Mathematics - 2013-12-27 (page 1 of 5)

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12:02 AM

@badass I guess Chris's sis went to bed...

@robjohn Perhaps.

@badass A good chunk of time went into looking for my answer that finished the last line of the proof

@robjohn That answer is a beauty too.

@badass I don't know why the link didn't hyperlink the text in the brackets

@robjohn It does that to me to if there are too many spaces around.

12:08 AM

@badass well, at least you can click on the URL

@robjohn yep, no biggie :-)

@robjohn Did you see "Twink's equation" for X-mas?

I think it's worth pinning on the star panel.

(where it is now, near the bottom)

$\displaystyle y=\frac{\log\left(\frac{x}{m}-sa\right)}{r^2}$

Yep

OK maybe its not his original work.

@badass I don't see it on the sidebar at all

@robjohn " Did you see Twink's equation? - 12h ago by badass"

12:18 AM

@badass Oh, I see that.

7th star

from the top

@badass Not any more :-)

:-O

@robjohn It's gone to fourth.

12:32 AM

$$
\begin{array}{ccc}
y=\frac{\ln\left(\frac xm-sa\right)}{r^2}\\
yr^2=\ln\left(\frac xm-sa\right)\\
e^{yr^2}=\frac xm-sa&;&e^{yr^2}+sa=\frac xm\\
m\left(e^{yr^2}+sa\right)=x&;&me^{yr^2}+msa=x\\
me^{yr^2}=x-msa\\
\bbox[5px,border:2px solid red]{\Large me^{rry}=x-mas}
\end{array}
$$

3

Is it just more or does TeX not display in chat?

@PaulElfish have you installed ChatJax?

Nope.

(Not to my knowledge)

Will give it a shot.

@PaulElfish I think we have not had an insurmountable problem getting it running on anyone's machine

@robjohn That is great to know! Thank you for the link.

12:37 AM

@badass Have a conditionally Merry Christmas?

There should be no restriction on X-mas :D

(-:

If $m \neq 0$, $r \neq 0$, and $(\frac{x}{m} - sa)>0$

Then

40 mins ago, by robjohn

$$
\begin{array}{ccc}
y=\frac{\ln\left(\frac xm-sa\right)}{r^2}\\
yr^2=\ln\left(\frac xm-sa\right)\\
e^{yr^2}=\frac xm-sa&;&e^{yr^2}+sa=\frac xm\\
m\left(e^{yr^2}+sa\right)=x&;&me^{yr^2}+msa=x\\
me^{yr^2}=x-msa\\
\bbox[5px,border:2px solid red]{\Large me^{rry}=x-mas}
\end{array}
$$

Also, the log is to the base $e$.

1:09 AM

@badass In pure math, $\log$ is generally assumed to be the base-$e$ logarithm

@badass I am not so sure about applied math

@robjohn Chemistry uses the base 10 log for the measurement of pH.

@badass That is how pH is defined, yes

lol

@badass happier?

:D

@robjohn why write 3 letters, when you can write 2?

we could get away with 1 letter but I think we would need a subscript

$L_e$

$L_{10}$

1:36 AM

hey guys how would i show that if set K is not compact it contains a monotone sequence that does not converge in K

@robjohn: Where did you steal that from?

Leslie Faulkner

Can I ask questions here?

@Leslie: Of course you "can" !

@Nick You mean the thing I MathJax-ed from Twink's equation?

Leslie Faulkner

So why is not possible to ask more questions on the front end website?

I am reading Dummit and Foote

and have ton of questions to ask

but the website restrict me in asking questions

If I answer, am I eligible to ask more questions?

Is there a limitation on questions I can ask here?

Can't the general linear group be extended to a field with the operations $(+, \times)$, i.e., the set of $N \times N$ matrices over a field with two binary operations and distributive law? I tried searching for the term general linear field, but was unable to find it online. All I was able to find was general linear group over a field. Is the general linear field not a useful concept?

I tried to ask on the front end website but the website does not allow me. So I am asking here.

1:46 AM

@robjohn: Is it seriously Twink's equation?

felices fiestas!

@LeslieFaulkner You might find some answers about limiting rates of actions on Stackexchange here

@Nick I have no idea. That is just how it is listed in the star-sidebar

@Leslie: It's a non-commutative ring, but not a field when $n>1$.

user image

@Nick where is that from?

1:49 AM

@robjohn: There's too much copypasta in the world

@nick: No, it's been showing up all over the place the last few days.

Actually that's me lol

XD

@Nick Did you copy that from somewhere else?

@rob: No, twinks equation, the moment he posted it

11 mins ago, by Nick

@robjohn: Where did you steal that from?

1:51 AM

@badass: Yeah, I'm expect myself in others

XD but I sure hope none of you take anything I say seriously.

Leslie Faulkner

Oh Ok. I forgot commutativity. Either way, why is it just studied as General linear group and not a general linear ring?

@leo felices fiestas!

@badass :-)

@leo :-)

The matrix ring is definitely studied. Groups get a bit more attention because of geometry and representation theory.

@nick: Don't turn yourself into a sham here.

Leslie Faulkner

1:54 AM

Is there a name for it like general linear group? or is it just called the matrix ring?

@leo @badass is an insult but @badass @leo sounds like a pro wrestler

Leslie Faulkner

Ok I found this. en.wikipedia.org/wiki/Matrix_ring

No slick name, @Leslie.

Leslie Faulkner

thanks to everyone

@Nick ha ha

1:55 AM

So if I wanted to show that there exists a monotone sequence in set noncompact set K that does not converge in K I know that if $x_n$ is a sequence in K then there exists a monotone sub sequence. But from here I don't know how to show it converges outside of K.

@user60887: $K\subset\Bbb R$?

@Nick yes, many normal things one say to him become hilarious

yes a nonempty subset of the real numbers

bad bad leroy brown @leo @Nick

@Ted: I'm not a sham. I'm a buff baby that can dance like a man,
I can shake-a my fanny, I can shake-a my can!
I'm a tough tootin' baby, I can punch-a your buns!
Punch-a your buns, I can punch all your buns!
If you're an evil witch, I will punch you for fun!

1:57 AM

So what does noncompact tell you?

user image

3

lol

lol

that it contains a sequence in K that has a subsequence that does not converge in K

No, every subsequence fails to converge to a point in $K$.

2:00 AM

oh I had it backwards

@PedroTamaroff como va todo?

Watch quantifiers with negation!

so if there is a sequence in $K$ such that every sub sequence fail's to converge to a point in K. Then I get two cases that either the monotone subsequence does not converge then im done or the montone subsequence does converge but by assumption it converges to a point outside the noncompact set K.

@Twink: I'm sorry for grinching your equation and posting it on facebook. Please forgive me. PS- it got 20 likes. That's like 20 likes for you!!

Yes, corresponding to $K$ being unbounded or failing to be closed.

2:04 AM

yeah

It wasn't twink's, @nick. He stole it too.

The secret to creativity is knowing how to hide your sources

uh-huh... and I thought I was the one commiting the mojo jojo act of pure evil!

That is either academic dishonesty, plagiarism, or theft @skull.

why does it matter that $k$ is closed or not?

2:09 AM

@Ted: You're not mad about the song, are you?

@TedShifrin It is not my quote Professor :-)

Compact in $\Bbb R$ means closed and bounded, @user60887.

nope @nick ... I'm not mad at all.

ahh ok. i don't know why my book does not include that in their definition

the definition is in terms of sequences?

yeah

2:11 AM

@Ted: Good because it usually nicks people off when I do it IRL

I can see why.

that's ok ... You can derive what I said using the least upper bound property.

@nick: Math geeks aren't known for their social skills. No need to excel at the latter, however.

@skull: I knew you would star that within seconds.

You have some classic lines Professor.

@Ted: I'm not a math geek, I'm a math physics psychology geek!

user image

Get it, Mobius strip...

[text](link) please

2:21 AM

next time, will do

@leo Nada mal. Tengo un examen final mañana, pero me siento preparado. =)

Mucho calor igualmente.

@pEDRO: gOOD lUCK, SENIOR PEDRO!

25 mins ago, by Nick

user image

25 mins ago, by badass

bad bad leroy brown @leo @Nick

great combo^

@PedroTamaroff excelente!

4 mins ago, by badass

[text](link) please

2:24 AM

aquí hay frío mas bien

3 mins ago, by Nick

next time, will do

@badass: how do you do that, the whole embed thing

@leo Je, que suerte.

Case 1: The monotone sequence fails to converge. Then it follows that it is unbounded which corresponds to the fact that set K is unbounded. Case 2: The monotone sequence converges to a point outside of set K which follows from assumption. Would that suffice?

Aca estamos en los 35 grados, o mas.

@user60887 Context?

2:25 AM

ufff

Im trying to show that if K is a noncompact set of real numbers then it contains a monotone sequence that converges outside of K

en San José varia como de los (a lo sumo 30) y baja a 18 19 en la noche

@Nick Format it like this: [text](link)

Guys what is repeated tetration called?

like this

bingo :-)

2:28 AM

um, no I mean like embed your post in mine

Repeated tetration

I just dragged them down one after the other.

@Ian: Please demonstarate!

Are you being cooked alive @pedro?

@Charlie: Do you know this woman?

2:32 AM

What woman?

user image

This fucking mobile version is awful

I don't

@Charlie indeed

@Charlie @Nick Hahahahah

XD ah well, nowI understand why to never post images and always link them

2:34 AM

Geez

37 mins ago, by Nick

user image

-_-

I'm a buff baby that can dance like a man,
I can shake-a my fanny, I can shake-a my can!
I'm a tough tootin' baby, I can punch-a your buns!
Punch-a your buns, I can punch all your buns!
If you're an evil witch, I will punch you for fun!

That usually cheers people up!

I am not cheered up

O_O Ofcourse you're not @cheered-up, you're @charlie

2:38 AM

Yes

um, Does anyone here have an Erdős number?

$\infty$ by now

@Charlie here >8(

ha ha

Oh skull!!!! Yes!

2:45 AM

@Charlie: You do know that Obama has now copyrighted grumpy cat's face don't you?

@Ian: Really? Infinity is finite?

nice link :-)

@Nick conventional matters. Heheheh

13 mins ago, by Nick

XD ah well, nowI understand why to never post images and always link them

@Nick No.

@Charlie: Ofcourse you'd say that.

2:49 AM

:)

@Charlie: I can imagine your face right now.

I'm given that $f(x) = g(x)/x$ for $x \neq 0$, and $f(0) = 0$, and also that $g(0) = g'(0) = 0$, and $g''(0) = 17.$ I need to find $f'(0)$.

So I've said that

Leslie Faulkner

Is this website in general rude?

$f'(0) = \lim_{h \to 0}\frac{f(h)}{h} = \frac{g(h)}{h^2}$

Leslie Faulkner

I am a new user and I am still figuring out how to use this website

2:53 AM

You can't @Nick

Leslie Faulkner

And I get yelled at

and then using L'Hopital, since the top and bottom go to $0$.

Leslie Faulkner

1

Q: Find a set of generators and relations for $S_3$

Can you help me with this? By trial, I came up with the generators and relation. However, how do I prove that the generators and relations uniquely determine $S_3$? Problem Find a set of generators and relations for $S_3$ Solution Let $a=(1,2)$, $b=(2,3)$. We have $ab = (1,2)(2,3) = (1,2,3)...

@Leslie: No, it's just today. I swear. Although I've been lying the entire day. Starting from when I stole Twinks equation.

$f'(0) = \lim_{h \to 0} \frac{g'(h)}{2h}$

and then using L'Hopital one more time

$f'(0) = \lim_{h \to 0} \frac{g''(h)}{2}.$

But I don't know where to proceed from here, since we don't know if $g''$ is continuous at $0$.

2:55 AM

@nsanger: Could you have tried ab-initio? it's longer but often gets you the right answer.

what do you mean?

@nsanger: You'll find a way.

^helpful

akh got it

Thanks for believing @Nick :D

@nsanger: Nope, I tried. Couldn't do it either.

How did you get it?

Okay so you get to the point where $f'(0) = \lim_{h \to 0} \frac{g'(h)}{2h}$

3:05 AM

yeah

Which is $\frac{1}{2} \lim_{h \to 0} \frac{g'(h)}{h}$

Oh!

and this is just $g''(0)$ yeah

so it becomes $\frac{1}{2} g''(0) = \frac{17}{2}$

Yeah I get it

great job!

haha, thanks.

3:07 AM

user image

Oh and by the way

that equation on general looks like this

user image

@nsanger:
It's a hyperbolic paraboloid

what is?

the equation f(x) = g(x)/x

So, that deserves a clap as well

user image

It's so hard to find descent clap gifs.

haha

@Ian: PENTATION! Repeated Tetration is Pentation! Not Penetration!

@Nick You confident about that?

3:15 AM

@leo: Yes

Oh well

@leo: But there doesn't seem to be a name for repeated sexation.

sexation seems nice

septation?

Sexation turns on, not?

3:21 AM

@leo: Sexation is a sensation
caused by temptation
where an exponent sticks his location
in a base's destination
to increase population
of the next generation
Do you get my explaination,
Or do we need a demonstration?

a diagram

user image

just see the pattern and re-do it with 3 arrows. That's sexation

ha ha

okay

I'll accept that

@Ian: Where the heck would you even need hyper operations like that?

@Nick no idea whatsoever, but see Graham's number (Ramsey theory, good start)

3:28 AM

@Nick, if you want a cool problem related to that diagram.

Show that if you perform that operation with $3$ ten times

i.e. $3^{3^{3} \cdots}$

ten times

then you will get the same last $10$ digits if you add another three, or two more threes, and so on ad infinitum

@Ian: I'm really beginning to appreciate Knuth's up arrow notation. When it comes to logarithmic calculations, I can finally see what I'm adding :D

@Nick there is a notation where there are numbers inside polygons. I'll try to find it

This one

3:45 AM

wow, cool room

hi, all

hello

hi

4:17 AM

how to filter expected value in fixed length group data?

may be media filter is suitable for this, but when peak value just as occurred in the media , may be that's invalid

4:52 AM

hello

Hello?

Hello!

We might be the only ones, I fear.

Yes

I have a question.

What motivates you to do mathematics?

I'll try to answer it

Hmmmm

Maybe it is irrelevant for this chat

There are no rules in chat :P

4:57 AM

I don't know.

oh , that's good :)

(except for the dont be a *** rule)

:P

True.

So, I'm not sure I can answer your question yet

But

The reason is that I'm not sure what motivates me on a day-to-day level. In the big picture level, I can trace my motivation back to a very particular moment in my life.

Okay.

I assumed that the first one is more relevant?

(wow that was a terribly constructed sentence)

4:59 AM

It's okay.

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