Mathematics - 2017-12-28 (page 3 of 4)

Balarka Sen

15:00

Other than Zariski, which is extremely dumb here

Krijn

No, me neither

But surely we have to be able to make sense of points $q \in Q$ converging to $\sqrt{2} \in \bar{Q}$

I think I have found what I am looking for

In a book called "Lectures on Hilbert schemes of points"

Balarka Sen

Sounds scary

I was thinking whether you need to work with etale neighborhoods instead of actual neighborhoods to state it but I don't know that stuff

Krijn

I'll send a picture, wait

Akiva Weinberger

Good exposition of Lambert's original proof of pi's irrationality

Pi is IRRATIONAL: animation of a gorgeous proof

►

Starting from $\tan x=\frac{\sin x}{\cos x}=\frac{\sum (-1)^nx^{2n+1}/(2n+1)!}{\sum(-1)^nx^{2n}/(2n)!}$ and manipulating, you get a continued fraction for $\tan x$.

Balarka Sen

@Krijn Ah I see the idea I think

Akiva Weinberger

15:11

This is used to show that the tangent of a rational number is irrational (as infinite continued fractions tend to be irrational).

However, $\tan\frac\pi4=1$, so $\frac\pi4$ cannot be rational, and thus neither can $\pi$.

Balarka Sen

They're also taking care of the tangent directions when the points do collide

Somehow that refines the topology of the moduli space a little more

Krijn

@BalarkaSen And in my 1-dimensional case those tangent directions are clear

Balarka Sen

'Cuz it's a blowup of X x X along the diagonal now

Krijn

So yeah, I'll just refer to this :D

Balarka Sen

Cool

@Krijn Ah true

Leaky Nun

15:15

@AkivaWeinberger nice channel

Akiva Weinberger

@BalarkaSen Are planimeters just supposed to approximate the area, or do they give the exact area in theory?

Balarka Sen

They do give the exact area in theory

Akiva Weinberger

OK so I have no idea how they work

What even am I integrating

Is it like $\int-\sin\tau dx+\cos\tau dy$ or something

Balarka Sen

I think one should think about what happens on the boundary of the region when you're tracing the planimeter along it

It should be work under a force field

On which you can Green's theorem to get area

Akiva Weinberger

Something to do with the angle of the wheel or something

Balarka Sen

15:21

Right

Akiva Weinberger

It's not $\int-\sin\tau dx+\cos\tau dy$, then?

Balarka Sen

I don't remember thinking like that when I did it

Akiva Weinberger

By the way

> @Akiva Did I ever tell you how the holonomic approximation issue was fixed

No I don't think so

Balarka Sen

Ah right so there was a perturbation of the circle that was involved when doing it, which we weren't using appropriately, or at least, the book didn't specify how bad it has to be

Or, even what notion of approximation we were using

Akiva Weinberger

Remind me exactly what the issue was

It's been a while

ÍgjøgnumMeg

15:27

does the notation $\mathfrak{p}A_\mathfrak{p}$ just mean the ideal generated by $\mathfrak{p}$ in $A_\mathfrak{p}$?

Balarka Sen

@Akiva This:

Nov 6 at 18:49, by Balarka Sen

@TedShifrin This is the relevant theorem, quoting Eliashberg-Mishachev: Let $K \subset V$ be a polyhedron of codimension $\geq 1$ and $\omega$ a p-form. Then there exists an arbitrarily $C^0$-small diffeotopy $h_\tau : V \to V$ such that $\omega$ can be $C^0$-approximated near $\tilde{K} = h_1(K)$ by an exact p-form $\tilde{\omega} = d\alpha$.

$V$ here is a manifold.

The counterexample we proposed was $\omega = -ydx + xdy$ on $K = S^1$ in $V = \Bbb R^2$

The point should be that everything is a $C^0$-approximation, so if $\omega_n$ are a bunch of exact forms approximating $\omega$ uniformly, it has to hold that $\int_U \omega_n \to \int_U \omega$ where $U$ is some neighborhood of the circle

But that's total garbage because those integrals are zero, and what they tend to is something nonzero.

OK?

Akiva Weinberger

Right

Balarka Sen

So the point is it's not really "approximation" in the usual sense. First off, everything has a Riemannian metric here. $V$ is a Riemannian manifold.

That's where the $C^0$-norm on $V$ comes from.

So we take a small neighborhood $U$ of $K$ and look at $h_1(U)$. That's an embedded submanifold of $V$

The $C^0$ norm on THAT dude comes from the induced Riemannian metric on $h_1(U)$.

Akiva Weinberger

In our example $V$ is the plane and $U$ is the circle?

Balarka Sen

Right.

Akiva Weinberger

15:38

Er, neighborhood of the circle

Balarka Sen

Yeah, yeah, that

What $h_1$ is going to do is to make that circle wiggly so that it's length increases

Akiva Weinberger

Mhm

Balarka Sen

And the induced Riemannian metric (not the induced metric as in, subspace of metric space) on $h_1(U)$ is going to be very long

Because, intrisincially, to join two points on $h_1(U)$ by a path you have to wiggle a lot.

So the distance between two points increases because of the wiggles

Akiva Weinberger

You mean $h_1(K)$

$h_1(S^1)$

Balarka Sen

Nah, I'm looking at a small neighborhood of $h_1(S^1)$, right? "Approximated near"

Just taking that neighborhood to be $h_1(U)$ for some nbhd $U$ of $S^1$

Akiva Weinberger

15:41

Oh OK I guess

So $h_1(U)$ is an open set and very wiggly

Balarka Sen

So the $C^0$ norm on $h_1(U)$ is very very different from the $C^0$ norm on $V$

It's not the "subspace norm"

Akiva Weinberger

What do you mean by $C^0$ norm

Isn't norm, like, distance from the origin?

Balarka Sen

Let's make that "metric" instead of "norm".

Akiva Weinberger

Oh, wait

Balarka Sen

The $C^0$ metric on $h_1(U)$ is not the induced metric from the $C^0$ metric on $V$

Akiva Weinberger

15:43

Are you measuring the distances between continuous functions on the thing?

Balarka Sen

Yeah

Akiva Weinberger

Like the sup norm?

Balarka Sen

Right

Akiva Weinberger

Why would the sup norm depend on the topology of the thing it's on?

Balarka Sen

Sup norm is supremum over $\|f(x) - g(x)\|$. What is $\|\cdot\|$?

It's induced from a metric in this case.

Akiva Weinberger

15:45

Wait what's the domain and codomain of $f$ and $g$ there

Balarka Sen

I was just taking an example. We're defining a sup norm for forms in any case.

The point is it requires having a norm in the first place

Akiva Weinberger

OK

Balarka Sen

You have to decide what norm you want everything to have

Let's make that general: what metric you want everything to have

You could say the following:

$V$ is a Riemannian manifold. So that gives a length metric $d$ on $V$

$h_1(U)$ is a subspace of $V$. Can't you give it the induced metric from $(V, d)$?

The answer is "No". That's the wrong notion. You give $h_1(U)$ the induced Riemannian metric first. And then you extract the length metric $d'$ on $h_1(U)$ to get the metric space $(h_1(U), d')$.

Notice that "induced metric of length metric of a Riemannian metric $\neq$ length metric of induced Riemannian metric"

Does that make sense?

Leaky Nun

2

Q: Find: $\lim_{x\to -\infty} \frac{\ln (1+e^x)}{x}$ (no L'Hospital)

Find: $\displaystyle \lim_{x\to -\infty} \dfrac{\ln (1+e^x)}{x}$ (no L'Hospital) I'm getting a hard time solving this limit. The book shows 1 as the answer, Wolfram Alpha shows 0. I could solve easily another problem when the denominator was $e^x$ but got stuck on this one. No L'Hospital...

limits-without-lhopital

sigh another "without" question

Akiva Weinberger

So how do we approximate $-y\operatorname d\!x+x\operatorname d\!y$ in the end

@LeakyNun You can't use L'Hôpital there anyway

Numerator goes to $0$, denominator goes to $-\infty$

Balarka Sen

15:51

@Akiva "Approximation" here means a double limit. The claim should be something like that for every $\epsilon > 0$ there is an $N > 0$ such that for all $n > N$, $\|\omega_n - d\alpha\|_n < \epsilon$

Where the forms, as well as the norms, are changing

It's a sad mess

But yeah when your norms change you have no reason to be able to invoke integrals and shtick

Leaky Nun

@AkivaWeinberger I just hate "without" questions

Balarka Sen

So that makes the whole $\int \omega_n \to \int \omega$ argument bollocks

Leaky Nun

and maybe they meant $x \to \infty$

the next time I see "without L'hopital" I swear I will start from epsilon-delta @AkivaWeinberger

Balarka Sen

I meant $\|\omega - d\alpha_n\|_n$ there

$\omega = -ydx + xdy$

@Akiva If you want to do it explicitly, say $h_n$ is the isotopy which makes the Riemannian metric larger by a factor of $n$ on $h_n(S^1)$, in comparison to $S^1$ (So it introduces loooots of wiggles at each $n$-th stage).

Define $\alpha_n = -ydx + xdy - \omega_n$ where $\omega_n$ is a 1-form on $h_n(S^1)$ which integrates to $2\pi$. $(-ydx + xdy)$ integrates to $2\pi$ on $h_n(S^1)$ (because it's homotopic to $S^1$), so $\alpha$ integrates to $0$ on $h_n(S^1)$. That means $\alpha$ is exact near $h_n(S^1)$. But $\omega_n$ is very small in $C^0$ norm near $h_n(S^1)$ because $h_n(S^1)$ is long.

Semiclassical

I’m okay with no-L’hopital questions if they make the effort of including a L’hopital solution in their question statement

Leaky Nun

16:02

@Semiclassical lol

Balarka Sen

So $\|\alpha_n - (-ydx + xdy)\|_n \to 0$ as you change the norm along with the form

Leaky Nun

why? @Semiclassical

Balarka Sen

$\alpha_n$ are your desired approximations

Semiclassical

In that case it’s “I know how to do this one way. Are there approaches I’m missing?”

Without that due diligence it smacks of “do my HW for me, and don’t use L’hopital because they haven’t taught us that yet”

Leaky Nun

@Semiclassical but the main reason people post "no-L'hopital" questions is, in my opinion, that they are told not to use it...

@Semiclassical right

Semiclassical

16:06

It’s really a matter of demonstrating your engagement with the material I suppose

Trey

16:20

how can I find this integral $$\int\frac{e^x}{x}dx$$ ?

GFauxPas

well, maybe a substitution will work

$\dfrac {\mathrm dx}{x} = \mathrm du$

?

any ideas? ;)

Akiva Weinberger

@Trey The antiderivative is not an "elementary function"

GFauxPas

oh wait, that doesnt work

silly me

Akiva Weinberger

This means that it can't be written in terms of polynomial, logarithms, trigonometric functions, or any combination of those using addition, subtraction, multiplication, division, or exponentiation

That is, while the function "exists", it can't be written down in terms of functions you know about

GFauxPas

Trey, people have created several functions whose integrands are $\dfrac{\text{well known function}}{\text{linear term}}$ because a lot of them come up often but dont have answers in term of elementary functions

wolfram alpha says the conventional choice here is

Mike Miller

16:25

@BalarkaSen So all you need is the weak homotopy type of a CW cpx with cells in no larger dimension than the manifold. That follows from irritatingly fancy algebraic topology: mathoverflow.net/q/201944/40804

GFauxPas

$\operatorname{Ei}(x) := - \displaystyle \int_{-x}^{\to +\infty} \dfrac {e^{-t} \, \mathrm dt}{t}$

the exponential integral function

Trey

I thought it was impossible

at least according to my textbook

GFauxPas

well, impossible to write in terms of elementary functions

but by the FtoC it has an antiderivative, so we just need to choose a convention and give a name to it

Balarka Sen

@MikeMiller Ah.

Also the comment below Hatcher's answer jesus christ

GFauxPas

Trey that's actually a common way to define the logarithm

Mike Miller

16:30

yah lmao

GFauxPas

$\int \dfrac {\mathrm dx}{x}$ doesn't have a solution in terms of elementary functions, so we create one

$\log x : = \displaystyle \int_1^x \dfrac {\mathrm dt}{t}$

Trey

What are some real life applications of these tricky integrals?

Mike Miller

your shirt look like a dishrag

►

Balarka Sen

multi-lel kekking

GFauxPas

Exponential integral

In mathematics, the exponential integral Ei is a special function on the complex plane. It is defined as one particular definite integral of the ratio between an exponential function and its argument. == Definitions == For real non zero values of x, the exponential integral Ei(x) is defined as Ei ⁡ ( x ) = − ∫ − x ∞ e − t ...

I liked to the "applications" section

and it gave me this whole novel to accompany the link :(

rumtscho

16:36

Hi, I have a question about linear optimization and wonder if it is on topic here. And if it is, if it is better here or on Computer science.

Mike Miller

It's not off-topic here but maybe nobody will be able to help

Clarinetist

@rumtscho You can try here - but optimization is a fairly specialized topic

rumtscho

Basically, I have to learn the linear optimization problem in very deep detail on my own, without tutors etc., with relatively little background in maths

Mike Miller

We only know about abstract nonsense

8

Clarinetist

@MikeMiller LOL

GFauxPas

16:37

"the" linear optimization problem?

Clarinetist

By the way, random fact of the day... this book exists:

amazon.com/History-Mathematical-Notations-Dover-Mathematics/dp/…

Had no idea

rumtscho

and now I reached a section which I don't understand at all, and need the intuitive idea behind it.

@GFauxPas that's what the textbook is called, yes.

GFauxPas

I wasn't aware there was one problem that deserved to be called "the" linear optimization problem

Balarka Sen

@MikeMiller "you've come to the wrong chat fool" - Big Smoke

rumtscho

The author describes the linear optimization problem in a highly abstract way, and continues to write up all known ways for finding (or approximating) solutions for it, from the useless naive ones to the practical ones.

GFauxPas

16:39

maybe he's being poetic

rumtscho

@GFauxPas let me look up the definition for you.

aargh

Clarinetist

I wish I could help, but I'm barely getting through convex optimization

rumtscho

my head is too stuffed with nonsense right now

it is the linear ordering problem, not the linear optimization problem.

Clarinetist

@rumtscho Try the CS Theory stack exchange

rumtscho

Which the book defines as "Given the complete directed graph Dn with arc weights cij for evey pair i,j, compute a spanning acyclic tournament T in An such that the sum of the arc weights is as large as possible"

@Clarinetist Maybe I should do it indeed. I tried the CS site first, but there the people in chat also told me that it is unlikely that anybody there will know about it.

I am a bit taken aback by the idea to go to the research level site, because I need a beginner-level explanation

I already have the research level explanation in front of me and simply don't get it

Clarinetist

16:43

@rumtscho What I would do is ask a question on there, something like asking what the intuition is behind it

I don't know anything about posting on the CS Theory website

If not there, I'd try Stackoverflow

Balarka Sen

@Mike I will file a DMCA strikedown on that stolen meme

Clarinetist

@rumtscho WAIT

rumtscho

what I need is called "Maximally violated k-mod cuts", it seems there are exactly two papers in the scientific literature on this subtopic

Clarinetist

@rumtscho It looks like there's a CS SE for non-research questions

rumtscho

one about the k-mod cuts in general, the other about mod-2 cuts

Clarinetist

16:44

If you consider your topic a research topic, use the theoretical CS one

Wow, StackExchange has gotten complicated since I first created an account here

rumtscho

and then there is the book from which I am learning, in which the information from these papers is presented even more densely than in the papers themselves.

@Clarinetist It was on their chat where I heard that probably nobody there can explain this stuff.

GFauxPas

have you tried giving up

rumtscho

@GFauxPas that would come next, yes

the trouble is, I know this prof, have had an exam with him before

Clarinetist

@rumtscho I would at least try asking a question, wait a few days, issue a bounty if you need to

rumtscho

and he will make sure to ask questions even about the most obscure topics in the material

Clarinetist

16:46

For example, I probably wouldn't use chat in MSE to answer a lot of the stats/prob questions I have heh heh heh

rumtscho

I know I won't have time to learn how to prove the theorems

GFauxPas

@Clarinetist are you saying you don't trust us? D:<

how dare you

rumtscho

but I would really like to at least know what these cuts are about. And why they are different from any standard Chvatal Gomory cut (which I was only able to understand because some nice professor from the MIT has publicly uploaded a nice entry level tutorial)

GFauxPas

ah, well, Chvatal cuts are, uh,

Clarinetist

I'll use chat if I ever decide to get serious about studying algebra or topology... but until then...

GFauxPas

16:49

probably ... helpful to know?

Clarinetist

Yeah, haven't even heard of those until now

Leaky Nun

5

Q: For limits-without-lhospital, is the intent to NOT use the definition of the derivative?

The infamous limits-without-lhospital tag. A lot of these questions are of the form $$\lim_{x \to a}\dfrac{f(x)-f(a)}{x-a}$$ form, and anyone who's seen the first few chapters of a typical calculus book would know the above is the definition of the derivative of $f$ at $a$ when the limit exists,...

discussion tagging

rumtscho

@GFauxPas Actually, they aren't. "It turned out that this approach cannot be utilized in practice because after the addition of many such cutting planes severe numerical problems occur".

This is how the section on them ends in the textbook.

GFauxPas

ah, well,

i obviously could have told you that

but i didnt becasue i dont even know how to pronounce it, let alone what they are. i know about dedekind cuts, if that helps

rumtscho

OK, not exactly. It also says "On the other hand, however, it was shown that the careful use of Chvatal-Gomory cuttning planes can lead to substantial improvements in linear programming" - I will have to remember that for the next time I have a convex polyeder lying around and am wondering exactly which cutting plane can be of use.

Clarinetist

16:53

@LeakyNun What of that question?

Leaky Nun

@Clarinetist can't agree more

rumtscho

@GFauxPas Actually, they are pretty easy after you have understood them.

Leaky Nun

@Clarinetist I hate "without" questions with a passion

rumtscho

It is about integer programming. You first "forget" all the integer conditions and build up your polyeder and find the maximum solution.

And after that, you cut the polyeder at the closest integer line below the optimal solution. Kinda like peeling a potato.

Clarinetist

@LeakyNun Yeah, these questions have been particularly frustrating. I think for most of these that I've answered (note: I haven't dug through them myself), I've answered with the definition of the derivative, which is usually covered MUCH MUCH earlier than L-Hospital is for a calc course. Then I get a comment about how I'm actually using L-Hospital...

GFauxPas

17:06

I wouldn't say LHR is the same as using the definition of the derivative though

ones a definition and ones proven using the strong mean value theorem

and anyway, LHR doesn't require the derivative be continuous, which is a big deal

Adeek

17:41

@MikeMiller I was wondering if you have good reference to algebraic K-theory ?

You probably know a lot K-theory for algebraic topology ?

Mike Miller

I know topological K-theory (to the extent of Hatcher's notes) but essentially nothing about algebraic K-theory

Semiclassical

K-theory is actually used by some people in condensed matter

There’s a pretty well-known table which lists off the topological indices of various cond-mat systems. It’s indexed by dimension and the relevant physical symmetries, but the latter is somehow equivalent to both a K-theory statement and a random-matrix statement

Silent

17:59

4 hours ago, by Silent

Please someone take a look here: (In my notations) Exercise 26's hint says to go this way: $A\implies C\implies D \implies B$. Does not that mean $C\implies B$? But $C\implies B$ is not true since $\Bbb R$ is separable but not compact.

I will appreciate help!

Semiclassical

18:42

@Silent from what you wrote in the problem, the implications were ordered as (using > as implies) A>B>C>D

So that has B>C but not C>B

Not sure I agree with how you’ve transcribed the implications, though. I have:

C>D (23), A>C (24), B>D (25), A>B (26).

Not seeing how they conclude B and D implies C, though

(The therefore in 25)

Daminark

19:16

Hey @Semi!

Semiclassical

19:52

Yo

Daminark

20:09

How's everything going?

Mohammed Rizqallah

20:22

hello everyone

how are you ?

Daminark

Hey!

Mohammed Rizqallah

Hey Daminark

I'm wondering if you're good at Combination , permutation and factorial ?

Daminark

Not particularly good but I can manage a bit.

Mohammed Rizqallah

ok try it if you would like

How many ways are there to arrange 3 chocolate chip cookies and 10 raspberry cheesecake cookies into a row of 13 cookies?

Semiclassical

Suppose you pick the locations of the three chocolate cookies first. How many ways are there to pick the location of the first chocolate cookie?

Salt

20:29

$11^3$?

Semiclassical

No.

Just the first one for now.

Mohammed Rizqallah

13C3 ?

Salt

I just pictured the 10 raspberry cookies layed out in a row and you have 11 choices where to place the first chocolate cookie among them.

Semiclassical

That’s the right answer for the full thing, yeah

Mohammed Rizqallah

ok so I have a same question

Secret

20:33

hmm, I am currently so far off in most of maths to maintain my maths projects and experiments in the Mathworks room. Sure I can switch from foundations to something more popular, but currently, I al so far behind in integrals and other stuff to do experiments on them without going off the trail

Semiclassical

@Salt hmm. That doesn’t give the right counting, but I’m not sure why

Salt

yeah, dunno

GFauxPas

I'm awful at counting

Semiclassical

I was going to say there’s 13 spots for the first cookie, 12 for the second, 11 for the third

And then you divide by 3!=6 since the order shouldn’t matter

Mohammed Rizqallah

@Semiclassical Yes , That my another thinking about ,, it's mean ,, 13 , 12 ,, so on > 13!

Semiclassical

20:35

So that’s (13)(12)(11)/3! = 13!/(10! 3!) = 13C3

So both of these ways give the same answer

Salt

oh... 11 choices for the first chocolate cookie, 12 for the second, but before and immediately after the first chocolate cookie are the same...so 11 for the second, and so on for the 3 choco cookie

Semiclassical

Hmm

So that gets a bit confusing

Salt

i think yall are overcounting something, but maybe i'm wrong

Semiclassical

Eh. There will be 13 cookies in a row at the end; pick three to be chocolate without regard to order. That’s 13 choose 3

Abra

can anyone see or foresee or even farsees how the number 8 is reached by the op here

Mohammed Rizqallah

20:40

@Semiclassical Can you tell me why did you say " 13*12*11 / 3! ?
why you stopped on 11 ?

Salt

but order counts in the final, 13c3 is 22x13...so actually it's less than 11^3

Mohammed Rizqallah

@Salt What did you mean in " 22 " ?

Salt

11*12*13/6 = 22X13

Mohammed Rizqallah

I'm just asking why you say " (11*12*13)/6 "
Why you stopped on 11 ?

Abra

@MohammedRizqallah use multinomials

Salt

20:44

13!/(10!3!) is 11*12*13/6

Abra

13!/(3!*10!)

Semiclassical

Because once you’ve picked the 3 chocolate locations, all that’s left are the 10 raspberry cookies

Mohammed Rizqallah

maybe we can say " the first one has 13 options , the second one has 12 options and so on , so that remember us in factorial ,, so it will be 13! "

Semiclassical

And their order doesn’t matter. So there’s only one way to put them down

Mohammed Rizqallah

Ok guys I got it , but look where i got puzzled ,
let us to see another example has a same Idea

How many ways can 3 boys and 2 girls set in a row ?

it's the same Idea

Semiclassical

20:47

Alternatively: there are 13! ways to pick three chocolate cookies then ten raspberry cookies. But there are 3! ways to order the chocolates and 10! ways to order the raspberries, so it’s 13!/(10!*3!).

Mohammed Rizqallah

We have to say " the first one has 5 places , the second one has 4 , and so on , so we get 5!

Semiclassical

There’s few enough instances in the boy-girl case that you can write them all out, so I suggest you do that

Mohammed Rizqallah

you mean it's 10 ?

but it's not

Abra

@MohammedRizqallah as i said, consult about multinomials

Semiclassical

That’s what I have. bbbgg, bbgbg,...

Mohammed Rizqallah

20:51

but it's not 10

this topic makes me puzzled

Semiclassical

All you’ve said is “it’s not 10”.

mick

Hi all

Clarinetist

@Semiclassical Do you know if U of MN has a tutor list of some sort?

mick

2

Q: Iterations of $x^2 + y^2$

We construct a sequence $S$ of distinct positive integers as follows 1) the sequence $S$ starts as $1,2,3$ 2) If and only If $x,y$ are in the sequence and $ x^2 + y^2 > 3 $ Then $x^2 + y^2 $ is also in the sequence. 3) the sequence is strictly increasing. 4) the sequence is completely determi...

number-theory sums-of-squares

Any ideas ?

Clarinetist

If I knew number theory, I'd help. But I don't

Semiclassical

20:52

If that’s not what yiur book says, then either the book is wrong or you haven’t stated the question correctly

Abra

@MohammedRizqallah why is it not 10 ?

Semiclassical

@Clarinetist department by department, perhaps

Clarinetist

@Semiclassical Particularly for math

Semiclassical

There’s a tutor list for the physics and Astro department for instance

Clarinetist

i.e., grad-level math

Mohammed Rizqallah

20:54

@Semiclassical it's not book , it's the doctor said that
he said " 5! " because " What I have been said "

Semiclassical

The math department may hav one of their own. I’d suggest emailing one of the department secretaries

Clarinetist

@Semiclassical K, thanks. I'll try them... I'd just like to avoid resorting to universitytutor.com because it seems... sketchy

Mohammed Rizqallah

@Abra @Semiclassical I tried to present it manually I got more than 10 cases

Abra

4+3+2+1=10

Semiclassical

@MohammedRizqallah then they either meant a different question than what you asked or they were wrong

Abra

20:55

where is the extra case ?

Semiclassical

And 5C2 = 10.

Mohammed Rizqallah

I stopped on 15 cases

Semiclassical

the only way to get more than ten is if the order in which the boys are placed matters. But the question as you wrote it doesn’t indicate that

Mohammed Rizqallah

No semi this is real question

do you mean this question in this case consider the ordering matter ?

mick

Who knows the graham-Pollock sequence ?

Graham-pollak sorry

Semiclassical

20:59

Consider the two arrangements: b1 b2 g1 g2 g3 and b2 b1 g1 g2 g3

Are these counted as different arrangements?

Blah. That’s three girls and two boys, but the idea is the same

Salt

i see why i overcounted

Clarinetist

Semi-serious question

Has anyone here ever read this book?

Mohammed Rizqallah

I consider this different " no matter about 3 b or g I got it

Clarinetist

amazon.com/History-Mathematical-Notations-Dover-Mathematics/dp/…

Salt

but anyway, you can just list the boys/girls question as a question about binary numbers...it's easy to list them in ascending order

Abra

21:02

@mick focusing more on discrete maths lately ?

GFauxPas

why does Amazon's "look inside" option on book previews show you the table of contents and publication information

i guess to see wahts in the book

but id have skipped to, like, the middle

Semiclassical

Okay. But all the problem says is to arrange 3 boys and 2 girls. So by my reading of the question both of these arrangements correspond to bbggg and are not distinct

Clarinetist

@GFauxPas I believe it's available online on the archive

GFauxPas

ah

user76284

Is there a notion of an 'affine' approximation of a computer program? i.e. You approximate a loop as occurring either 0, 1, or infinite times (non-termination).

Clarinetist

21:03

@GFauxPas archive.org/details/b29980343_0002

Salt

00011, 00101, 00110, 01001, 01010, 01100, 10001, 10010, 10100, 11000....which of course is 5c2 = 10

Semiclassical

Main reason is this: The number of ways to arrange 5 children named Alice, Bob, Charlie, Danielle, Eugene in a row is 5!

Mohammed Rizqallah

@Semiclassical you mean that " if the ordering matter like " g1 g2 b1 b2 b3 " and " g2 g1 b1 b2 b3 " is different . we have to say theses ways are 5!

Semiclassical

So 5! is what you get if all the children are distinguishable

Sure. Just take Alice to be g1, Bob to be b1, Charlie to be b2, Danielle to be g2, and Eugene to be b3.

Mohammed Rizqallah

but if the ordering doesn't matter , we have to say " 13*12*11 / 3! ? right ?

I got it

Semiclassical

21:08

Right. If you didn’t know their names but only the genders, there’s no difference between having Bob ahead of Charlie vs Charlie ahead of Bob

Mohammed Rizqallah

but the question didn't determine with ordering or not , in this case what I should understand the question ?

yes Got it

Semiclassical

This is where things get annoying.

In counting questions, it often comes down to assumptions

Mohammed Rizqallah

I got it , I'm really appreciate it @Semiclassical

you got tired of my asking ,, Really Thanks alot and sorry

Semiclassical

And it’s easy to write a question in a way that it’s not obvious what is being assumed

If it’s not clear what assumptions you’re making, I suggest asking for clarification

Mohammed Rizqallah

@Semiclassical Yes you're right , I'll

Abra

21:11

@mick why did you link to a district in germany in your solution-attempt ?

Mohammed Rizqallah

@Semiclassical @Abra Thanks alot :) I appreciate it

Semiclassical

Np

Mohammed Rizqallah

Do you always be here ? in this room ?

Abra

@MohammedRizqallah the answer can be 12*4 only if the question is worded differently

as is, the answer=10

Mohammed Rizqallah

Aha , Got it

Abra

21:16

restrictlessly of any conditions, it is 5! (boys girls don't matter)

Mohammed Rizqallah

@Semiclassical @Abra Guys it's really nice to meet you , honestly I like to get you as new friends if you don't mind,
So Can I get your profile on another websites to keep on touch ?

Semiclassical

This is pretty much the only site I have an active profile on, so no

Abra

you can find me here time to time, but just for elementary maths and CS related questions

Mohammed Rizqallah

Yes for that just ,
however , thanks alot

Secret

21:34

in The h Bar, 21 mins ago, by bolbteppa

flirting with pseudoscience I'd say

I don't like people who only point what is wrong with you and not telling what is right

These people will only give links to the correct material, point out that you are wrong, but afterwards, completely ignore you when you ask them after reading the link and whether you understood correctly

It does make me wonder whether they love to point out others wrong and we have to exploit this habit of them by deliberately rephrase the latter question so as to force that behaviour to be triggered

The problem is that such is impractical as for every deliberate misinformed question that is ask, it cost you reputation and hence future probability of your question being responded

Why does these people always get away from the mess they cause

They are just like hitler, a karma houdini

How is this relevant to the math chat? Well, there are at least 3 users belong to this category

(O f***, too early to quote the h bar and now that is a misquote!)

My point about the math chat still holds though

mick

3

Q: Iterations of $x^2 + y^2$

We construct a sequence $S$ of distinct positive integers as follows 1) the sequence $S$ starts as $1,2,3$ 2) If and only If $x,y$ are in the sequence and $ x^2 + y^2 > 3 $ Then $x^2 + y^2 $ is also in the sequence. 3) the sequence is strictly increasing. 4) the sequence is completely determi...

number-theory sums-of-squares

Is that question suitable for mathoverflow ?

Secret

I felt it might help to think of this problem geometrically: The required sequence will be 1,2,3 and all points of the integer lattice that intersect circles of positive integer radii (since the square of any integers is an integer)

I have no idea how relative density is defined. A linearly ordered set is dense if for every x,y there exists a x such that x< z<y

The integers are not dense in the usual definition of dense set, let alone a subset of them

mick

21:49

I do not understand Abra ('s joke ? )

Salt

He's using a different definition of dense.

But I would follow Dan Robertson's comment on a (possibly) better way to state the question.

Abra

@mick nvm it's rather a bug in main site's design

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$Mathematics$ Mathematics