Mathematics - 2012-11-02 (page 1 of 7)

« first day (821 days earlier) ← previous day next day → last day (4203 days later) »

12:01 AM

Hey, quick topology question here.

I'm thinking about the Ehresmann fibration theorem.

I'm wondering if I'm applying it validly. If I have a proper submersion from M to N, I know I have a fiber bundle. Let's say that I can topologically identify the inverse of any point as some fixed manifold X. Do I now know that X is the fiber of this fiber bundle?

hi @Charlie back so soon?

@skullpatrol yes...just taking a look

@leo people

@Charlie too late to fix it :-( but thanks :-)

@leo anytime

:)

@skullpatrol i think he would like to hear it

@skullpatrol you said everything :P

I think he just needs to feel important...

We all do...

sometimes.

12:08 AM

Nice to see some math talk, I was confused for a while when it was all chemistry for two hours

@JohanLarsson hahaha

@skullpatrol yeah..we all do

@JohanLarsson That was an organic reaction :-D

@skullpatrol he seems to need it all the time

@skullpatrol ba dum tss

I bet we all need it all time

@leo people are self centered

12:11 AM

Anyone with an opinion on Octave vs Scilab?

Find me somebody to love.

@skullpatrol Nice

@Argon hello

@Charlie Hello again. You will be pleased to hear that I've memorized the functional groups I need.

I mean people need to feel that what they are doing is useful, so that other people can says "hey, that's useful so you are useful/important/etc". Otherwise one might feel that what one does is pointless

get sad

@Argon Good, Aaron!Hope you never forget it, like i never forgot!

12:14 AM

and so on...

@Argon You must have a good memory.

@leo but need all the time is a patology

@Charlie perhaps, yes

we need some shots of it sometimes

maybe not all time

@leo yes

@skullpatrol do you like queen?

yep, some of it

12:18 AM

@skullpatrol i like it a lot

Any help with proving mathbin.net/111373 converges to 3?

@GregRos as k -> infinity?

Yup

I say 4

It does converge to 3 :P I've proved it and Wolfram Alpha says so.

My proof is just too long.

12:19 AM

but I'm wrong 8 hour/day

I think it does as well.

@JohanLarsson Have you read this?

@skullpatrol yep thanks anyway

Maybe a crucial point is that f(1) = 2.

I mean a_1 = 2

@GregRos I'm reading it wrong then, I think it looks like a trivial 4

12:21 AM

I need some stuff about the determinant-way of define the rank of a matrix

@Argon when is your exam?

chemistry

February

How do you figure a trivial 4?

@leo I have known that but effectively forgotten it

@Argon february?february?

12:22 AM

@JohanLarsson me too

4a/a -3/a a-> infinity

3/a -> 0

February

4a/a

=4

$$\lim_{k\to\infty}a_{k+1}=\lim_{k\to\infty}\frac{4a_{k}-3}{a_{k}}$$

@JohanLarsson the rank of a matriz is just the largest $r$ so that there is a nonzero minor of the matrix

12:23 AM

but I'm probably wrong in my first step

That's a recurrence relation.

a_k is the previous item in the sequence, not a constant.

Letting $S = \lim_{k\to\infty} a_{k+1}$

@Argon i'm drowsy...

$$S = \frac{4S-3}{S}$$

better go to sleep...

12:25 AM

$$S^2 = 4S-3$$

@Charlie Ok

Good Night

:)

Thanks

interesting

@GregRos $$S^2-4S+3=0$$

@Argon Good night!

@Argon You're welcome!

@Charlie Have a nice sleep.

@Charlie Without Jasper haunting it like he says.

there should be mathbin integration in this chat

12:27 AM

@Argon thanks

I can't assume it's convergent before I show it

Can I?

@JohanLarsson There is (if you mean Latex)!

Night, @Skull!

@Charlie later

Also, can I rigorously perform the substitution for S?

12:28 AM

@GregRos You can probably show it is bounded and monotonly increasing w/ induction.

Or formally. Or whatever term might be appropriate.

Yeah, that's what I've been doing. It turns out too long.

@Argon you mean pasting the Latex here?

@JohanLarsson Yep. Use MathJax

I meant rendering the links as equations

ok

@JohanLarsson Oh. You can write Latex directly with MathJax'

12:30 AM

idk, I'm confused now

@JohanLarsson Make a bookmark with the Javascript

i.e. javascript:(function().....

on the page

Click on the bookmark when in chat, and all the Latex magically renders!

magic!!

Magic

ty

@GregRos You may like: en.wikipedia.org/wiki/Recurrence_relation

Use a basic characteristic equation.

12:33 AM

I actually checked that. But the article that covers this is actually continued fraction, since it turns into a continued fraction.

Which would allow me to solve it easily

But unfortunately it would require proving continued fraction thorems

so I guess I'll have to stick with my long solution

Depends how rigourous you want to be :)

Hmm, less how I want it to be, and more how the teacher does :P

2

True!

@JohanLarsson Did you get it to work?

$$\sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}$$

yup thank you, renders really nice

Great

12:36 AM

mhm

@GregRos Sad but true.

$$\frac{1}{\pi} = 12 \sum^\infty_{k=0} \frac{(-1)^k (6k)! (13591409 + 545140134k)}{(3k)!(k!)^3 640320^{3k + 3/2}}$$

At first I wanted to just do this off the bat. mathbin.net/111377

Hey guys (and gals, if any), how do you "unwind" the floor (or ceiling) function? That is, given $b=floor(\ln_2(n)+1)$, how do you write the equation for $n$? Is it even doable?

Simpler version $b=floor(x)$. But clear x is not the ceiling of b!

@GregRos This yields the above quadratic.

12:42 AM

yes, I meant I wanted to do it because it "looks" like it's correct

And it is correct sort of.

Hey guys (and gals, if any), how do you "unwind" the floor (or ceiling) function? That is, given $b=\lfloor \ln_2{n}+1 \rfloor$, how do you write the equation for n? In simpler terms, if $b=\lfloor{x} \rfloor$, what is $x$? Clearly, $x$ is not merely the ceiling of $b$. Is it even doable?

I hope that's better! :D

yeah there is something that might help

Floor and ceiling functions

In mathematics and computer science, the floor and ceiling functions map a real number to the largest previous or the smallest following integer, respectively. More precisely, floor(x) = \lfloor x\rfloor is the largest integer not greater than x and ceiling(x) = \lceil x \rceil is the smallest integer not less than x. Notation Carl Friedrich Gauss introduced the square bracket notation [ x] for the floor function in his third proof of quadratic reciprocity (1808). This remained the standard in mathematics until Kenneth E. Iverson introduced the names "floor" and "ceiling" and the cor...

@Jeff Well you cannot find the value of $x$. All you know is that is it between $\lfloor{x} \rfloor$ and $\lfloor{x} \rfloor+1$.

Hey gang

@Jordan Hey!

12:51 AM

Is there an easy way to find the coefficients of a quadratic? I am doing a program where I have a procedure that creates a quadratic with given a b and c but I need to work back from that

There are a few things that might help you figure out what you want to find

is there any sort of mathematical tricks that I can use to find the values? Obviously c is going to be x=0

@Jeff This is because, for example $ \lfloor{1} \rfloor = \lfloor{1.5} \rfloor $

@Jordan What do you have to begin?

Points?

@Argon right. that's what i figured. but i guess in the first eq i posted, I can just maybe assume $b$ is an integer, then subtract 1... etc.

@GregRos thanks. been there, skimmed that. :D

@Jeff ? $b$ has to be an integer

12:53 AM

Anything but for example I have the quadratic $2x^2 + 3x + 4$ evaluated at any x value, I do not know the coefficients though because they have already been processed in the system.

Can you get the roots?

All I know is that I have a quadratic where $x=0$ results in a 4, how would I find a and b?

@Argon. Right. So my point is, if I just keep in mind that $b$ is an integer, I can just try to unwind (that is, solve for $n$) $b=\ln_2{n}+1$ - in other words, I can just ignore the floor symbol.

@Jordan Polynomial interpolation would do it

There are tons of quadratics where x = 0 results in a 4. Specifically, all of those with +4 constant.

12:55 AM

@argon that sounds complex

@Jordan :) It's not that bad. I will explain it to you, if you need

@greg Yes but I know that the c is 4 for sure

I need this down in 2 hours :P

That's all you know?

I can plug in any x value and see the result of it

@Jordan I see. 1 sec

12:57 AM

I can also do any string of that quadratic modified in any way by the quadratic evaluated by anything

Is finding the roots via approximation a solution?

for example fora linear equation mx+b I would simply evaluate at zero for the b and then subtract the b to bet m when x is 1

no

@Jeff Well, $b$ may differ by $1$ from $\operatorname{lb} n + 1$!

well maybe, but it isn't suppose to be complex I dont think

It's not complex.

12:58 AM

Well it is for programming, it would be more than 4 lines I think :P

@Jordan That is complex?

Actually it might not be if you write it recursively :P

(define (get-linear-b proc)
 (proc 0))
(define (get-linear-m proc)
  (- (proc 1) (get-linear-b proc)))

That is how I find a linear b and m

@Jordan Everything is here: isezen.com/2012/01/15/quadratic-interpolation-three-point

Oh. You can try finding f(1) and f(2). that will give you a relation, e.g. A + B + C = f(1), 4A + 2B + C = f(2)

1:02 AM

@Jordan what language is that? Haskell?

scheme

scheme

wow haskell looks nothing like that lol

that's a pair of linear equations, so.

(define (make-quad a b c)
  (lambda (x) (+ (* a (sqr x)) (* b x) c)))

I've only seen F# briefly

Hi @anon

1:04 AM

hello

All these old languages look similar, old

lol

As opposed to what?

also haskell looks nothing like scheme. At all.

Hello, can anyone give me a quick definition of divergence,pleased dont say the sequence that doesnt converge i want detailed definition

Do you have the definition of convergence?

"does not converge" is the definition of divergence, and it is implicitly just as detailed as the definition of convergence, only logically negated.

1:09 AM

@anon can it not be parallel?

so I wonder if you understand the details in the definition of convergence. if so, the idea that divergence is the absence of convergence shouldn't cause you any issues.

neither converging nor diverging?

no

@Pilot Basically, If $|f(x)|= L < \infty$ as $x \to c$

there are bounded diverging sequences, if that's what you mean, and sometimes people connote unboundedness with divergence

1:10 AM

@Greg yes, I have defined divergence like this : divergent seq doesnt have limit,but I am pretty sure there is better definition

why are you pretty sure of that?

You can put your definition into different terms.

I had defined it previously and have seen in literature

but cant remember

In general, you can just the definition of a limit

and negate it for any L

e.g. for any L there exists ℰ such as that for every δ...

there are rules to move logical negations inside existential and universal quantifiers, and you can apply that to the $\delta$-$\epsilon$ definition if you wish

1:13 AM

then would it be correct to say for any k in N and any a in metric space there exists epsilon>0 such that d(a_k,a)>epsilon

?

That occurs for any sequence.

no

no, what if $a=a_k$ for some $a,k$ after all?

which will necessarily occur

d(a_k,a) greater than or equal to 0,now?

You have to preserve the order of quantifiers.

1:16 AM

no, the exact same response applies - do you understand my reply?

there exists N s.t for all k>N?

that's a sentence fragment and there is more than one way to modify your original statement with it so I have no response

I am writing some latex up for it

$$\begin{array}{c} \neg\exists x\in X~\forall \delta>0~\exists n\in\Bbb N~\forall k>n:~d(x_k,x)<\delta \\
\forall x\in X~\neg \forall\delta>0~\exists n\in\Bbb N~\forall k>n:~d(x_k,x)<\delta \\
\forall x\in X~\exists\delta>0~\neg\exists n\in \Bbb N~\forall k>n:~d(x_k,x)<\delta \\
\forall x\in X~\exists\delta>0~\forall n\in \Bbb N\neg\forall k>n:d(x_k,x)<\delta \\
\forall x\in X~\exists\delta>0~\forall n\in \Bbb N~\exists k>n:d(x_k,x)\ge\delta \end{array}$$

these are all equivalent formulations of divergence

ahhhhhh!

the infamous 'drunk A' symbol and

using the rules $[\neg \forall x:P(x)]\iff [\exists x:\neg P(x)]$ and $[\neg \exists y:Q(y)]\iff [\forall y:\neg Q(y)]$

the badly mounted shelf symbol ¬

1:22 AM

I see now. Thanks a lot.

I sort of hope I will never ever have to use those symbols, ever.

@Pilot I guess a clean equivalent formulation would be "every $x\in X$ has a ball around it in which the sequence has only finite intersection"

@GregRos then don't be an analyst or a logician, that's all I can say

@GregRos And you lost me with your equation

Is "A ball around it" formal terminology?

$B(a,r):=\{x\in X:d(x,a)<r\}$ is a(n open) ball in a metric space

1:26 AM

How does that allow multiple cluster points?

so yes, "ball" is perfectly standard terminology in topology and analysis

I see your point

aw dicks

disregard the equivalent formulation then

@GregRos Do you think "sphere" sounds more formal?

as pp notes, this finite-intersection statement says that a sequence has no limit points whatsoever, which is not the same as not having a limit

1:27 AM

out of curiosity, what do you work with/study?

Something and ends with -oid.

steroids

you're not porton in disguise are you?

I draw some CAD and write some C#

+ some math that does not expose me to the shelf

I smoke some weed and pop some caps.

1:30 AM

Here's how to amend the statement: a sequence $(x_k)$ in a metric space diverges if every $x\in X$ is contained in a ball with noncofinite intersection with the sequence

Wouldn't using letters and words and no topology be clearer tho?

Oh, I did some C#. now I study.

also I code in F# for fun.

I used letters and words and ideas specific to metric spaces in my statement..

Only reason I ever heard of cofinite is that I read a bit about ultrafilters.

... If I am thinking of the right term.

what is an intersection of sets?

a smaller set?

1:41 AM

$A\cap B:=\{x:x\in A\text{ and }x\in B\}$, i.e. the set of all elements common to both. (we define the intersection of any number of sets similarly)

If we have a family of sets $S_i$, where the indices can come from any set, but you can think of them as being indexed by the naturals for most situations, then the intersection of all $S_i$ is the set $\{x: x\in S_i \text{ for all i}\}$.

first thing that was possible to understand in a while

what is the informal definition of a set?

@JohanLarsson No idea.

A collection of things

But not all things.

1:46 AM

can it be continuous?

is R a set?

the set of real numbers is a set

a set can be a continuum in the sense that (a) it has the same cardinality (counting size) as the real numbers or (b) it is a complete metric space, or perhaps other properties can be described as "continuous"

holy root beer that is a bluey blue color

(googling a lot of words now)

@JohanLarsson Have fun with cardinality.

user19161

@anon Are you talking about me? I'm glad to be your root beer anytime. =)

[x] cardinality (number of elements of the set)

1:51 AM

I don't see anything else quite as blueingly blue as your blue avatar - yes I am talking about you

@JohanLarsson How do you define number of elements for infinite sets?

infinity?

isoclasses of sets under the relation of bijection!

user19161

@JohanLarsson Yes, math is full of fanciful terms because the mathematicians want to show off their English.

What anon said.

1:51 AM

@JohanLarsson the problem is, there are provably different sizes of infinity... :-)

luckily I don't speak English

It's a lot more intricate than $\infty$.

You can represent each cardinal with an ordinal (well-ordered set).

without the axiom of choice there are incomparable cardinals aren't there? (checking my facts)

Yes.

So, I was assuming AC there.

user19161

@johan Welcome to this chat. We have the same initials. That makes you a special bro.

1:53 AM

do you trust Wikipedia as a source for math stuff?

@JasperLoy lol

user19161

@JohanLarsson Yes, it is correct 99 per cent of the time, just like books.

I'm flooding the chat with some noob noise now when its a lil slow

user19161

I trust Wikipedia not just for math but everything.

user19161

Wikipedia can contain nonsense, but so can books or the professor.

Wikipedia is a very good resource for learning math. A few errors here and there are definitely worth it given how much it covers.

1:55 AM

@JasperLoy ok, maybe maths fits wikipedia good

I trust wikipedia for most things

I have been unlearning math for ten years now

user19161

Many things I consider important in life I learn from Wikipedia the last couple of years. Thanks Jimmy, you changed my life.

user19161

@anon You almost never ping people so one has to read every line in the transcript and then decide what you are talking about. And we should meet for root beer one day. =)

one downside with wikipedia is that the accessability is so good so you sometimes dont bother to learn it properly. Trust that it will be easy to find it next time

@JasperLoy I ping when I feel it is important the intended recipient receive my message. Otherwise, I am content with talking to the wind and may not have a recipient in mind.

user19161

@JohanLarsson You are right. I use Wikipedia as a bird's eye view to see the big picture. After that, as I always say, real men read real books.

user19161

1:58 AM

@anon You misspelled "receive".

so I did

It's all in the past...

user19161

anon's avatar is very colourful: you certainly brighten up my life. =)

anyone familiar with dh parameters

user19161

@peoplepower What's in the past? Books?

2:00 AM

@JasperLoy The error. That is all.

user19161

@peoplepower Very deep comment bro.

I'm not ashamed to say I enjoyed that

user19161

Sorry, Jonas has infected me with "bro" too deeply. I need antibiotics!

user19161

@JohanLarsson Ah yes, and also the MIT OCW.

user19161

But to be honest, I think just go and read books.

user19161

2:03 AM

No amount of video lectures and online tutorials is as good as books.

user19161

So my motto is "books, books and more books".

I think that is a really good way to get that birds eye veiw

user19161

But for geniuses like Jonas, his motto is "no books, real men read papers".

I see them as complements, books are more for reference

who is jonas?

sounds like a swede

user19161

Another frequent chatter.

user19161

2:07 AM

By the way @johan has anyone told you you can see LaTeX in this chat as well?

yes

did not get it to autorender yet

user19161

Hey dear @anon, the LaTeX has become unpinned.

this was a really friendly chat by the way

we can make it unfriendly if you were interested in more rough-and-tumble

I expected a little flaming and hate for bringing noob

just follow your heart!

2:09 AM

newcomers are a constant here, they come and go regularly

You do not know how to define divergent sequences in terms of balls, gtfo.

user19161

Yes, people also are born and die every day.

and their first question is can I ask a question?

Etiquette Guidelines | $\LaTeX$ support for chat

11

user19161

@anon Talking about constants, it is interesting how many think Euler's constant refers to e when it does not. To be fair, e would be Euler's number.

2:11 AM

you speak of Euler-Mascheroni?

user19161

Yes!

I wonder if there is an adelic version

user19161

@anon I remember you mention ice cream. Is vanilla your favourite flavour?

" should not be confused with the base of the natural logarithm, e, which is sometimes called Euler's number or Euler's constant." - Wikipedia

Mmmm... Root beer float...

2:13 AM

yes, although I'll go for turtle pie over plain vanilla.

user19161

OK, let's have some ice cream one day if I make it to grad school there. =)

so be it (=

user19161

Hmm, I see that anon has gotten LaTeX right this time.

I had half a mind to put it entirely in lowercase on purpose..

user19161

Donald and Leslie would become sad pandas.

user19161

2:17 AM

Wow, LaTeX is even written in LaTeX this time, haha.

what is the La in latex?

user19161

It stands for Lamport.

user19161

Leslie's last name.

ok tex is text right?

user19161

Initially there was only TeX.

2:19 AM

I originally thought it was an abridgement of lay-tech (as in, technical document writing for the laity)

user19161

Yes I think so for text.

user19161

Then after that there was AMS-TeX.

user19161

And also LaTeX.

user19161

Now AMS-TeX got combined with LaTeX.

I could have sworn PLC had a pdf on galois connections, but I can't find it anywhere.

2:20 AM

5

Q: Get Transformation Matrix from Points

I have built a little C# application that allows visualization of perpective transformations with a matrix, in 2D XYW space. Now I would like to be able to calculate the matrix from the four corners of the transformed square. Here is a screenshot to help you understand what I am working with: ...

linear-algebra matrices algorithms transformation

user19161

Today, it has become AMS-LaTeX or simply LaTeX.

user19161

One almost always loads the amsmath etc packages when writing lotsa math.

that question is just Ax +b = y?

user19161

It is now LaTeX2e, LaTeX3 is being worked on with no definite schedule, just like my life.

user19161

@JohanLarsson Hmm I guess different people may have different conventions. But in most analysis books I have seen, Euler's constant is reserved not for e.

2:25 AM

you lost me now

user19161

Hmm, how many analysis books have I seen, I think OVER 9000!

I'm still lost

user19161

Still lost? What's the problem?

user19161

We were only talking about Euler's number and Euler's constant.

ok

user19161

2:27 AM

So one is $e$ and the other $\gamma$.

incidentally, $e^\gamma$ is arguably just as natural as $\gamma$ in analytic number theory

the wikipedia article def adds to the confusion

user19161

Well @johan in math very often one word means different things and different words mean the same thing.

when it says Euler's constant should not be confused with Euler's number or Euler's constant

user19161

Definitions are only fixed up to 90 per cent.

user19161

2:29 AM

There is some room for modification here and there, according to the preferences of the author.

but its not like poetry when originality is above all

user19161

Some call it Cauchy inequality, some Cauchy Schwarz and some Cauchy Schwarz Bunyakovski.

that sounded familiar^^

user19161

And even that inequality has several different forms.

user19161

Also, note that where there are different definitions of the same term, sometimes they are equivalent and sometimes not.

2:32 AM

is that the same as the triangle something?

user19161

Triangle inequality? Nope, they are different.

[x] swing
[x] miss

is it possible to get wikipedia rendered as latex instead of gifs for equations?

user19161

I am not sure how Wikipedia works...

user19161

But if that happens, it might become slow.

user19161

People already have problems loading math on this site.

2:37 AM

that is a bit surprising

gnight

user19161

OK.

I just devised a most elegant proof of Goldbach's conjecture, but it is too much to type in this chat.

2

Bye.

@JasperLoy Naah, $\TeX$ is for tech. Techinal documents. $\LaTeX$ I am note sure.

@Charlie Hehe. Nice.it.is. :-)

3:38 AM

stanley has a new book on algebraic combinatorics. awesomeness.

« first day (821 days earlier) ← previous day next day → last day (4203 days later) »

Transcript for

Nov '122

$Mathematics$ Mathematics

Associated with Math.SE; for both general discussion & math qu...

join this room
about this room

00:00

06:00

12:00

18:00

all times are UTC

$Mathematics$

site design / logo © 2024 Stack Exchange Inc; legal

mobile