Mathematics - 2012-11-29 (page 5 of 5)

10:00 PM

Are there negative Erdos numbers?

@OldJohn No, I don't think it would be undeserved. If you are worried about misrepresentation, I wouldn't be. People who know what an Erdös number means, know what it means :-)

@aDangerousIdea Since Erdös is the root of the tree, It would be difficult to know what that would mean.

a Dangerous Idea

If you wrote a paper with his grand father would that be negative?

robjohn

@aDangerousIdea There might be imaginary Erdös numbers for people who wish they wrote papers with him...

8

Old John

@robjohn true!

robjohn

@OldJohn You could have an Erdös number of 3i :-)

Old John

10:03 PM

@robjohn I would be happy with that!

a Dangerous Idea

How about -3i

Old John

@aDangerousIdea doesn't sound so nice - even though $i$ and $-i$ are pretty much indistinguishable :)

robjohn

@aDangerousIdea let's not start the left-right, clockwise-counterclockwise discussion

Matt N.

Now then. That's it for today here. Be seeing you!

a Dangerous Idea

later

cassandra0

10:05 PM

bye!

robjohn

@MattN. l8r

2l8

Charlie

@Jordan are you alright?

pourjour

someone help please math.stackexchange.com/questions/247612/…

Old John

@pourjour Asalaamu aleykum

Argon

@OldJohn Do you speak Arabic?

Old John

10:08 PM

@Argon badly

pourjour

@OldJohn 3alaykom osslamo wa ra7mato lahi wa barakatoh

Argon

:)

pourjour

@OldJohn h=7

3=a

Old John

@pourjour yep - I understood that one :)

pourjour

@OldJohn hhh It was long time

we've not talk

Old John

10:10 PM

I would have written it "wa alaykum salaam, wa rahmatu llahi wa barakaatuh" (because I have still not mastered the arabic text spelling process)

Argon

My Arabic = aiwa

Old John

@Argon that is very useful!

Argon

Hahaa!

Old John

@pourjour yes - did I tell you I was in Abu Dhabi last week?

pourjour

@OldJohn woow you're traveling a lot!

robjohn

10:12 PM

@pourjour won by 7 seconds!

Argon

@OldJohn "Bukra Fil Mishmish"

Charlie

It's been a long time that i don't learn a new language.... i began to learn Marathi....but it's kind hard...

Argon

@Charlie Vut about Deutch?

cassandra0

Prove it's irrational: $$\sum_{p\text{ prime}} 2^{-p}$$

Old John

@Argon mishmish is apricot, I think - but I don't understand the rest :(

Argon

10:14 PM

@OldJohn It is apricot - very good!

Bukra = morning

pourjour

@robjohn hh yep but I've already a hint in the book $h(x)=\frac { f(b)-f(a) }{ g(b)-g(a) } (g(x)-g(a))-(f(x)-f(a))$

Old John

@Argon so "in the morning there are apricots" ????

Charlie

@Argon i really don't have time to improve my german, french, spanish...

robjohn

@pourjour so what is causing the problem?

pourjour

@robjohn I use rolle's theorem but I don't get the result

Argon

10:16 PM

@OldJohn Yep

@Charlie How about Portuguese?

robjohn

@cassandra0 If it were rational, there would have to be some repeating pattern to the primes

Charlie

@Argon I like my portuguese. it's really good. i speak it since i was 9 month, when i started to learn some language

robjohn

@pourjour So you have some point c in [a,b] where $h'(c)=0$ right?

Argon

@Charlie Sounds good :) I need to brush up on it still!

cassandra0

yes!

pourjour

10:17 PM

@Argon I don't know

Charlie

@Argon Você gosta da língua portuguesa?

Argon

@pourjour What?

robjohn

@pourjour Then $f'(c)(g(b)-g(a))-g'(c)(f(b)-f(a))=h'(c)=0$

Argon

@Charlie Traduz Google faz.

robjohn

@pourjour Divide out

Argon

10:18 PM

Eu sei zilch

pourjour

@Argon sorry I want to send the message for robjohn

Charlie

@Argon "translates google does" it's written

Argon

@pourjour Oh, haha, no prob

Charlie

@Argon zilch?

Argon

@Charlie "Google translate does"

pourjour

10:19 PM

@robjohn let me try ok?

Argon

@Charlie Yep

thefreedictionary.com/zilch

Charlie

@Argon in portuguese stays: Google tradutor sabe

Argon

@Charlie Traduz Google é horrível!

Charlie

@Argon o google tradutor é execrável

Argon

@Charlie *tradutor

@Charlie HAHA "google translator is execrable"

Charlie

10:22 PM

@Argon i like letter x in portuguese. has many sounds: ss, z, c

Argon

@Charlie cs

That's about it

Or Z

Charlie

@Argon i like ç best cedilha

Argon

@Charlie Cedille! Like French!

Old John

Palestine have got their vote at the UN ...

cassandra0

vote for what

Argon

10:23 PM

Geez

Charlie

@Argon yes! but you cannot start a word with this letter

Old John

non-member observer state status

Argon

@Charlie Watch me: çar

@OldJohn What were they before?

cassandra0

interesting

Old John

@Argon nothing

Charlie

10:25 PM

@Argon you can't, você não pode começar uma palavra com essa letra! é a regra mais absoluta da gramática!

Argon

hmmm

Charlie

@Argon and also don't start a word with double letters

Argon

@Charlie Aaron :'(

Charlie

@Argon do you that there's a poor soul here called:"facebookson"?

Argon

@Charlie REALLY?

Charlie

10:27 PM

@Argon YES

Argon

@Charlie In New Zealand, someone is named "Talula Does the Hula From Hawaii..."

Charlie

@Argon GEEZ

user19161

I like it that although my stars are decreasing my rep is increasing.

cassandra0

hi

Argon

@WillHunting You are back to the blue square?

user19161

10:29 PM

@Argon Yes, I think I prefer the blue square, just like amwhy.

robjohn

:7067886 $h(b)-h(a)=(f(b)-f(a))(g(b)-g(a))-(g(b)-g(a))(f(b)-f(a))=0$

user19161

@robjohn Wow, that spoiled my eyes!

Charlie

I wanna hang myself

robjohn

@Charlie why?

user19161

...

Charlie

10:31 PM

@robjohn the exercises are not working..simply not right...

user19161

@Charlie Do you mean you can't solve them?

Argon

@Charlie !!!

Charlie

@WillHunting yes :'(:'(

user19161

Or is there a mistake in them?

pourjour

@robjohn yep I found it now how can I calculate the $lim \frac{sin(x)-x}{x^{3}}$ when x tend to 0

user19161

10:32 PM

It's OK, I never do exercises in books.

user19161

But I think I will do some in future.

Charlie

i feel useless when i can't solve my exercises...

a trash

cassandra0

@Charlie, I feel like that too when I couldn't solve

pourjour

@Charlie me too I have the same feeling

user19161

It's OK, math is not everything. Have a beer.

Charlie

10:34 PM

i don't drink.. but i would like to have junk food

Old John

@WillHunting I thought you didn't drink?

user19161

@OldJohn You are right! It's just an expression!

Old John

@WillHunting :)

Charlie

:'( infinitely

Johan Larsson

Alcohol is not a cure, alcohol sux

user19161

10:35 PM

But I think it's nice to have a beer once in a while. I think I should get some later, since it's Friday.

Charlie

@JohanLarsson :D

user46225

hi

Charlie

@user46225 hi

user19161

@user46225 Welcome to this chat!

user46225

Brian Scott gave me a nice answer to this question: math.stackexchange.com/questions/247528/… but there's another thing I don't understand which I adressed in the comments, could you take a look?

kahen

10:36 PM

math.stackexchange.com/questions/247610/… <-- have I left out any necessary details? I think not, but I'd like to be sure.

Charlie

@Argon are you happy that i'm goint to kill myself?

2

user46225

I think it would be a bit pointless to open a new question for such a small thing

Argon

@Charlie No!!!! That's why I put !!!!!!!!!!!

user19161

@user46225 Hmm, you can also wait for him to respond.

Charlie

@Argon oh

@Argon i'm counting the days to 8/12. my favorite jewish holiday is yom kippur. everyone should commemorate it. it's beautiful day. should be universal holiday.

user46225

10:37 PM

@WillHunting yes... but I'm anxious to finish understanding the proof!

user19161

@user46225 Ah OK, maybe someone here will help you then. I am only a banana...

user46225

@Will: quite the mathematical banana, judging by your profile!

user19161

@user46225 I only aim for low hanging fruits = trivial questions!

Argon

@Charlie It is a very special and odd day. I always feel different on Yom Kippur.

user19161

These days, I aim for ground fruit! =)

Charlie

10:40 PM

@Argon interesting

user19161

By the way, which fruits grow on the ground?

Charlie

@Argon what about pessach?

user46225

watermelon!

Argon

@Charlie ...And not from hunger :)

@Charlie One of my favourite holidays!

Charlie

@Argon hahahahahahahhahahahahahahhah

user46225

10:41 PM

although it would be awesome to have watermelon trees

Argon

@Charlie I love Matzah a lot :), so I don't mind not having bread. It's a really fun holiday!!

Charlie

@Argon my favorite holiday is Christmas

Argon

@Charlie What do you do?

user19161

@user46225 Hahahaha! Maybe I should call myself a watermelon then!

Charlie

@Argon everyone is together and it's such a good energy

Argon

10:43 PM

:)

Charlie

Excuse me gentlemen, out for dinner!

user46225

@Will: well, you found yourself a profile description then ;)

Argon

@Charlie Have a yummy one!

Charlie

@Argon thanks!

Old John

Right - off to celebrate with my Palestinian brothers - g'night all

cassandra0

10:45 PM

@user46225, what is the definition of discrete?

Charlie

who starred my creepy messages???

geez

Argon

@OldJohn Good night

Jordan

@Charlie I just have a bad attitude, and no one to really vent to and I know it shouldn't be here, I know what I need to change and how, just something I need to work on

user19161

@user46225 I see you are interested in algebraic number theory and galois theory.

user46225

@cassandra0: a topological space is discrete if every point has a neighborhood which intersects just the point

Peter Tamaroff

10:45 PM

@Charlie Wadafack?

cassandra0

@user46225, oh I understand thank you

user46225

@cassandra0: in this case $V\simeq \mathbb{R}^n$ with the usual topology

cassandra0

I can intuitively see that a discrete subgroup must be a lattice

Peter Tamaroff

@cassandra0 It means the space is not going around with slutty clothes and stuff.

user46225

(I mean, isomorphic as vector spaces, and it inherits the usual topology of $\mathbb{R}^n$)

cassandra0

10:46 PM

lol

user46225

@Will: at least that's what I've been studying as of late :)

user19161

@PeterTamaroff HAHAHAHAHA, never expected that to come from Pedro.

cassandra0

so how would I prove this, hmmmm clearly 0 is isolated

by some epsilon ball

Peter Tamaroff

@user46225 How is $\Bbb R^n$ discrete?

user19161

@user46225 Gave you a few votes to get you up and moving! (We can't do too many or it will be reversed automatically the next day!)

user46225

10:48 PM

@Peter: didn't say it was, no?

Peter Tamaroff

@user46225 You said, "In this case..."

user46225

@Will: thanks! :)

cassandra0

if $v \in V$ then $v \mathbb Z \subseteq V$

Peter Tamaroff

I misunderstood.

user46225

@Peter: Ah, I see. "in this case" = "in the aforementioned post", sorry :)

cassandra0

10:50 PM

perhaps we should consider the smallest nonzero vector $v \in V$, by the structure theorem $V \simeq v\mathbb Z \times V'$

the problem is we need some decreasing measure to prove this would terminate

user46225

@cassandra0: I've seen proofs of this theorem by induction (e.g. in Milne's ANT), and what you describe works perfectly for the base of the induction, if I understood you correctly

I found those proofs really awful, then I went to Neukirch and found this one which is slicker, but there are details I don't understand :\

robjohn

@pourjour can you use L'Hopital?

cassandra0

@user46225, how do we show that this induction terminates?

user46225

@cassandra0: well... I didn't really finish reading that proof, since I found it ugly, and then I found this one which is fundamentally different, I think :P

cassandra0

I guess we could show that if $\bar v \cdot \mathbb Z^n$ is a dim $n+1$ lattice in $\mathbb R^n$ then we can find points arbitrarily close to the origin

therefore the lattice must have dimension $\le n$

hm

no this is wrong

what's ugly about this proof is the structure theorem is just ISOMORPHISM

2

so we lose the geometry when we just look at it

we have to view the group through the isomorphism to see the geometry

user46225

10:58 PM

well, I'm more algebraically-oriented myself, maybe that explains why I like it best ;P

cassandra0

this is geometry

user19161

@cassandra0 Wow, SHOUTING.

cassandra0

what's this about finite index, isn't $\Gamma = \Gamma_0$?

user46225

that's what you want to prove

Brian has answered to me in a comment, I have to digest it though

cassandra0

they never prove $q = 1$ do they?

user46225

11:01 PM

well, yes

you end up having $r\leq m$

and also $m\leq r$, so...

well

that's not enough

okay, that's not really what you prove

but they are the same up to scaling

cassandra0

ah gamma is not equal to gamma_0, because you might choose a basis for it which is say double the basis for gamma

then it misses out half the points gamma has

user46225

yes, exactly

cassandra0

the point is you can just start with that, then fix it

so they use te fundamental parallelogram (of gamma_0) to fix it: by seeing which points of gamma lie inside that

so they do $\Gamma_0/q \subseteq \Gamma \subseteq \Gamma_0$

user46225

@cassandra0: gee, I don't have that much intuition about what is going on

cassandra0

11:16 PM

@user46225, which part?

user46225

(or really, I barely have any intuition... :P)

cassandra0

I'll draw you a diagram

so you can see what I see

user46225

well, your last three lines were quite mysterious to me

thanks a lot!

@WillHunting hahaha, I hadn't seen your message. That earned cassandra's message a star!

cassandra0

First of all here's Gamma in green (which we don't yet know is a lattice) with Gamma_0 (generated by the basis {a,b} chosen arbitrarily) i.imgur.com/oEDGw.png

er I labelled a wrong it should be the one nearest the origin

Now here's Gamma_0/q in red i.imgur.com/fb6xA.png

(I couldn't be bothered drawing much more of it)

q=3

user46225

I'm following you

cassandra0

11:26 PM

So you see why $\Gamma_0/q \subseteq \Gamma \subseteq \Gamma_0$? And this has been proved without using that $\Gamma$ is a lattice

but it (actually only need the $\Gamma_0/q \subseteq \Gamma$ bit) immediately implies that $\Gamma$ is a lattice

user46225

hmmm, I don't know, I'm not convinced

cassandra0

that's ok but do you see why Gamma contains the lattice Gamma_0 like in my picture?

user46225

Gamma_0/q, no?

cassandra0

Gamma_0/q in red contains Gamma

but Gamma_0/q comes later

just think about Gamma in green and Gamma_0 in pink in the first picture

user46225

yes, that I see

cassandra0

11:32 PM

the construction of Gamma_0 ensures that it's a lattice contained inside Gamma

user19161

Hey @limitless! Have you done your homework?

cassandra0

so the next step is to take the fundamental paralellogram with sides a and b

user19161

@cassandra0 It's parallelogram.

Limitless

@WillHunting, lulz. No. I have yet to get around to it.

I've been laying here pondering why I have a headache.

user46225

@Will: it's "fundamental p." in my notebook :P

cassandra0

11:34 PM

do you know what that is?

user46225

yes, I do

"fundamental mesh" is what Neukirch calls it

user19161

@user46225 The SE day starts at 0000 GMT, I might be able to give you some more votes then. =)

cassandra0

the number of points in the fundamental mesh in my example is 3 (the origin and two points along the way to b)

user46225

yes, I see

cassandra0

you don't count the points on the outside edges of the fundamental domain because of 0 <= x_i < 1

user46225

11:39 PM

@Will: oh, please just upvote what you think it's worthy! thanks in any case :)

cassandra0

so do you see why Gamma_0/3 is the red lattice?

by S/3 I mean {(x/3,y/3)|(x,y)in S}

Argon

Hi everyone!

user46225

yes

cassandra0

QED??

a subgroup of a lattice is a lattice

csss

A and B are events satisfying P(A) = P(A|B) = 0.6. Are A and B disjoint or not? What is P(A_complement |B)?

user46225

11:45 PM

why does it prove that Gamma is a lattice?

csss

I would say they are disjoint, and P(A_complement|B) = 0.4.?

cassandra0

Let H be a lattice (so it's freely generated and has finite dimension) and G a subgroup of H, then G is a lattice since it's also freely generated

(H = Gamma_0/q)

a Dangerous Idea

@Jordan You said you know what needs changing and you know how to change it. What do you think needs changing?

user46225

now I understand. but isn't it the same as what Neukirch does?

Jordan

@aDangerousIdea I just need to study more

cassandra0

11:52 PM

well yeah that's the proof I thought you didn't fully understand

a Dangerous Idea

@Jordan That is what I said at the beginning, all you can do is study hard.

user46225

Yeah! thanks for the geometric insight. Now I understand the proof better (I "only" understood it algebraically)

cassandra0

are there any aspects you still don't get?

user46225

not at the moment, no

thanks a bunch!

cassandra0

ok :)

user46225

11:56 PM

well, I gotta go now

see you all!

later

bye

Bye!

hi @argon

@cassandra0 Hi!

11:58 PM

:)

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$Mathematics$ Mathematics