Mathematics - 2012-11-02 (page 5 of 7)

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7:00 PM

@pourjour, what do you mean exactly?

@jdoe can u show me plz the solution I mean the detail

@pourjour, what more do you want than I wrote?

@ガベージコレクタ do you see the link on that page that says "start ChatJax"?

ガベージコレクタ

@robjohn Of course I can see the link.

@jdoe hwo did u used the banach theorem

7:01 PM

@ガベージコレクタ okay. what browser are you using?

ガベージコレクタ

@robjohn: chrome

@pourjour, I did two steps: 1) Prove the sequence U_n tends to SOME limit 2) find that limit

@ガベージコレクタ is your bookmark bar visible?

Tex Extension for Chrome (I have not tired it)

@pourjour, (1) is done by proving that the associated function f(x) contracts some interval by a scale factor 9

ガベージコレクタ

7:02 PM

@robjohn I don't know which part is regarded as a bookmark bar?

@ガベージコレクタ look here

@pourjour, (2) just solve a quadratic equation or take eigenvalues of the matrix, any way works.. and make sure you get an answer inside the interval [1,2]

@jdoe why the interval [1;2]

ガベージコレクタ

@robjohn I have show the bookmark bar

@pourjour, it can be any interval that contains 1 and it must contain the fixed point too (which is \sqrt{3}) and be a contraction, so I think [1,2] is a simple one to choose

7:04 PM

@ガベージコレクタ okay, now click and drag the "start ChatJax" link to the bookmark bar and drop it there.

ガベージコレクタ

@robjohn: Done, I can see the rendered TeX. THanks

@ガベージコレクタ okay, so now you can use MathJax in chat. :-)

ガベージコレクタ

@robjohn Yes. Thanks

$B(x,y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}$

aha

7:07 PM

@Nimza I was using that as a test for ガベージコレクタ :-)

@jdoe how about this " f(x) contracts some interval by a scale factor 9"

:)))

@pourjour, yes?

@pourjour, it means if a and b are distance d apart, then f(a) and f(b) are closer than d/9 apart

I wish someone will answer my question :(

@jdoe what's the story of the 9?

@pourjour, any number > 1 will do

no I didn't

@pourjour ab + 2a + 2b + 4 >= 1 + 2 + 2 + 4 = 9

oh that is >= we need > so let's use 8

7:22 PM

@jdoe you mean this formula |f(a)-f(b)| = \frac{|a - b|}{|ab + 2a + 2b + 4|}

yes

but <= eta^{-1} * that

@jdoe what is the relation between that and Un has a limit

@pourjour, it's what you need to apply banach fixedpoint theorem

@jdoe so if you prove this |f(a)-f(b)| = \frac{|a - b|}{|ab + 2a + 2b + 4|} you can use banach theorem

no

|f(a)-f(b)| < eta^{-1} |a-b|

with eta>1

@pourjour, |f(a)-f(b)| = \frac{|a - b|}{|ab + 2a + 2b + 4|} is just the definition of f

user19161

7:35 PM

-1

Q: in which numeral system 2+2=5 or 2*2=5 is right?

Does it exist numeral system,in which 2+2=5 or 2*2=5 is right?Is it possible?Can you help me,please

user19161

This question should be nuked!

;((

user19161

And it got an incredible answer.

my question needs answer

7:57 PM

@JasperLoy What day is it today?

user19161

@Argon It's Friday! Yay! youtube.com/watch?v=kfVsfOSbJY0

Got to get down on Friday :)

@Argon hello aaron

user19161

@Argon I was wondering where you were when you pinged me!

@Charlie Hey Marilia! Chem test went well!

8:00 PM

@Argon really????I'm proud of you!

:)

Hey @OldJohn !

@Argon Hi there

Hey @jayesh I'm sorry :( couldn't say before...TOO busy

@Argon you really like to say my name,huh?

@Charlie Yup. Who wouldn't?

user19161

@Argon I prefer to say AARON!

8:03 PM

@Argon yeah, who wouldn't it's a beautiful name!

@Charlie Well, @Jasper, I guess!

@Argon Jester, hmm i mean, jasper, he's ...nevermind

Haahhahaa

user19161

@Charlie I like to be a jester.

just curious:why someone who says over and over that has no feeling keeps acting like had something..and from one hour to another, changes its behavior with the person who claims not to have feelings for...

8:07 PM

??

user19161

@Charlie What are you talking about? Incomprehensible.

@JasperLoy as incomprehensible as you, mr. Loy

user19161

@argon You see? What do you see?

user19161

@Charlie OK, who are you talking about?

@JasperLoy Nothing at all, sir :)

user19161

8:09 PM

@Argon I see, madam.

@JasperLoy you know what i'm talking ABOUT JASPER DON'T MAKE SAY IT!!!!!!!!!!!!!!

user19161

@Charlie Are you talking about the person you like?

user image

I can't unknot this...

@jdoe THAT'S UNKOT?????

@jdoe I can unknot it if you let me use 4-d space :)

8:11 PM

apparently... maybe it's an april fools unknot

user19161

@Charlie Maybe because he is a nutcase? I don't know.

@JasperLoy he's not ...but you....

user19161

@jdoe That looks a little like me...

@jdoe now you killed me..

user19161

@Charlie Well, anyway I don't even know who or what you are talking about, really.

8:15 PM

@jdoe thanks about everything

@JasperLoy you're not stupid .i know you know.

user19161

@Charlie No, in this case, what you wrote is so unclear.

@JasperLoy whatever, Jasper.Nevermind. I really try to be so kind to you, but you refuse it. And you've been really rude to me , for reasons that i don't understand.

user19161

@Charlie Rude? Where?

@JasperLoy all the time.

user19161

8:18 PM

@Charlie I think you just don't get me.

@JasperLoy ohhh.....okay.

user19161

@Charlie Like I said, we all look at the same thing in different ways, maybe. Maybe I am thinking of X, you are thinking of Y and others are thinking of Z. QED.

@JasperLoy but you just over react

hey people listen to STAYIN ALIVE- BEE GEES and foget all your problems

:D

8:22 PM

@pourjour see the city breakin' and everybody shakin'

user19161

@pourjour If one can listen to that and forget all your problems then your problems are not really problems.

@Charlie is that a song

@pourjour hahahaha stayin alive

user19161

@argon Do you usually get lotsa HW over the weekend?

it's a good music (classic music make you feel good especially this one because of the instrumental)

8:24 PM

1

Q: Equivalence of Valuations - Trouble Understanding Proof

I want to understand the proof of the following theorem. Here is what I have got so far: Theorem Every non-euclidean valuation $v$ on a field $K$ is equivalent to $v_{\mathfrak p}$ for some prime ideal $\mathfrak p$ of $\mathbb O_K.$ proof: Let $R_v$ be the valuation ring of $K$ w.r.t $v$ is in...

abstract-algebra ring-theory field-theory algebraic-number-theory ideals

this is my question :S

@JasperLoy Depends on the week. Not too bad this week because I had lots of tests (and $\therefore$ less homework).

do you think I made it too long? I jsut wanted to provide background

user19161

@Argon I hate that symbol. My eyes!

@JasperLoy What's wrong with $\therefore$?

@JasperLoy do you know what when I have real problems I play games or I hangout or I kick my cat

user19161

8:26 PM

@Argon Well, first of all it is almost never used in math texts at the undergrad level and beyond.

@pourjour kick the cat..hmmm

@JasperLoy So?

user19161

@Argon And secondly, the use of logical symbols like that should be reduced to a minimum unless you are dealing with formal logic.

user19161

@Argon And also, I think three dots really look ugly.

@JasperLoy Ehh... I like it to end proofs on tests.

8:28 PM

@Argon yeah.i prefer tombstone.not QED.

user19161

@Argon Aha! I was like you, perhaps. Now I would just write "therefore".

user19161

But I prefer "hence" to "therefore".

@charlie yeah I have a funny cat it doesn't harm me using it's fangs ( a peaceful cat)

@pourjour hahahahahha hilarious!

I need a good finish after my proofs for funsies. What should I use at the end? QED? Tombstone? Box?

8:29 PM

@charlie hhhhhhhhh :D

user19161

@Argon Nothing.

@JasperLoy Boring

user19161

@Argon Leave the teacher gasping for more.

@JasperLoy I can do that. All I need to do is give the first half of a proof.

user19161

@Argon And she will give you an F.

8:30 PM

@JasperLoy While grasping for more.

Oh, got perfect on a math quiz today!

user19161

@Argon Grasping, is she grasping you? Oh noes!

@JasperLoy Haha she would kill me if I actually failed a test

user19161

@Argon Well done!

@Argon tombstones

for sure

user19161

Maybe I know what you mean @charlie, but it is not over-reaction. Maybe it is just my dramatic nature which automatically magnifies everything.

8:35 PM

@JasperLoy hmmm...and i'm too fastidious

user19161

Wow I got so many badges today, I think 5.

@JasperLoy Impressive

user19161

Hey @anon do you like the Rebecca Black Friday song?

@Argon but tell me:how was your test

@Charlie Which one :)

8:37 PM

@Argon chem

@Charlie Good, I told you!

Yay

@Argon and...

what kind of questions, these things

@Charlie Oh. I needed to name alkaes, ynes, enes

and draw them

I needed to correct wrongly named alkanes, alkynes and alkenes

@Argon hmm

@Argon are you a chemical element (argon)

8:39 PM

I needed to identify functional groups in hydrocarbons

@Argon good

@pourjour Why yes :)

That was it

I think everyone looked at my question and gave up

user19161

@Argon I also managed to make each of my 3 accounts have a score of multple of 5. =)

@JasperLoy Like Pedro?

user19161

8:40 PM

@Argon Yes, hehe.

:)

@argon so you're addicted to chemic

@pourjour ?

$rep \equiv 0\, (\mod 5)$

user19161

@jdoe Nope, I did not even look at it but gave up already. =)

@argon you're wild about chem ?

8:43 PM

@pourjour Not really. Just I had a chem test

user19161

@pourjour By the way, there should not be a space before the question mark.

You know what's the problem with boring people?

They are boring?

@JasperLoy no

Henning Makholm

@JasperLoy French typography uses spaces before "large" punctuation such as ?, !, :. "pourjour" sounds like a French name.

8:45 PM

@Argon We get used to them.And then we start to absorb their boringness

user19161

@HenningMakholm That explains it! I see this very often on SE!

@Charlie :) I'm so sorry for influencing you negatively.

user19161

It seems only you and I like the Fri song @argon.

@Argon you didn't do anything :)

i'm naturally crazy

@JasperLoy weirdos

8:46 PM

@anon i told him...

@JasperLoy How many YouTube downvotes did it get?

Henning Makholm

@JasperLoy They also tend to write quotes « like this » instead of "like this".

user19161

@anon You are right! OK, do you like Bieber's "Baby"?

@Charlie I'm boring though!

Good evening, gentlemen.

Henning Makholm

8:47 PM

@MattN. Hi Matt.

@MattN. Good evening!

@MattN. Good e'en

@Argon and who is not?

@Charlie You

@Argon hahahahahaha

8:48 PM

Is there anyone who would talk to me about set theory?

@JasperLoy no, but that one isn't bad, it just isn't my type of music

user19161

@MattN. Unfortunately Asaf is not in chat.

I'm thinking about models and cardinalities and I'm slightly confused.

user19161

@anon Hmm OK. What's your favourite music then?

@JasperLoy I'm afraid that he won't be returning soon. We need to appoint a new Set Theory guru.

Henning Makholm

8:49 PM

@MattN. Shoot.

user19161

@MattN. Hmm, you need some set theory expert then...

if you switch your models up all hell breaks loose. I think I came across a JDH answer that said even which sets are finite or not can differ, though I may recall that incorrectly

@robjohn Why not?

@Argon self imposed exile. I am not sure why.

@JasperLoy thanks about the note

8:50 PM

@robjohn Strange.

@HenningMakholm Nice thank you : ) Ok: if I remember correctly, we can have a model of ZFC in which the cardinality of $\omega_2$ is $\aleph_1$. Do I remember correctly?

I have never chatted with him.

@JasperLoy I like a little hip hop / r&b stuff, more hard rock and a little metal, and a little technoey or substeppy stuff. (I am horrible at naming categories of music.)

@robjohn do you know about henry T.?

user19161

@robjohn aka robjohn =)

8:51 PM

(I will have to read up on all this but for now chatting about it would be of great help)

@JasperLoy ms word is tired of correcting all the sentences with question mark

Henning Makholm

@robjohn My second-hand impression is that he left in temporary anger one day, and then after he cooled off it dawned upon him how much more time he had when he isn't in chat.

What Henning said.

It wasn't entirely anger necessarily. He made a comment that got him flagged. Gigili involved, of course.

user19161

@anon Rock and metal? Powerful! I like Mariah Carey and Italian opera.

8:52 PM

@Argon don't you have any other test soon?wanted to remember the things i don't see about two years...

@JasperLoy You sure have a unique taste in music

The closest thing to opera I like is inner universe from gits' opening theme.

Henning Makholm

@MattN. Oops, scratch that. NO. $\aleph_1$ is defined to mean the cardinality of $\omega_1$, and $\omega_2$ by definition has the next higher cardinality, i.e. $\aleph_2$.

incidentally the only trilingual song I've heard of

user19161

@argon You should know my favourite Mariah song!!!

8:53 PM

:6745787 Yep! Nice, so far so good. Also, if I remember correctly, we cannot do this for $\omega$. $\omega$ has the same cardinality in every model. The reason for this is that we can describe it as a formula. (or several, to be precise)

@Charlie Math test Monday, Physics test Tuesday, Chem and physics labs Friday. Computer test Friday... and probably some quizzes in between

Henning Makholm

What you can have is a model where $2^{\aleph_0}$ is $\aleph_2$.

@JasperLoy Hmm....

@HenningMakholm Ok. Then back to that question. I am absolutely sure that we can make some sets have lower cardinality than in the standard model.

I'm pretty sure the aleph and ordinal numbers are stable with respect to model switch ups - it's the the operations on them and the numbers attached to actual sets that differ

user19161

8:54 PM

@anon Hmm, now that changes my mental image of you. =)

@Argon hmmm

ROCK RULES

@JasperLoy What?

Henning Makholm

@MattN. Well, we're on thin ice here already, because the notion of "cardinality" only makes good sense inside a particular model. It is not intrinsic to a set.

user19161

@Argon Check out my profile...

@JasperLoy Oh, right :)

8:55 PM

@HenningMakholm But these are both cardinals. I thought that if we could change something it would be the cardinality of a set, not the cardinal itself. (since the latter is just a name)

@JasperLoy "When you believe"

@JasperLoy how so?

user19161

@Argon QED.

$\therefore$

@anon Do you like metallica?

8:56 PM

@HenningMakholm Indeed. But cardinals make sense. Where for example $\aleph_0$ means in bijection with $\mathbb N$. Although I am not sure how this same statement can be made about $\aleph_1$.

user19161

@anon Well, I just did not expect rock and metal! But this is interesting...

Henning Makholm

@MattN. $2^{\aleph_0}$ is just (more or less by definition) a different way to say "the cardinality of $\mathcal P(\omega)$, whatever that is".

@JasperLoy
$\therefore$
$\therefore$$\therefore$
$\therefore$$\therefore$$\therefore$
$\therefore$$\therefore$$\therefore$$\therefore$

@Charlie I tend not to like early stuff by metal bands, but I like a whole bunch of metallica.

@HenningMakholm Yes, I agree.

user19161

8:57 PM

@Argon Hehe, you can't piss me off...

@anon nice, really nice

@JasperLoy $\frac{1}{0}$?

@HenningMakholm It's a different way of writing $|\{0,1\}^{\mathbb N}|$ which we can show is in bijection with $P(\omega)$.

actually most people probably tend not to like early stuff by any band but probably don't realize it

user19161

@Argon Hey I think your therefore has choked my mathjax!!!

8:58 PM

@JasperLoy There's only 10!

Henning Makholm

@MattN. Yes -- ZFC is underdetermined enough that $\aleph_1$ has almost no certain properties, except being "the first uncountable cardinal", and what little follows from that.

when /sci/ first started on 4chan a bunch of users broke it when mathjax was installed by doing massively nested sub and supscripts

@JasperLoy I would be a very bad Set Theory guru

then they disallowed nesting x levels deep for some x

@anon 4chan is insane. I avoid at all costs.

user19161

8:59 PM

I don't even know what is 4chan, irc, etc...

@anon yes, yes.i knew a few songs, only.then i started to listen to others songs they made. i'm not fanatic , but i like to listen.

Henning Makholm

@JasperLoy Congratulations!

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