Mathematics - 2013-01-25 (page 5 of 5)

math101

6:00 PM

ohhh I seee

Limitless

Hm.

f s

???

Limitless

@OrangeHarvester Doesn't that assume $S_n$ converges?

Orange Harvester

@Limitless Yes, convergence has to be proved separately, as i already said before.

Limitless

@OrangeHarvester Just making sure I was following you. That seems to be the hard part in this question, however. Since $x_n$ is defined recursively, it doesn't permit itself to be so easily manipulated straight from the definition of a limit.

Tiro

6:05 PM

Hey what do you understand , when it's said :
Calculate \sqrt { -3-4i }

f s

you can use dollar signs for latex

Tiro

$\sqrt { -3-4i } $

doesnt work o_O

f s

yes

it does you need to check out the link on the right that says latex support for chat

Orange Harvester

@Limitless yes.

f s

@Tiro it will show you how to make a bookmark which you can use to have it displayed

Jonas Teuwen

6:08 PM

@math101 Why are you such an asshole?

math101

@JonasTeuwen I am learning from you :P

Fair enough.

Its even steven

It is.

I was trying some reverse psychology on you but I guess it didnt work :(

user19161

6:12 PM

I am now drafting my reason for account deletion for my other accounts. I will think about it again and send it next week if confirmed.

user19161

So @math how is using the site for answering your questions? Better than tutoring right?

math101

There are pros and cons to both :)

Tiro

$\sqrt { -3-4i }$

Om

g

f s

does it work now?

Tiro

nope

f s

6:14 PM

o

Tiro

Where is the link actually ?

f s

check out the link on the right

Tiro

right where ?

f s

at the stars

above them

the top starred comment

Tiro

sorry ;(

f s

6:16 PM

no problem

Tiro

$$$\sqrt { -3-4i }$$

$$\sqrt { -3-4i }$$

user19161

@math101 By the way, what chapters does your course cover? Are you just going to do single variable differentiation and integration or multivariable as well?

f s

@Tiro the thing you need to do is make the bookmark which is explained in the link and click on it when you want the latex to render

math101

@JasonBourne Its all over the place. This week we had to study Section 1.3 and 4.1

@JasonBourne It seems like only single variable differentiation and integration

ixtmixilix

6:53 PM

i feel really stupid for it but i can't understand the formula for k-permutations of n

i was thinking of asking a question but it just seems so basic

nPk(n,k) = n(n - 1)(n - 2) .. (n - k +1)

but nPk(3,3) and nPk(3,2) are both six, right? so how does that even happen?

user19161

@math101 Ah, not too hard then.

Ed Gorcenski

@ixtmixilix Because nPk = n!/(n-k)!

And 0!=1! = 1

So nPk(3,3) = 3!/(3-3)! = 3!/0! = 3!/1 = 6

And nPk(3,2) = 3!/(3-2)! = 3!/1! = 3!/1 = 6

As far as "why" this is the case, think of it this way

ixtmixilix

ok. but how six be derived from the non-factorial formula for both pairs of values?

Ed Gorcenski

nPk(3,3) is the number of ways of ordering 3 things out of a total of 3

nPk(3,2) is the number of ways of ordering 2 things out of a total of 3 -- but if you're ordering two things, you're just leaving one outside of the group. It's kind of the same thing.

Let's say you cook fish, chicken and eggs, and you can cook them in a pot, pan, or in the oven. If you cook all 3, there are 6 ways that you can cook them.

ixtmixilix

ok

i'd just really like to know how the first formula works, though

Ed Gorcenski

7:04 PM

If you only cook two, then one of them is being left in the fridge -- combinatorically, this is just like cooking one in the refrigerator

What do you mean how it works? nPk(n,k) = n!/(n-k)!

ixtmixilix

nPk(n,k) = n(n-1)(n-2)..(n-k+1)

Ed Gorcenski

Right.

So

Expand your factorials: n! = n(n-1)(n-2)...(n-k+1)(n-k)(n-k-1)...(n-n)

(n-k)!=(n-k)(n-k-1)(n-k-2)...(n-k-(n-k))

When you divide, they cancel

Leaving just n(n-1)(n-2)...(n-k+1)

ixtmixilix

ok, that makes a bit more sense

i'll have to look at that more closely

user19161

7:20 PM

@math101 Ha, so for this online degree they use materials written by others online? How convenient!

ixtmixilix

i was doing an open university degree in math

...then my wife and i split up and i left england...

user19161

Hey guys, I submitted my deletion request for my other accounts. I now belong completely to Math. Yay!

Ed Gorcenski

Why delete the other accounts?

math101

@JasonBourne I agree :)

Nimza

Hello, help me please, where can I find a proof of the fact that two maps $f,g \colon S^{n} \to S^n$ are homotopic iff their degrees agree?

Ethan

7:39 PM

Is there a standard notation for continually composing indexed functions similar to the way the letters sigma and pi are used for continually summing and multiplying indexed terms?

Like $$f_n(f_{n-1}(f_{n-2}(...(f_2(f_1(x))))...))$$
Where $f_i(x)$ is a function of x

Charlie

@JasonBourne :DDD

Nimza

@Ethan you can denote composition as $\cdot$ (binary operation), then pi is ok, I think. I think there are no standard notation for this

Nick Kidman

Heyyo

Anyone here with knowledge of type theory?

Charlie

@NickKidman Nick!

Theorem

@Nimza : your question is interesting

Nick Kidman

7:45 PM

no, no "Nicky"

Orange Harvester

Nicole! I am Jayesh Badwaik! :-)

Nick Kidman

@Ethan: reference.wolfram.com/mathematica/ref/Fold.html

Theorem

@Nimza : you mean to say that $f$ and $g$ are polynomial maps ? i don't quite get it .

Nimza

@Theorem no, any continuous maps

Theorem

@Nimza : then what do u mean by degree ?

degree of the space from where u are mapping ?

u meant dimension i guess ?

Nimza

7:55 PM

@Theorem $f_{\ast} \colon H_{n}(S^n) \to H_n(S^n)$ or $f_{\ast} \colon \mathbb{Z} \to \mathbb{Z}$, so $f_{\ast}(1) = \alpha$, $\alpha$ is a degree of $f$ by definition

Nick Kidman

@OrangeHarvester: Hi Jayesh

Orange Harvester

@NickKidman Hello. Howz it going?

Nimza

@Theorem en.wikipedia.org/wiki/Degree_of_a_continuous_mapping

Theorem

@Nimza : Thanks , i will see .

Nick Kidman

Turing complete languages let you express code that doesn't halt. What is the strongest known class of languages, in which only lets you produce code halts? Can there be a language which lets you express exactly all effectively computable functions, but no uncomputable ones?

robjohn

8:22 PM

@math101 Sorry, I was out to the store. What's up?

I'm too late, it appears.

Nimza

If I'm not mistaken, we can compute degree of continuous mapping $f \colon S^1 \to S^1$ as $\frac{1}{2 \pi i} \int\limits_{f(S^1)} \frac{1}{z} dz$. Is it possible in further dimensions to compute it via integral of some form?

Ilya

8:49 PM

@Nimza: hey

Nimza

@Ilya Hello Илюха!

Ilya

разговоры еле слышны

MSE погрузился в тень

Nimza

:))

Ilya

как оно?

Nimza

что-то ничего интересного, а у тебя?

Gustavo Bandeira

8:52 PM

@NickKidman Hey! Thanks for answering my question.

Ilya

спать охота, чем скоро и займусь

oops, we're not alone

>_>

<_<

0_o

Nimza

^_^

Gustavo Bandeira

@Ilya Relax. I don't mind, really.

Ilya

@Gustavo: neither me

Gustavo Bandeira

@Ilya Neither Jesus.

Nimza

8:53 PM

xaxaxaxa

Orange Harvester

Looks left, looks right, and takes out a gun?

Ilya

@Nimza oh no, you know this story? :D

Nimza

@Ilya hm, I think not...

Ilya

@Nimza phew...

Nick Kidman

@GustavoBandeira: Which one??

Gustavo Bandeira

9:03 PM

@NickKidman Functional graph.

Ilya

@Nimza: are we connected on facebook?

Nimza

@Ilya look :)

Ilya

@Nimza check two videos with Zebro

Theorem

Hi everyone :)

anything interesting out here :D

@Ilya : Hi ilya , have we met before ?

Matt N.

@MichaelGreinecker Are you around?

Ilya

9:18 PM

@MattN. check videos on my FB page from today

@MattN. and why do you need Michael?

@Theorem perhaps, I've seen you here in chat. Why?

Matt N.

@Ilya I have a question about forcing.

Ilya

@MattN. icic

Matt N.

@Ilya Did you make it?

Ilya

of course not

I'm wasting my time here instead :D

Matt N.

Then why is it so exciting?

@Ilya : D

Ilya

9:20 PM

I'm not in a favor of robots, but this one is so cute an impressive!

Matt N.

Win : )

Hello!

Michael Greinecker

Hello!

Matt N.

@MichaelGreinecker Can I ask you something about Farah & T.?

Michael Greinecker

@MattN. I don't think I will be of much help, but I'm not offende if you do. I gave up on it relatively quickly after I got stuck on a typo on the first page...

Ilya

@MichaelGreinecker :D

Matt N.

9:25 PM

@MichaelGreinecker You don't last long, do you? : )

Ilya

a very nice excuse to give up, in fact. I don't like such books where you can get stuck because of a typo/incorrect argument

Michael Greinecker

@MattN. Well, I update my pror over the general exposition and decided I might be better off with Kunen. The problem is well documented now: math.stackexchange.com/questions/194626/…

Matt N.

Ok, on page 124: "...This model is even transitive, but we wanted our models also to be countable (for a good enough reason see e.g. Corollary to Theorem 2.1), ..."

Michael Greinecker

Typo is an understatement.

@MattN Yes?

Jonas Teuwen

@Ilya I am your president soon.

Ilya

9:28 PM

@JonasTeuwen chased by trolls?

Jonas Teuwen

I also need a secretary. You seem like a good one.

No, of the PhD community.

When my spine has improved, I have no trouble chasing you with my scepter!

Matt N.

@MichaelGreinecker I am not sure how countability relates to that corollary. Actually, it is not clear to me if this refers to Theorem 2.1 in this chapter or to the theorem 2.1. in chapter 2. Neither seems to give a reason to need a countable model.

Michael Greinecker

@Jonas Shouldn't you delegate chasingsm hangings etc to your underlings?

Matt N.

Now my question is: is this a typo? And if yes, is there a nearby theorem that needs countability?

Jonas Teuwen

I take much pride in doing that myself.

My Indian called me a 'douche' last time.

Ilya

9:30 PM

@JonasTeuwen I didn't elect you, so I may join opposition

Jonas Teuwen

There is no opposition under my rule.

Ilya

you're like Putin

Jonas Teuwen

Everybody likes me.

Actually it is more like 'this shit is so boring, give it to the guy that calls himself president'-type of job.

Ilya

I guess my political career got screwed when I refused being a PhD representative

Matt N.

@JonasTeuwen You had an Indian? That is very Imperialistic of you.

Ilya

9:33 PM

I'm already desperate in my time management

Jonas Teuwen

Yes. he is there to organize parties.

Ilya

@MattN. you are saying as like it's something bad

Jonas Teuwen

I take it as a compliment.

I want total order and control.

Imperialism fits very well in that picture.

Ilya

then I'll join you

linear order?

Jonas Teuwen

I only have a problem: no police force to enforce it.

Ilya

9:35 PM

@JonasTeuwen you have Sauron by your side ;)

Theorem

gnt everyone :)

Jonas Teuwen

PromooD paramilitary organization. Do you want to be the head of the yet-to-be-founded department?

Matt N.

@Ilya Depends how he treats him.

Ilya

@JonasTeuwen ministry of defence fits me well

Jonas Teuwen

Ilya's Guerilla PhD Warfare Techniques.

Ilya

9:36 PM

indeed

ok, gonna take a 10-hours-long-nap

bbl

@JonasTeuwen don't take this world under control without me

Michael Greinecker

@MattN. I think you need countable transitive models to construct a generic filter.

Ilya

and don't invade Russia!

Jonas Teuwen

@Ilya You will get a very important position once the PhD Reich is in place.

Ilya

cool

now I'll have sweet dreams, thx

Jonas Teuwen

Do you want a scepter?

Matt N.

9:40 PM

@MichaelGreinecker You need transitive so that it's easy to show that the forcing partial order $P$ is an element of the ground model $M$. But where does countable come in?

robjohn

Hey all :-)

Matt N.

Sorry, was afk feeding the cats.

@robjohn Hello mean square : )

@MichaelGreinecker Transitivity is explained on page 126.

Well, if you have Kunen, maybe it's explained in there what countability is good for? I think one can do forcing in uncountable models but countability must give some nice properties.

Michael Greinecker

@MattN You need transitivity also because a lot of stuff is absolute-for-transtive-models and that makes life easy. That countability helps in constructing generic filters is explained on page 1...

@MattN Kunen uses countability exactly for constructing a generic filter.

Matt N.

@MichaelGreinecker Ah, is that a typo, too? Mine says: "...Observe that for a countable $\mathcal D$ a $\mathcal D$-generic filter always exists; ..." -- should the first $\mathcal D$ be an $M$?

(I haven't started to read the book, merely using it to look up stuff at the moment)

Jonas Teuwen

@WillJagy I have said it different to the guy. Just "thank you for who you are".

Michael Greinecker

9:47 PM

@MattN In the beginning, it dscusses this stuff just order theoretically. But at leat in Kunen he takes P-genericity where P is partial order on a subset of the model (it is of course still transitive).

The typo starts at the first exercise...

Matt N.

@MichaelGreinecker But isn't the $\mathcal D$ also a typo? (before the exercise)

Jonas Teuwen

Michael Greinecker

@MattN No. $\mathcal{D}$ is a family of dense sets $D$. And you want a filter that intersects all of them.

Matt N.

@MichaelGreinecker Ah, stupid, misread. Thank you. I'll check out Kunen about countability.

Thank you, you just saved me several hours : )

Michael Greinecker

@MattN You are welcome. The great thing abut Kunen is also that he has a book that explains all the logic stuff you need to know before...

Matt N.

9:54 PM

But the type setting... :,(

user19161

My accounts have been deleted. Math is the only one now.

Matt N.

@JasonBourne What? Why?

user19161

@MattN. I want to focus on one site and not be addicted to many.

Matt N.

I didn't know you were addicted.

user19161

My answers and questions there remain.

user19161

9:56 PM

Nothing of value is lost.

user19161

At most other users lose the rep I gave them.

Matt N.

Sure, I wasn't criticising.

mick

Hi everyone ... apart from jonas of course

Matt N.

Ok, I'm going offline. See you all soon!

user19161

@MattN. I didn't say you were. =)

user19161

10:00 PM

@MattN. Bye, take care!

mick

by @MattN.

Michael Greinecker

Bye, @MattN

mick

@robjohn How are your cats doing ?

Who wants to see a ghost on video ? ( watch closely )

watching monty python

Old John

Hi folks - just popping in for a few minutes

Orange Harvester

@mick too many I have seen ghosts, they don't surprise me anymore.

@OldJohn Hi!

Jonas Teuwen

10:07 PM

Hi - then back to beer?

user19161

@OldJohn Hey John! I only have one account now ie math!

Jonas Teuwen

Wow - it seems to be full of (ex-)psychotics here.

Old John

@JasonBourne whisky - it is Burn's night here :)

user19161

@OrangeHarvester Have you really seen ghosts?

Old John

@JasonBourne good idea - less distractions :)

mick

10:07 PM

@OrangeHarvester question is if the video is real of course

user19161

@OldJohn I am just wondering why other users rep have not dropped yet, maybe it takes time to filter through.

Orange Harvester

@JasonBourne Yes.

@mick that's a tough nut to crack.

user19161

@OrangeHarvester Care to elaborate a little?

mick

@OrangeHarvester want to see it ?

Old John

@JasonBourne probably the script to do that only runs at certain times

Orange Harvester

10:09 PM

@mick Yes. Always ready, even though it s 4 am here. :P

mick

OK but watch closely or youll miss it
http://www.youtube.com/watch?v=z0d1ydu7eSA

Orange Harvester

@mick I know that like. :P

user19161

@OldJohn Ah, I am also waiting to lose 100 rep from association bonus!

mick

@OrangeHarvester what you mean ? know that like ? you know it or you like it ? It is false not ? cant believe nobody doubts it in comments ...

Old John

@JasonBourne ah yes - that too

robjohn

10:15 PM

@MattN. Hey, there :-) Sorry, I've been off dealing with flags, etc.

user19161

@robjohn I missed the chat drama. =)

robjohn

@mick all of our animals are doing quite well.

@JasonBourne I did pretty much, as well.

mick

@robjohn Good. Can your cats do algebra ?

user19161

@robjohn But at least as a mod you get to see them later!

robjohn

@JasonBourne not really.

user19161

10:17 PM

@mick They probably know banana math: 1+1=2.

Orange Harvester

@mick Ohh, Just saw the the video. I thought it was one of those where you have to watch carefully, and suddenly something pops out, and scares you.

But I did not see the ghosts.

where is it?

mick

@OrangeHarvester the ghost pushes the women in the beginning. watch fullscreen and closely.

robjohn

@mick they can catenate...

2

Orange Harvester

@mick yes I saw it!

It must be a spoof of someone playing with a video editor.

mick

i starred rob. :)

@OrangeHarvester so you think its a fake too ? it got to the front page of youtube though and nobody comments about fakeness. kind of weird.
I did research and seemed there have been ghost claims by actual ppl too ... on the otherhand it might be those stories that motivate someone to make a fake video.
Why does not anyone say FAKE on the comments ?

Orange Harvester

10:22 PM

@mick It is too subtle too notice. You are trying to think what is in the video, and then you start watching after the crash happens.

mick

@JasonBourne 1 mouse + 1 mouse = 2 mouse

Orange Harvester

The woman fainted it seems.

mick

@OrangeHarvester what are you suggesting ? that its not fake but an optical illusion ?

Orange Harvester

@mick I am suggesting someone messed with the video.

mick

Yes I suppose so. But I wonder why nobody says fake in the comments. Usually comments are full of fake and gay comments :)
fake profiles or removals ?

Orange Harvester

10:30 PM

@mick that I would not know. :-)

mick

still mysterious then ...

Orange Harvester

I live in a country where people still believe that a clay statue has started drinking milk and then when a scientist tried to expose the people, he is sued for offensive/defamation/disrespect to sentiments/religion of people. ;-) Its not that mysterious for me. :P

mick

Can (pi^x)^-1 be written as a dirichlet series ?

@OrangeHarvester the funny thing is these stories always seem more plausable when far away then near you. locals rarely believe unless they are religious ... not very convincing ...

Orange Harvester

@mick you should have seen people flocking to the "supposed" miracle to offer their portion of milk. :P

Here

And what happens to rationalists who try to debunk them

mick

back to my dirichlet question then :)

Orange Harvester

10:46 PM

good choice.

mick

so is 3.14^-x expressible as a dirichlet series ?

Orange Harvester

Oh you were asking me...

no I do not know what a dirichlet series is

sorry.

mick

a0 + a1 2^-x + a2 3^-x + a3 4^-x + ... is a dirichlet series.

Orange Harvester

okay.

user19161

@mick 2 mice.

mick

10:58 PM

@JasonBourne finally someone notices !! :D

user19161

@mick I am THE SE GN after all.

mick

se gn ?

user19161

@OrangeHarvester Do you know that Sai Baba is a cheat? He has been exposed through videos.

Orange Harvester

@JasonBourne Of course. It is like common knowledge.

user19161

@OrangeHarvester Many people still worship him. I used to read his writings in the past.

Orange Harvester

11:03 PM

@JasonBourne Even if he is a fraud, he can make up some writings and then strut them as his stuff. Given the vagueness of philosophy he is bound to get some of the things right.

mick

@JasonBourne bad spelling for a spelling nazi :)

user19161

@OrangeHarvester Rather, nobody really knows for sure what right is.

mick

@JasonBourne right is the opposite of left !

user19161

@mick The problem is, nobody knows what is left when you remove all that is a facade.

Orange Harvester

@JasonBourne Yeah. Also, sometimes, the frauds know more about human behavior than normal people, they just choose to use it differently. Does not mean they are fools who do not understand human nature. They do, they are just being jerks.

mick

11:05 PM

@JasonBourne ion spin decoherence or something helps ;)

Orange Harvester

@JasonBourne Ahh, well, actually we might know what is left and what is right. Dextroglucose, electron spins, QED etc etc (and here QED means Quantum Electro Dynamics.)

user19161

@OrangeHarvester I see different kinds of "smartness": cunningness and true wisdom. I can differentiate between the two.

Orange Harvester

@JasonBourne There can be a fine line, sometimes no line at all.

mick

differentiate with respect to x ..

i think black cats are left

@robjohn Can you express pi^-x as a dirichlet series ?

user19161

@OrangeHarvester Hmm, I wonder when the users will lose their rep from my deletion. I thought it would happen immediately.

Orange Harvester

11:08 PM

@JasonBourne UTC 0000.

Half an hour to go I think.

user19161

@OrangeHarvester How do you know?

Orange Harvester

@JasonBourne I remember from sometime ago, about how all rep is recalculated at UTC 0000, but if you want to recalculate, you can do so manually once everyday.

user19161

@OrangeHarvester Oh, anyway, the serial upvoting/downvoting script runs at 0300.

user19161

@mick Sure, but first note that there should not be a space before the exclamation mark.

Orange Harvester

@JasonBourne Hehe, then my voting must have been especially dangerous. They detected like within half an hour of what I did, and it was nowhere near 0300.

user19161

11:12 PM

@OrangeHarvester You still laugh? You are not supposed to do that.

user19161

@OrangeHarvester That was because I made a fuss out of it and a mod investigated.

Orange Harvester

@JasonBourne I am not supposed to laugh? Since when?

@JasonBourne Ohh, okay.

mick

Goodnight fellows !

user19161

@mick !