BalarkaSen just as with everything else huh

Alizter

@mick So is chess compared with smartphones.

UserX

@robjohn can you think of anything?

Alizter

I feel like I should be using @Ted for some learning. But what to learn...

Balarka Sen

i don't have any phone. decided that i'll never ever get one for myself.

too phony :P

Alizter

@BalarkaSen That is ok if you don't leave the house all day.

Balarka Sen

10:11 PM

anyone who wants to contact me has to mail... and be patient.

mick

@Alizter i play chess and watch tv ... so ?

Alizter

sigh @mick too tired to explain again

Jasper Loy

Every comment that says Chris's Sis is arrogant gets highly starred. This is absurd.

4

mick

@Alizter goodnight ! :)

Alizter

@JasperLoy oops missed

Balarka Sen

10:12 PM

@JasperLoy Every comment saying anyone is anything gets highly starred

mick

@JasperLoy happy ?

Balarka Sen

Jasper is silly

^ star it

mick

@BalarkaSen happy ?

Balarka Sen

no. let's not get star-crazy

mick

@Alizter :p

Alizter

10:13 PM

@mick Stop staring everything.

mick

@Alizter but they asked for it !

:)

star this :p

Balarka Sen

oh noes

mick

lol

UserX

Is Chris's sis really the sister of a Chris?

Alizter

It was Chris before

robjohn

10:14 PM

@UserX You want something that you can't do by FTC, but you can do by some neat substitution?

mick

@UserX how about the arithmetic-geometric mean ??

UserX

@robjohn I don't understand. If you substitute a value then you'll eventually use the FTC.

mick

moderators are unstarring i guess

Balarka Sen

yes

Alizter

Children stop.

UserX

10:16 PM

@robjohn it's clear what I want. An example understandable by a high-school student that evaluates a definite integral without the FTC

Alizter

Is something pedro would say

mick

43 views , still no upvote !!

@Alizter yes daddy

Balarka Sen

@Alizter no that'd be STAHP

Jasper Loy

@Alizter He would say STAHP.

Balarka Sen

jinx, @Jasper

Alizter

10:17 PM

@mick someone downvoted lol

mick

@Alizter you ?

Alizter

@mick no. I don't care for your question.

mick

@Alizter euh .... thanks .... euh no , no thanks

throws table at downvoter ! :)

Jasper Loy

It is two more months to Christmas. I am so excited.

UserX

@mick Seldom is a custom-made problem interesting to others

mick

10:19 PM

things are Always intresting , they just fail to see it ....
thats why i dont downvote !

Alizter

@JasperLoy What do you want Santa to bring you?

mick

@Alizter i want a proof of collatz

im silly.

Jasper Loy

@Alizter Hmm, too private to say in this chat, LOL.

Alizter

Back to primes

mick

@JasperLoy womenizer ? :)

Jasper Loy

10:23 PM

I have many things I want for myself and also for others.

mick

@JasperLoy how cute

Alizter

12 holy books?

Jasper Loy

My greatest wish would be to solve my mental problems soon and live a normal life.

@Alizter I already have those in my shelf.

Alizter

for others, for others

Jasper Loy

Ah, there is something I want to do for others that could get me into trouble with the authorities here...

It is something morally right but possibly legally wrong...

Alizter

10:24 PM

Streak?

mick

MSE is no fun when your questions get ignored :(

UserX

@jasperloy go on

Jasper Loy

@Alizter I don't know what a streak is, but I won't say it here, LOL. When my best friend returns next month, I will discuss with him what I should do about the matter.

Alizter

@mick Stop reminding us. Edit it properly or something.

mick

@Alizter its a good question by itself.

Balarka Sen

10:25 PM

@mick

UserX

@mick Noone said MSE is fun.

Alizter

@JasperLoy It is the process of expressing your self by running butt naked in a public area.

Jasper Loy

My 12 holy books by the way cost over 1000 USD.

UserX

Plus, it's a community network. Ask why does 1+2+3+4+... =-1/12 and you-'ll get more attention

Jasper Loy

@Alizter What does running around naked achieve? Nothing. It is stupidity.

Balarka Sen

10:27 PM

@UserX -1/12

Alizter

@JasperLoy Apparently freedom. Haven't been seeing these results lately.

UserX

Edited

Alizter

@mick What balarka said

mick

@JasperLoy its to express that the event should not be taken so seriously !

Jasper Loy

@Alizter If I have something to say, I would say it without running around naked.

Alizter

10:27 PM

@JasperLoy It is something that sometimes happens at sporting events.

mick

I think more girls should do it :)

Alizter

Taken out of context it is a bit crazy.

@mick Why is that?

Jasper Loy

@Alizter That will definitely put me into jail for 2 months here.

mick

@Alizter take a wild guess :)

Alizter

@JasperLoy But it is morally right and illegal. Thus your condition is satisfied. Now take $\epsilon > 0$ and let $f\in$...

@mick Hmmm. Nope. What?

Jasper Loy

10:29 PM

@Alizter Are you and Sarah discussing your math problems now?

Alizter

@JasperLoy She has not sent me a single email since last week

Wasn't she here yesterday or the day before or something?

Jasper Loy

@Alizter Hmm OK. I guess she is a busy person. I am very free. But next year I should be very busy. I would be happy to finish 6 holy books next year, but hey maybe I can do all 12.

Alizter

@JasperLoy One for each month?

Chris

So you guys keep pinging ME when you chat up @Chris'ssis.

6

Because you write "Chris sis" or some such.

Balarka Sen

LOL @Chris

Chris

10:32 PM

Please cease and desist.

Jasper Loy

@Alizter Yes, if possible. I intend to do nothing but math every day from morning to night next year.

Alizter

@Chris change your name to bob or something :P

Chris

No, screw you. I had this name first.

Alizter

@JasperLoy Don't forget to sleep and eat.

Balarka Sen

No, seriously guys, let's star that.

He shouldn't get pinged for no reason.

Jasper Loy

10:33 PM

@Alizter Of course, I will also need time to solve my mental problems next year, and some time for window shopping as well.

Alizter

@Chris Ok. Don't complain when we are too lazy to write sis.

Chris

ty @BalarkaSen

Jasper Loy

Testing. Does @Chris'ssis ping Chris?

mick

ok this might sound hostile and arrogant and more stuff like that , but , if you think its so easy to improve my question , why dont you guys edit it ?
but keep in mind that x > 0 is essential.
Apart from changing the order of the sentenses/def's of the question i doubt it can be improved alot !

Chris

Hold, please.

Jasper Loy

10:34 PM

@chris Can you answer my above question?

Chris

No new pings.

Alizter

@mick we are trying to help you not lecture you.

mick

yes , but like I said apart from maybe relocating x > 0 I do not see how to improve the question alot. " improve " is vague advice ...
If someone asks : how to jump higher ? and you answer " improve your jumps " , that does not help much ...

for instance : adding context ... there is no context to add !?

also adding incorrect tag's seems immoral to me.

its not a bessel function !

Alizter

@mick Alex and I were telling you OUR opinions on what would make the question more popular. Since you are too stubborn to do anything I cannot help you.

It looks like bessel function

$J$ is used for bessel

mick

but its not ...

Alizter

10:37 PM

why not name it $f$?

Who is going to know that?

I called my dog cat. But it is actually a dog sorry guys.

mick

do you really believe f will get more attention then J ?

Alizter

People will think your dog is a cat.

poor notation

Your notation sucks!

Calm down Balarka

As Lang used to say

10:39 PM

Lang invents his own terminology in his books.

mick

I Always learned in class that you can " choose any letter you want " :)

Jasper Loy

For example, calling a ring entire.

Alizter

@BalarkaSen Pressure notation in physics sucks. Badum tss

robjohn

@Chris'ssis: I've added about all I can to my Soddy-Gosset answer. The first section is straight from my paper of 5 years ago, but the later sections are improvements on the later sections there. I am pleased with $(21)$ and $(22)$; they have a nice feel to them. I might rewrite the paper using that answer.

Alizter

@mick Yes. You can also call your dog "cat".

But is that a descriptive name?

Balarka Sen

10:40 PM

nothing is worse than $$\frac{\Xi}{\overline{\Xi}}$$ on a blackboard :P

mick

ok i will call it " f " then.

Jasper Loy

@robjohn You published 5 years ago, outside of academia? That's amazing. I only have toilet paper.

Alizter

When you tell someone, my "Cat" barks what will they think?

mick

@JasperLoy can i borrow it , im out.

Jasper Loy

@mick Have a nice time shitting bro.

mick

10:41 PM

@Alizter that it is not math you are talking about :p

robjohn

@JasperLoy Never published, except by mentioning it on sci.math. With the new additions, I might try ArXiv

mick

@JasperLoy euh thanks :)

Alizter

sigh Spanish accent: How do eiy reeech dees keeeeds?

Jasper Loy

Look, if you have the guts to star something, don't be a wuss and unstar it, lol.

mick

@robjohn where is the paper you talk about ?

Alizter

10:42 PM

Good night all

Balarka Sen

ahem I'm the wuss you are talking about, @Jasper

Alizter

except for mick

mick can fix his question

Jasper Loy

@Alizter See you in your dreams!

So I figure that at chris pings chris'ssis and at chris'ssis pings chris as well?

Balarka Sen

I'm gonna go too.

Byes.

robjohn

@mick dropbox.com/s/jqwwubn09c99p4r/soddy.pdf the first part is copied to this answer

Alizter

10:43 PM

@JasperLoy It is not symmetric

Jasper Loy

Then there is no real solution to the problem, we need a nonreal solution.

Alizter

chris -> chrissis & chris,

bye

mick

lol , i replaced J by f ... and now i noticed i commented about J , not f and that cannot be undone :p

AmagicalFishy

I just deleted an answer I wrote because I think it may have been erroneous

Ted Shifrin

may have?

AmagicalFishy

10:48 PM

but I'd like to check here: Is the least upper bound property different than having a least upper bound?

Ted Shifrin

yes

AmagicalFishy

Ok. It was definitely erroneous.

Ted Shifrin

The property asserts that every nonempty set that's bounded above has a least upper bound.

Semiclassical

@robjohn: did you think of anything new regarding that Fourier series / series summation question that came up? if there's not something obvious i was planning put a new question together

AmagicalFishy

Ah, alright. I was unaware of that, and answered as if having a least upper bound and having the least upper bound property were the same thing.

Oh, also, Ted, thanks for your help the other day (a couple of weeks ago, you helped me out w/ some tensor stuff)

Ted Shifrin

10:49 PM

There are plenty of ordered sets in which the least upper bound property does not hold.

You're welcome, @Amagical. In the meantime, I've had plenty of downvotes for no good reason, so I'm glad :P

AmagicalFishy

Haha. Well, I'd upvote you in chat if I could!

Ted Shifrin

Ha ha

Balarka Sen

Is there a way to canonically well-order $\mathbf{Q}_p$? Just askin'

Ted Shifrin

there's rarely a natural/canonical well-ordering, @Balarka. Do you have something in mind?

Balarka Sen

Nopes. Thus my question.

AmagicalFishy

10:53 PM

What is $\mathbb{Q_p}$?

Ted Shifrin

Ah, the 5000 dollar question.

Balarka Sen

$p$-adic rationals, @AmagicalFishy

Ted Shifrin

You'll need to explain, methinks, @Balarka.

robjohn

@Semiclassical You might as well put up a new question. I haven't come up with anything, and I need to leave for a while

Ted Shifrin

hi @robjohn

Semiclassical

10:54 PM

ok, thanks

robjohn

@TedShifrin hey, Ted!

Balarka Sen

fractional field of $\mathbf{Z}_p=\{(x_i) \in \prod \Bbb Z/p^i : x_{i + 1} = x_i \bmod p^{i+1}\}$, @Ted

mick

did someone post the integral discussed here before on main ?

AmagicalFishy

Explanation would be excellent, actually (I am also reading the Wikipedia)

Mike Miller

@Ted Fun fact: The smooth Poincaré conjecture is true in dimensions 12 and 62.

robjohn

10:55 PM

@mick The one that Chris's sis and I were discussing?

Ted Shifrin

Huh? I thought the smooth Poincaré conjecture was true in all dimensions $\ge 5$.

mick

@robjohn yes

robjohn

@mick I don't think so... I think we were just discussing it on chat.

Mike Miller

@Ted That would contradict the existence of exotic spheres, of which there are lots. Topological is true in those dimensions.

robjohn

it was not that difficult

mick

10:56 PM

pity

but nice still

Ted Shifrin

Hmmm, my h-bordism is rusty.

AmagicalFishy

Do you have a quick sentence on their significance, Balarka? (Just so it sticks in my mind what they are. :v)

robjohn

@TedShifrin you should have painted it...

Ted Shifrin

yeah, along with all those wanton downvotes, @robjohn ... which continue. I think somebody's afoot.

Balarka Sen

@AmagicalFishy i'm not sure what you want

Ted Shifrin

10:57 PM

p-adics are totally not intuitive

mick

Let f(x) be an elementary nonrational function
is the integral of f(f(f(x))) ever possible in closed form ?

robjohn

@TedShifrin I have some info that I can pass on to the community managers and see if there is something they can do

Balarka Sen

@TedShifrin i don't agree with you.

they are intuitive if realized as cantor sets

mick

I mean indefinite integral

Ted Shifrin

thanks, @robjohn. Not like I can't afford the rep. It just offends me. I put a comment on one of the answers asking the downvoters to complain what's wrong ... of course, they won't.

mick

10:59 PM

maybe a hard question of me

Ted Shifrin

Sort of, @Balarka.

Mike Miller

@AmagicalFishy The reals are a completion of the rationals with respect to a certain natural norm . But there are other ways to complete the rationals (and get a complete field); these other ways give you the p-adics. They look very different than the reals!

robjohn

@TedShifrin Oh, I understand. I remember when the mods were being targeted, and then I was when the others were not. It is frustrating

Balarka Sen

@MikeMiller bunch of names :P

Semiclassical

@BalarkaSen: can you elaborate on that? it sounds familiar but p-adics aren't something i know in depth

Ted Shifrin

11:00 PM

I still wonder if René has friends he's put up to it, @robjohn :D

mick

goodbye friends ...

Balarka Sen

@Semiclassical inverse limit of the canonical inverse system of p^k-cyclic groups

Ted Shifrin

When he gets off suspension, I'm sure fireworks will start.

AmagicalFishy

@MikeMiller Ah! I had no idea that was even a thing.

Thanks. :D That's awesome

mick

whats an inverse limit ?

Ted Shifrin

11:01 PM

LOL ... indeed ...

Balarka Sen

for example you have $x^2 = -1$ if you have a solution mod 5^k, you can extend that to a solution mod 5^{k+1} by hensel's lemma

Ted Shifrin

@Balarka: You're throwing around jargon. It doesn't help non-experts.

AmagicalFishy

(I'm not sure what Hensel's Lemma is)

mick

bye

Ted Shifrin

OK, dinner guest is here. Bubye, all. Thanks, @robjohn.

Balarka Sen

11:02 PM

@TedShifrin I know I am, I can't possibly start lecturing about basic algebra RIGHT AT THIS MOMENT

Semiclassical

it's the thing that says you can lift solutions in the way balarka just described (don't mean to be circular, but that's pretty much it)

robjohn

@TedShifrin L8r

AmagicalFishy

(Consider this: I am now taking Real Analysis, so I know how to complete the Reals, and that's about it. :P)

Semiclassical

i think what i'm reaching for in the back of my head is the connection between cantor sets and stuff in symbolic dynamics

Balarka Sen

@AmagicalFishy OK, then look for the p-adic metric.

AmagicalFishy

11:03 PM

So the idea of there being other ways of doing it that fruit totally different numbers is crazy

Semiclassical

which admittedly i'm struggling to remember from a dynamical systems class at least six years ago

Balarka Sen

it's the metric induced by norm $|x| = p^{-k}$, $p^k$ being the largest prime power dividing $x$, @AmagicalFishy

Semiclassical

so i'm probably talking nonsense :P but i know in that course the notion of different metrics came up

Balarka Sen

that gives you a metric space $\mathbf{Z}_p$

you can also show that it's a field. then take the fractional closure.

a bit of background always helps the helper, @AmagicalFishy

Semiclassical

actually, looking at wikipedia, i might be remembering sort of correct

anon

11:05 PM

@BalarkaSen integral domain, fraction field

AmagicalFishy

Sorry 'bout that. (I'm writing down what you're saying so I can do it later tonight)

Balarka Sen

@anon whatevs

Mike Miller

@Ted We know as a corollary of hCob that if a n n-manifold is homotopy equivalent to an n-sphere, it is indeed homeomorphic. So the smooth Poincaré conjecture is equivalent to the question of whether or not there are exotic spheres in dimension $n$... and it's open when there are.

Balarka Sen

@AmagicalFishy first try showing that the norm i wrote above is really a norm on $\Bbb Z$

AmagicalFishy

Thanks, though; this will give me some good stuff to do :D

Semiclassical

11:07 PM

just found this while searching google

not sure what the hell to think of it

ncbi.nlm.nih.gov/pubmed/9714931

a paper with the title "Human subconscious as a p-adic dynamical system."

Balarka Sen

ROFL, @Semiclassical?

AmagicalFishy

Excellent. Show that $|x| = p^(-k)$ is a norm which gives the space $\mathbb{Z_p}$, show $\mathbb{Z_p}$ is a field, take its fractional closure

Semiclassical

yeah, i dunno

Balarka Sen

@AmagicalFishy no, show it's an integral domain

i typoed, anon corrected

Semiclassical

as an analogy, it might be a cute one

as a paper? riiiight

AmagicalFishy

11:09 PM

Ah! Alright, thanks

Balarka Sen

Actually @AmagicalFishy this should be easier :

AmagicalFishy

that would have resulted in some frustrating futility

Balarka Sen

Define $|\bullet| : \Bbb Q \to \Bbb R$ as $|x| = p^{-k}$ where $x = p^k \cdot m/n$, $m$ and $n$ are not divisible by $p$

Show that $|\bullet|$ is a norm. Derive the corresponding metric.

Semiclassical

@BalarkaSen: btw, here's the line from Wikipedia that caught my eye (and which seems vaguely familiar)

from the page on subshift maps of finite type: "A variety of different metrics can be defined on a shift space. One can define a metric on a shift space by considering two points to be "close" if they have many initial symbols in common; this is the p-adic metric. In fact, both the one- and two-sided shift spaces are compact metric spaces."

Balarka Sen

The metric completion of the metric space $(\Bbb Q, |\bullet|)$ is our $\mathbf{Q}_p$, @AmagicalFishy

anon

11:11 PM

the completion is Q_p

thanks anon

here to help

@anon right. sorry.

Very excellent.

This will probably show up as a question on the site in a couple of days, haha. Thank you. :)

Balarka Sen

glad to be of no help

gah why am I even helping with my stupid jargon-talk whereas i should get back to topology.

AmagicalFishy

11:14 PM

You helped a lot! I meant, if I get stuck during one of the steps or want to verify that I've carried them out well

I'd post it as a question

Balarka Sen

@MikeMiller I studied Baire category today

Mike Miller

@AmagicalFishy Just be careful with how you do completions; it won't make sense to use the Dedekind cut approach here. You need to think in terms of Cauchy sequences.

AmagicalFishy

Noted!

Balarka Sen

@Mike you never say hello to me. blah. am i that (mathematically) silly? :P