Mathematics - 2012-08-23 (page 1 of 4)

user19161

00:04

@peoplepower He might be in all 4 categories...

peoplepower

So we cannot assume that he and she are distinct in the following sentences: "He went to the store. She went shopping."

robjohn

@peoplepower Is that not acceptable?

peoplepower

@robjohn I was not making an opinion, I was merely realizing something.

robjohn

@peoplepower The name is generally a male's name, if Henry is actually Henrietta, or a female using a male's name, they would have to expect some mistaken assumptions.

@peoplepower unless there was a quick change between those statements, I would make the assumption that we were talking about two separate people.

peoplepower

00:22

@robjohn Because the context does not give any reason to deny our assumption that he and she should be distinct?

Anyway, I'll give you the final word. This does not mix very well with free groups as I see the two subjects. :)

BenjaLim

@HenryT.Horton Hey

robjohn

@peoplepower in general, each person is designated "he" or "she". Am I just out of the norm today in thinking that? I realize that there may be exceptions to the gender specification, but even then, I think they consider themselves a "he" or a "she".

@peoplepower I guess it all depends on the definitions. I was simply going on what I see as the social context. Other contexts may have different definitions.

skullpatrol

or in transition, no?

robjohn

@skullpatrol that would be the exceptions, but they usually consider themselves as "he" or "she", even in transition.

Henry T. Horton

Just refer to me as an "it"

BenjaLim

00:28

@HenryT.Horton Can I ask you something

Henry T. Horton

Hi Benny boy @BenjaLim

robjohn

@HenryT.Horton or "er"?

BenjaLim

In Hatcher proposition 1.36

He says that for any subgroup $H$ of $\pi_1(X,x_0)$

there is a covering space $p : X_H \to X$ such that $p_\ast(\pi_1(X_H)) = \pi_1(H)$ @HenryT.Horton

@HenryT.Horton Now I think that this $X_H$ is exactly the same thing as $\tilde{X}/H$

where $\tilde{X}$ is the universal cover of $X$

@HenryT.Horton is this correct?

@HenryT.Horton Now I don't have it all clear in my head yet but if you look at how $X_H$ was obtained

@HenryT.Horton the second condition was that we identified $[\gamma]$ and $[\gamma']$ in the universal cover by saying that $[\gamma\overline{\gamma'}] \in H$

@HenryT.Horton Isn't the second condition exactly saying that $\gamma$ is in the orbit of $\gamma'H$??

So should it not be the case that $X_H$ is exactly the orbits of points in $\tilde{X}$ under $H$??? @HenryT.Horton

robjohn

@skullpatrol: was that a capuchin as your previous avatar?

skullpatrol

@robjohn Yes :-D

robjohn

00:33

@skullpatrol Oops, it just got replaced by the Hulk

skullpatrol

@robjohn People were kicking sand in my poor capuchin's face...

robjohn

@skullpatrol that's not very nice. They're supposed to shock the monkey.

Henry T. Horton

Does Hatcher use $\overline{\gamma}$ for the same path with reversed orientation?

skullpatrol

@robjohn To teach it learned helplessness?

Henry T. Horton

If so, then $[\gamma] \in H[\gamma']$

robjohn

00:38

@skullpatrol no, to cater to the musical lyrics :-)

BenjaLim

yes

Henry T. Horton

oops

BenjaLim

@HenryT.Horton yes the overline is the reverse path

skullpatrol

@robjohn Wow, he looked young in 1982 ;-)

robjohn

@skullpatrol Well. it was 30 years ago (and I was in grad school)

Peter Tamaroff

00:40

Mariano posted on Facebook that William Thurston died. He was a teacher at Cornell Univ., and MO user. =/

BenjaLim

@HenryT.Horton The group of deck transformations of the universal cover only acts transitively on the fibers of the basepoint of $X$ yes?

@HenryT.Horton These deck transformations and universal covers are confusing as fuck

robjohn

@BenjaLim fog, perhaps? :-)

fog is confusing. the other is not

skullpatrol

In fact the other is quite explicit...

Peter Tamaroff

@BenjaLim Face the heat!

Henry T. Horton

If the deck transformations act transitively on one fiber, they act transitively on all fibers

This is the definition of normal/regular/Galois cover

skullpatrol

00:46

May I also suggest that you don't need to "ping" every sentence within the same message?

robjohn

@skullpatrol Why

@skullpatrol not?

Henry T. Horton

@robjohn I'm reporting this abuse of yours to the owner of this room as well as some moderators.

robjohn

@HenryT.Horton :-)

BenjaLim

@HenryT.Horton what do you mean on all fibers?

robjohn

Wow, I'm the only mod here. I wonder where the others that sleep in here are.

user19161

00:50

Guys, all of you are trolls!

skullpatrol

@robjohn Be
@robjohn cause

Henry T. Horton

@JasperLoy Funny how you're the only one who looks like a troll.

BenjaLim

@HenryT.Horton I mean

you have a basepoint $x_0$ of $X$

the deck transformations of the universal cover act transitively on the set $p^{-1}(x_0)$?

Henry T. Horton

Yes son

See Prop 1.39

skullpatrol

@JasperLoy Don't
@JasperLoy call
@JasperLoy me
@JasperLoy a
@JasperLoy troll

:-D

BenjaLim

00:54

@HenryT.Horton Ok I was just clarifying. However this does not mean that the group of deck transformations of the universal cover acts transitively on all of the universal cover yes?

Henry T. Horton

The universal cover is always a normal cover

No?

A deck transformation preserves fibers

So you can't go from one fiber to another via a deck transformation

So it is transitive in each fiber, but not on all of $\tilde{X}$

BenjaLim

Ahh!!!!!!!!!

I think I get it!!!!!

Henry T. Horton

Me too

user19161

We need moral fiber.

BenjaLim

@HenryT.Horton Can you look at example 1.48

Henry T. Horton

00:56

I'm taking my first algebraic topology course this semester

BenjaLim

@HenryT.Horton I get that $ab$ acts on the universal cover by translation by two units

that is clear to me

@HenryT.Horton Now I understand from the above that if I wanted to construct a covering space corresponding to $\langle (ab)^2 \rangle$

This would be the orbit space $\tilde{X}/ \langle (ab)^2\rangle$ yes?

@HenryT.Horton

where $\tilde{X}$ is the universal cover

@HenryT.Horton shown in the example 1.48

Henry T. Horton

Didn't you post something about this on main

BenjaLim

yeah something like that yes

but now I'm trying to understand the orbit spaces

skullpatrol

@JasperLoy Some day you will.

user19161

@skullpatrol Yes, there can be miracles when you believe.

BenjaLim

01:00

@HenryT.Horton For example to construct a covering space of $\Bbb{R}P^2 \vee \Bbb{R}P^2$ corresponding to the subgroup $\langle (ab)^2 \rangle$

@HenryT.Horton I would need to look at the orbit space $\tilde{X}/\langle (ab)^2 \rangle $yes?

@HenryT.Horton Also correct me if i'm wrong, but if $\tilde{X}$ is the universal cover, then $G(\tilde{X})$ cannot act transitively on $\tilde{X}$ otherwise this would contradict the fact that the action is a properly discontinuous action yes?

For example if we are working in a metric space

choose $x$ and choose some ball small enough about it

let $x'$ be another point super duper close to $x$

Henry T. Horton

@BenjaLim Yes

Gustavo Bandeira

I'm reading an introduction to functions, he describes trigonometrical functions, rational functions, exponential functions, etc. So... $f(x)=\frac{log_2(\sin(x))^2}{179}$ is a Ratrigologational function?

skullpatrol

@JasperLoy So, if you don't believe there can be no miracles?

Henry T. Horton

@BenjaLim It cannot be transitive on $\tilde{X}$ because deck transformations preserve fibers

BenjaLim

ok.......... @HenryT.Horton

user19161

01:05

@skullpatrol Then that's not called a miracle, that's called "you're lucky" in my context.

Henry T. Horton

@JasperLoy You're lucky I haven't smashed your face in yet.

skullpatrol

LOL

BenjaLim

@HenryT.Horton Really

this covering spaces shit is confusing as hell

Henry T. Horton

I wish I had a space to cover.

user19161

@BenjaLim Just smash the shit in the professor's face.

user19161

01:07

@HenryT.Horton You can cover me if you want.

BenjaLim

@HenryT.Horton I am really stupid. The orbits are disjoint of course.

@HenryT.Horton One thing I find hard about AT is.

On the one hand there's the pretty pictures

on the other a ton of technical shit

the difficulty is in making the bridge between the two

skullpatrol

@HenryT.Horton Leave my friend Jasper alone, because to get to him, you are going to have to go through me pal.

Gustavo Bandeira

@skullpatrol Henry with Black T-Shirt, Jasper arguing with him, Skullpatrol with white T-shirt comes later

Henry T. Horton

Jasper and I have a long history that has nothing to do with you, you gym rat!

Gustavo Bandeira

@HenryT.Horton Gym monkey would be more adequate, isn't it?

user19161

01:13

That day I said we should all shower together. Today I will say, let's all get into bed together!

2

Henry T. Horton

I don't have a bed. Hope you enjoy the concrete floor.

Gustavo Bandeira

@JasperLoy !!!

wrong link.

@JasperLoy Right one

skullpatrol

01:31

now, now gentlemen let's not get too emotional

Bryan Dunsmore

Hola mis amigos.

skullpatrol

hi

Bryan Dunsmore

How's it going in here?

Peter Tamaroff

@BryanDunsmore Un hispanohablante!

Bryan Dunsmore

Woah buddy. I'm not that good. =P

Peter Tamaroff

01:40

@BryanDunsmore Its just a fancy word. You can google it.,

Bryan Dunsmore

Apparently that translates to a Spanish speaker. So what about one? =P

Peter Tamaroff

@BryanDunsmore Strictly, it means a person who has spanish as his mothertongue, but what evs.

@BryanDunsmore What do you mean by "So what about one?"

Bryan Dunsmore

@PeterTamaroff It roughly translates to "A Spanish speaker." So I'm asking what about a Spanish speaker?

Peter Tamaroff

@BryanDunsmore I don't get what you're asking,

Bryan Dunsmore

@PeterTamaroff Forget it. =P

Peter Tamaroff

01:45

@BryanDunsmore Rephrase!

Bryan Dunsmore

@PeterTamaroff It forget?

Peter Tamaroff

@BryanDunsmore Come un!

Bryan Dunsmore

@PeterTamaroff Come a?

J. M.

@HenryT.Horton So, Horton spaces are Africa?

Peter Tamaroff

@BryanDunsmore What does it mean "What about a spanish speaker?"

robjohn

01:48

@J.M. hey there! I go dormant for a few minutes and the cat drags in some mods!

Bryan Dunsmore

@PeterTamaroff It basically means, 'Why are you saying, "A Spanish speaker."'

Peter Tamaroff

@BryanDunsmore No idea.

robjohn

@BryanDunsmore I have some Harman-Kardon speakers, but they are quite local.

Peter Tamaroff

Except in serious contexts, I don't think things out before I speak.

Bryan Dunsmore

@robjohn Harmon-Kardon speakers?

Peter Tamaroff

01:49

"Manufacturer of a wide range of home and car audio and video products?"

J. M.

@robjohn Oh, hey rob. :)

Bryan Dunsmore

So off-topic, but I have an essay on anything I want due August 31. What should I do?

robjohn

@BryanDunsmore Harman-Kardon is a local company that makes very good sound equipment

J. M.

@BryanDunsmore In a pinch, I'd stare out the window and write about whatever I'm seeing outside...

Bryan Dunsmore

@J.M. I'm not really in a pinch so I was thinking something in maths/cs.

Peter Tamaroff

01:51

@BryanDunsmore You should totally write about....

robjohn

@BryanDunsmore what class is this for?

Bryan Dunsmore

Ooh! Suspense!

@robjohn English. We have monthly essays. =/

skullpatrol

Even in August?

Bryan Dunsmore

Yep... I have like two or three essays due that day. =(

skullpatrol

(summer vacation)

Bryan Dunsmore

01:53

We are a farming state so school starts mid August.

J. M.

"A good short story should have religion, royalty, mystery, and sex. Thus, here is a minimal example: "'My God', said the Queen, 'how on Earth did I get pregnant?'""

6

Peter Tamaroff

@BryanDunsmore Tell me a number between 18 and 516

Bryan Dunsmore

@PeterTamaroff 345

Peter Tamaroff

1922: Geodesic Dome

Walther Bauersfeld Richard Buckminster "Bucky" Fuller

Bryan Dunsmore

Ah yes. Something I am deeply knowledgeable about. =P

Peter Tamaroff

01:55

@BryanDunsmore You still have 497 options.

Shoot.

Bryan Dunsmore

Haha. Can I have a list? =P

J. M.

Peter Tamaroff

@BryanDunsmore I'm looking around Pickover's "Mathbook".

Bryan Dunsmore

@PeterTamaroff Maybe I should just do something about CS...

Peter Tamaroff

Thue Morse Sequence?

Bryan Dunsmore

01:57

I'm still not that well "versed" in the advanced Mathematics. Studying Abstract Algebra...

Peter Tamaroff

That one is totally CS

Bryan Dunsmore

Ah yes... Now how do I turn that into an essay? =P

Peter Tamaroff

@BryanDunsmore Well, that is your thing to do!

J. M.

...or you can try describing how a lot of practical problems are NP-complete...

Peter Tamaroff

Icosian Game?

Bryan Dunsmore

01:59

I'm truly up for anything as long as I can write a thesis statement. =P

@J.M. Never bothered to learn NP-complete actually...

skullpatrol

@BryanDunsmore how about "what I did on summer vacation"?

2

Bryan Dunsmore

@skullpatrol I did nothing. =(

How about this? pdos.csail.mit.edu/scigen

skullpatrol

@BryanDunsmore write about how that helps you develop

J. M.

@BryanDunsmore That's if you're in an even worse pinch... :)

Bryan Dunsmore

Idk. I'll try to come up with something in math tomorrow. Not like we do anything in there anyways. =/

J. M.

02:08

That boring, eh?

Education can be a drag sometimes...

Bryan Dunsmore

Ya. I'm in Hon Algebra II and we are reviewing Algebra I. And people are having trouble with it. >-<

I understand that not everyone is at the same level but god-dammit this is an honors class!

J. M.

@BryanDunsmore Clearly, the filters in place have big holes in them...

Bryan Dunsmore

Ah yes. All honors classes in my school is a joke. It's not even actual thinking, it's just more homework.

J. M.

@BryanDunsmore Then, why bother? Is this for the bragging rights to be in AP?

skullpatrol

@BryanDunsmore What would you call "actual thinking"?

Bryan Dunsmore

02:12

Idk. Some classes are actually good. Like Physical Science. We actually do labs every day and write conclusions on them daily, etc.

@skullpatrol Discussion. Problem solving. Not regurgitating what the teacher says. =/

J. M.

@BryanDunsmore I must say, though... kids like you are few and far between.

skullpatrol

@BryanDunsmore What Algebra textbook are you using?

Bryan Dunsmore

Eh. The only classes I look to attending are Science and NJROTC.

@skullpatrol skjervold.files.wordpress.com/2010/07/algebra_2_textbook_2.jpg

skullpatrol

@BryanDunsmore You may find this book challenging for your level.

Bryan Dunsmore

@skullpatrol I actually got A First Course in Abstract Algebra by Fraleigh.

So right now I'm trying to read it on my off-time.

skullpatrol

02:22

@BryanDunsmore Normally, in high school after Algebra comes Geometry and then an introduction to Analysis.

Bryan Dunsmore

@skullpatrol In the US we go Algebra I => Geometry => Algebra II.

I really like Algebra so I figured I would study Abstract Algebra. I actually discussed this with Anon and someone else (Sorry.)

skullpatrol

Why are you sorry?

Bryan Dunsmore

I'm saying sorry that I don't remember the other person. =P

skullpatrol

Oh.

So you have done Geometry and are moving on to Algebra II?

Bryan Dunsmore

Yep. I'm in Algebra II right now.

leo

02:27

hello there

skullpatrol

@BryanDunsmore So, if you want to read ahead, I would suggest an introductory Analysis textbook, since that is the next course, no?

Bryan Dunsmore

@skullpatrol After Algebra II is pre-calculus.

skullpatrol

Pre-calculus = Introduction to Analysis

Bryan Dunsmore

Haha. Names confuse me.

2

Q: $1867k =\ldots 1992$, $k\in\mathbb{Z}^+$. Find the minimum value of k.

The number $1867$ is multiplied by a positive integer $k$. The last four digits of the product are $1992$. Determine the minimum value of $k$. $1867k =\ldots 1992$

algebra-precalculus

Yeah! I actually understand this from reading my Abstract Algebra book! =D

Well I have to go. School in the morning. =(

skullpatrol

02:50

@leo hi

Jayesh Badwaik

wow, this is one inspired post.

skullpatrol

05:20

hi @robjohn

skullpatrol

05:38

Mighty quiet in here...

user19161

@skullpatrol Boo!

skullpatrol

@JasperLoy AAAHHH!!!

user19161

@skullpatrol Is it Halloween? I see your new avatar!

skullpatrol

It can be, if you want :-)

user19161

I just got some spam asking me to order "vigara". :-)

user19161

05:47

Should I reply and tell them the correct spelling?

skullpatrol

no

user19161

Maybe they will send me some free "vigara" since it is my birthday.

skullpatrol

hi @MarianoSuárez-Alvarez

@JasperLoy is that how you want to spend your birthday?

@MarianoSuárez-Alvarez I'm sorry to hear about your fellow mathematician passing away.

user19161

06:44

@skullpatrol You not sleeping yet?

skullpatrol

not yet

@JasperLoy Did you write your spelling correction?

Gigili

@BenjaLim: Thank you for your help. I will send you emails whenever I face a problem like that. You're extremely helpful.

Jayesh Badwaik

07:15

@JasperLoy Happy birthday dude.

user19161

07:32

@skullpatrol Nope!

user19161

I gave Chrome another try but it really does not work well with chat or mathjax, so goodbye forever Chrome. I will stick to Firefox for life.

user19161

@JayeshBadwaik So any spam after you put your email addy there?

skullpatrol

08:01

R.I.P.

robjohn

08:22

@skullpatrol Thurston died?

N3buchadnezzar

Hey

robjohn

@skullpatrol I see, on Tuesday :-(

There were a lot of Thurston students when I was in grad school. They was doing a lot of knot theory at the time, so I assume that was what he was doing.

N3buchadnezzar

08:37

Could someone look at this?

Old John

@N3buchadnezzar I was just reading that as we speak :)

N3buchadnezzar

@OldJohn Thanks!

I sometimes feel so stupid for not being able to understand anything =(

Old John

The question is just asking for the largest set you can take and still keep the function injective and surjective

N3buchadnezzar

@OldJohn So I would write the answer as $A \subset x\leq0 \vee x\geq0$ ?

Old John

so, for the first one, you can take the whole of $\mathbb{R}$ as the domain

N3buchadnezzar

08:39

I am just trying to learn the "proper" pesky notation here =)

Old John

@N3buchadnezzar I think you can just write the domain as $A = \mathbb{R}$

N3buchadnezzar

I did not think $x^3$ was bijective on $\mathbb{R}$..

Ilya

@robjohn: hi! how are you?

N3buchadnezzar

Injective yes, but surjective?

Ilya

haven't seen you for a while

Old John

08:41

@N3buchadnezzar yep - it is both

robjohn

@Ilya Hey there! Pretty good. Had to proctor an exam today.

Old John

it is surjective since every real number has a cube root

Ilya

@robjohn which is using your software?

N3buchadnezzar

@OldJohn And for the next one $A = [-\pi n,\, \pi n] \ n \in \mathbb{N}$ ?

Old John

@N3buchadnezzar no - that would be too big

robjohn

08:43

@Ilya yes. It's nice to see it in action.

N3buchadnezzar

@OldJohn Oh right, since arcsin is only defined on [-\pi/2,\pi/2]

Old John

you could take $A = [-\pi/2,\pi/2]$ as one possible choice of $A$]

skullpatrol

@robjohn Is the exam given on the computer?

Ilya

@robjohn good luck!

Old John

OR you could take $A = [\pi/2,3\pi/2]$ or ....

robjohn

08:45

@skullpatrol It is.

@Ilya Oops, it is tomorrow :-) The exam was yesterday.

Ilya

@robjohn :)

N3buchadnezzar

If $A = \mathbb{R}$ what would $f(A)$ be then?

Old John

@N3buchadnezzar for which function?

N3buchadnezzar

x^3

robjohn

@N3buchadnezzar $\mathbb{R}$

Old John

08:47

in that case, $f(\mathbb{R})$ would be $\mathbb{R}$

skullpatrol

@robjohn Are students allowed to use pencil and paper?

robjohn

@skullpatrol Yes. Usually the exams are open book.

N3buchadnezzar

And $f^{-1}(A) = \mathbb{R}$ too, if I understood that correctly.

robjohn

@skullpatrol but the answers need to be entered on the computer, if that was what you were asking..

N3buchadnezzar

Or is the cube root only defined for positive values..

Old John

08:49

cube root is defined for all $x$

skullpatrol

@robjohn Yes, that was what I was asking :-)

robjohn

@N3buchadnezzar since $(-x)^3=-x^3$ it is defined for all values

Old John

so $f^{-1}(\mathbb{R}) = \mathbb{R}$

Time I went - got to do some shopping for my wife's birthday ...

Jayesh Badwaik

@JasperLoy No. I am thinking either crawlbots are really dumb, or stackexchange is really good or my email address is exceptionally worthless or gmail spam filter is too good.

Ilya

@robjohn: may I ask you a question w.r.t. proper written English? I have to show $B$ for which $A$ is sufficient. I write "If we show $A$ then $B$ holds because of the fact C which says that $A\rightarrow B$."

shall it be "$B$ holds" or shall it be "$B$ will hold"?

Jayesh Badwaik

09:02

I am not an expert myself but I think B will hold is more correct.

B holds when A holds
If we show A, then B will hold.
If A holds then B holds.

N3buchadnezzar

@robjohn Any tips on the matrix =)

robjohn

@Ilya "will hold" definitely

@N3buchadnezzar which matrix?

N3buchadnezzar

This one math.stackexchange.com/questions/185775/… =) I think that the only solution is $x=0$, but yeah..

Jayesh Badwaik

@N3buchadnezzar The thing is you have been given a function. Now you only have to specify the largest domain in which the funciton is bijective.
So for example, for (a) the answer would be R

and so on.

I hope you did not see the (b) else I might have just spoiled it for you.

N3buchadnezzar

Yeah! From the awesome people in chat I was able to solve the first ones.

Jayesh Badwaik

09:15

and others?

N3buchadnezzar

Now I am stuck on the matrix one. I think that $A=\mathbb{R}$ since the right hand side and the left hand side are alike.

Jayesh Badwaik

c or d?

N3buchadnezzar

@JayeshBadwaik c

it should be $$\begin{bmatrix}
1 & 0 \\
1 & 2
\end{bmatrix}$$

Jayesh Badwaik

You missed a row notation there i think in the main question

Yup

Think of it like this: Suppose the function is not bijection.
Then For distinct $(x_{1},y_{1})$ , $x_{2},y_{2}$ the value of function should be the same. See if that is possible.
I probably advise a lot ot contradiction methods, is this okay @robjohn?

Ilya

@robjohn: thanks!

robjohn

09:22

@Ilya no sweat :-)

Ilya

@robjohn rexona for men?

robjohn

@Ilya rexona?

Ilya

deodorant

against sweating

anti-transpirant

rexona.nl/?gclid=CI_w2tW2_bECFeEntAodfAUAow

ah, "aka Degree in US"

robjohn

@N3buchadnezzar $A$ would seem to be all of $\mathbb{R}^2$.

N3buchadnezzar

@robjohn Since the two sides are alike right?

robjohn

09:26

@N3buchadnezzar since the matrix can be inverted, you can solve for any value on the right

skullpatrol

09:48

hi @ZhenLin

Transcript for

$Mathematics$ Mathematics