Mathematics - 2012-03-02 (page 1 of 4)

yayu

12:00 AM

so that means, I can design 33 yes/no questions

and every person will have a unique answer, right

Asaf Karagila

In theory, yes.

anon

a unique set of answers (in theory)

Asaf Karagila

In practice this is nearly impossible due to psychological effects and such.

yayu

now, I can make trusism like "does the sun rise in the east- yes/no?"

Asaf Karagila

@anon You're barking dangerously close to a question tagged as set-theory with that comment of yours!!!

anon

12:02 AM

You might as well make all 33 questions about longitude/lattitude. The correspondence between answers and people will change over time though. :P

Also, you'd have to be more precise than any human could in practice be...

Asaf Karagila

This is one of those things which are mathematically trivial but applicatively are nearly impossible. It gives the impression that applications of mathematics are far far more powerful than they really are.

yayu

or technically, I can ask each person their SSN or equivalent.. havent I singled everyone out in less than 33 bits?

Asaf Karagila

In theory you can assign every person a 33 bits number, and have the 33 questions "Is your n-th bit 0?".

My ID number (Israel equivalent of SSN) is unique in Israel, but it is possible that in some other country someone else has the same number.

yayu

hmm

sorry 13 decimal digits... how is this the same as 33 binary digits

if there were a universal decimal ID number , it'd have (7e12) or 12 digits

Asaf Karagila

You should know that many of those numbers have error correction codes in them, so in effect they are less than 13 digits, and not every combination is possible.

My ID number is 9 digits long, whereas the last digit can be calculated from the first 8, so to verify that indeed it is a real ID number.

So not all 9 digits combinations are even possible.

yayu

12:10 AM

what I mean, line everyone up.. first person is 000000001 and last person is 7,000,000,000

assuming there is no error

in number allotment.

how come 10 decimal digits has the same information content as 33 binary digits

Asaf Karagila

It doesn't.

robjohn

Note that $e^{-\pi x^2}$ is its own Fourier Transform, then $$
\begin{align}
\int\left(\int f(x)\;e^{-2\pi ix\xi}\;\mathrm{d}x\right)e^{-\pi\xi^2\epsilon}e^{-2\pi iy\xi}\;\mathrm{d}\xi
&=\int f(x)\left(\int \;e^{-2\pi ix\xi}\;e^{-\pi\xi^2\epsilon}e^{-2\pi iy\xi}\;\mathrm{d}\xi\right)\mathrm{d}x\\
&=\int f(x)\left(\int\;e^{-\pi\xi^2\epsilon}e^{-2\pi i(x+y)\xi}\;\mathrm{d}\xi\right)\mathrm{d}x\\
&=\int f(x)\;\frac{1}{\sqrt{\epsilon}}e^{-\pi(x+y)^2/\epsilon}\;\mathrm{d}x
\end{align}
$$

yayu

I dont understand

Asaf Karagila

10 decimal digits have exactly the same information as 10 decimal digits.

robjohn

Darn, Jonas has already left.

Asaf Karagila

12:12 AM

2^33 = 8,589,934,592.

This means that you can encode precisely that many numbers in exactly 33 bits. Not one more, and not one less.

If you have at most that many people, you can assign each of them a number.

SSN and such numbers do not work that way. They have a clever way ensuring that people won't fake numbers that they are not supposed to have.

So numbers assigned by the government to identify a person completely are always such numbers which encode some code-correction data, to ensure that the number is valid.

Furthermore, it is easier to remember 10 decimal digits than 33 binary ones, so we are often assigned decimal numbers.

yayu

hmm. i see now.

btw, wondering about the code correction. Israel has 7 million people, how many digits are the id numbers there?

Asaf Karagila

8+1 verification digit.

I think that the ID numbers space has about 10 million combinations possible with nowadays assignments, but that can be expanded if they start using more leading digits (nowadays we have 0,1,2,3 and in rare cases 4).

robjohn

Has anyone else seen a lot of upvote/unupvote and accept/unaccept activitiy, then a similar upvote or accept the next day on their Reputation page? It's almost as if the accepts and upvotes were being moved a day ahead.

yayu

I see now... so you have 100 million (10^8) possible id numbers, and with the correction digits, total 400 million , for a population of less than 10 million.

Asaf Karagila

How did you deduce 400 million?

yayu

12:23 AM

correction digits of 0,1,2,3

Asaf Karagila

@robjohn No. Someone is jerking you around.

@yayu No. The correction digit is not the leading digit, it's the last digit.

It is calculated by the other 8.

We have 100 million numbers but we use a space of 10-20 mil.

yayu

oh.. i misunderstood the verification digit

following on the earlier thread... is the 33 bit mathematically the lower bound for identifying a person?

I mean, I can think of questions like...

"are your eyes blue?"

and that would eliminate some 70% of the population

Asaf Karagila

What about those with bluish eyes, like blue-gray eyes or blue-greenish eyes?

robjohn

@AsafKaragila :-p read this

yayu

suppose we live in a universe where people have distinct eye colors

or I could make an adaptive questionnaire..

Asaf Karagila

12:29 AM

@robjohn Yes, I read that already. I also recalc every few days so I am unaffected by this.

@yayu Suppose that you have assigned everyone with a unique number, then. You either live in this universe or you live in some abstract universe, you can't have both.

yayu

Example..
1. Are you caucasion - No.
2. Are you hispanic - Yes.
3. (Start with most populated Hispanic country X, if no move to next most populated) Are you a citizen of X? -Yes
4. (Start with most populated city in aforementioned country, say Y. If not, move to next most populated) - Are you a resident of Y?
and so on...

I can imagine that with enough information, I can succesively narrow down a person's neighborhood much before 33 questions

robjohn

@AsafKaragila I usually recalc once a day or perhaps two as well, but the global recalc seems to have moved some upvotes and accepts around. It also affects me in that I don't need to recalc any more.

Asaf Karagila

@robjohn Until they show the progress towards Epic in the profile page I'll keep visiting that page every now and then.

robjohn

@AsafKaragila I can see my Epic progress on my text reputation page.

Asaf Karagila

Yes, I meant that one.

robjohn

12:36 AM

@AsafKaragila Ah, I still visit it so that I can see if anything strange goes on with my rep. Some things happened a few weeks ago and I had no record of how things looked before. If that happens again, I want to have a snapshot of things before to compare.

@Asaf: if you have the inclination, see if you follow Didier's answer to the second part of this question more easly than mine. He doesn't answer the first part but he's gotten one more vote than I did.

Asaf Karagila

I'm finally getting tired.

I might do it tomorrow if you remind me.

robjohn

@AsafKaragila okay, no sweat. I was just curious.

Asaf Karagila

Well. I think I can finally get myself to sleep.

Which is good, since staying awake and not doing the alg. top. assignment has become an agonizing burden!

robjohn

@AsafKaragila It is almost 3 AM. I wish you luck in getting to sleep

Asaf Karagila

Thanks. So long.

robjohn

12:52 AM

@AsafKaragila For all the fish. en.wikipedia.org/wiki/So_Long,_and_Thanks_for_All_the_Fish

Asaf Karagila

Yes. I read the guide. Whenever I have a bag, I have a towel in it.

Do you think I'm a nincompoop??

robjohn

@AsafKaragila :-) I didn't mean to draw you back, I just wanted to draw your attention when you returned.

@AsafKaragila why would I think that?

Asaf Karagila

Because you adding a reference implies that I did not already recognize this overly used reference.

My favorite reference would probably be "We apologize for the inconvenience".

robjohn

@AsafKaragila well, often on this site, it is hard to know what is assumed with others. Cultures differ.

Asaf Karagila

But seriously... not to read the guide??

robjohn

1:02 AM

@AsafKaragila perhaps I was a bit hasty in my considerations.

Asaf Karagila

Indeed you were. Oh well, no biggie.

So long (this time for real!)

robjohn

There is a Café at the End of the Universe at the Griffith Observatory, perhaps I should simply put myself on the menu there.

It is actually not much more than a snack bar.

N3buchadnezzar

1:19 AM

@robjohn Hi =)

robjohn

@N3buchadnezzar Howdy, has your day been good?

N3buchadnezzar

IT is 2 am

still doing homework

robjohn

@N3buchadnezzar so it has been a long day, and it doesn't sound as if you are having fun right now.

N3buchadnezzar

@robjohn It deppends

I am almost done

Having problems with a heissian matrix to determine the extrema of a function :/

robjohn

how big a matrix?

N3buchadnezzar

1:28 AM

4x4

robjohn

Do you have a CAS to help?

or do you need it symbolically?

N3buchadnezzar

My only problem is that the solution just defines the maxima and minima, no tests or anything. Which makes me unsure if the testing is neccecary

@robjohn How has your day been ?

robjohn

So-so. I spent most of it proctoring a couple of exams today. Not terribly exciting.

N3buchadnezzar

@robjohn OH MY GOD THAT IS SO AWESOME

N3buchadnezzar

1:46 AM

Could anyone tell me if I have calculated correctly?

I need to evaluate some limits

$$ f(x,y) = \frac{x^4 - x^2y^2}{x^4 + y^2} $$

I am need to show wheter the limit $\lim_{(x,y)\to (0,0)}$ exists

I am fairly sure this limit does not exist.

Then I need to show wether the first partial derivatives exists in (0,0) or not

I think that $$\lim_{(x,y)\to(0,0)} f_x(x,y) = 0 $$ is this right?

David K.

@N3buchadnezzar wolframalpha.com/input/…

@N3buchadnezzar Similarly: wolframalpha.com/input/…

N3buchadnezzar

@DavidK Is there any easy way to show this by hand?

I tried using the defininition, but it gets messy-

David K.

2:06 AM

@N3buchadnezzar Try taking the limit with $x=y$, and then take the limit with $y=x^2$.

N3buchadnezzar

@DavidK That is what I did to show that f(x,y) is not continuous at (0,0)

David K.

@N3buchadnezzar Doesn't this imply that the limit doesn't exist?

N3buchadnezzar

@DavidK Indeed

This is why I love MSE

10

Q: Largest circle between $y=x^n$ and $y=\sqrt[n]{x}$

Something I have been wondering about for a while. Let us look at the area between $x^n$ and $\sqrt[n]{x}$ when $x\in [0,1]$. Where $n$ is a positive integer. Below is an image. With a given n, how large of a circle can you fit between $x^n$ and $\sqrt[n]x$? I know that the circle must lie on...

Jeff

2:45 AM

Hey all. Why does a question get locked? Why can't I vote on a locked question? (e.g., math.stackexchange.com/questions/11/does-99999-1)

robjohn

@DavidK Hmmm. Mathematica gives $f_x(x,y)=\dfrac{2xy^2(2x^2+x^4-y^2)}{(x^4+y^2)^2}$

and if you follow the curve $y=x^2$ to $(0,0)$ it seems to blow up

$f_x(x,x^2)=\dfrac{4x^7}{4x^8}=\dfrac{1}{x}$

I think there seems to be a bug in Alpha's limit taking procedure.

David K.

@robjohn Hmmm.... Yes. I hadn't computed the limit of $f_{x}(x,x^{2})$.

robjohn

Of course, if you follow the path $y=0$ into $(0,0)$, you get $0$.

Jeff

@robjohn: You're icon makes me think you're always mad. :D

robjohn

@DavidK That's $f_x(x,y)$ evaluated at $(x,x^2)$ just to be clear

@Jeff If you check my profile, you'll see that it's just because I'm the Mean Square. :-)

Jeff

2:56 AM

@robjohn ha ha :D

David K.

@robjohn Yes. I agree that there seems to be some type of bug with Mathematica's/wolfram's limit procedures. When I perform operations in different orders, I get different results.

robjohn

@DavidK Are the operations commutative?

David K.

@robjohn Is there a way to enter code in this chat?

robjohn

@DavidK You mean like x=cos(y)^3?

use ``

single backquotes

David K.

@robjohn f'[x_, y_] := (2 x y^2 (2 x^2 + x^4 - y^2))/(x^4 + y^2)^2

@robjohn Limit[D[f[x, x^2], x], x -> 0]

@robjohn Limit[f'[x, x^2], x -> 0]

robjohn

3:05 AM

Those are two totally different things.

Hopefully you get a different answer for the last two

David K.

@robjohn Indeed.

robjohn

The third should be $\infty$

I haven't computed the second.

David K.

@robjohn It is. The second is 0.

robjohn

So, was that the example of operations in a different order?

David K.

@robjohn How do you get Mathematica to evaluate something like: Limit[f[x,y],{x,y}->{0,0}] ?

I can only get it to do one variable at a time..

robjohn

3:10 AM

@DavidK I don't know if you can. I don't see it under the manual for Limit

David K.

@robjohn Didn't think so. However, Wolfram Alpha claims to be able to do it...

robjohn

Note that the paths $(x,x^2)$ and $(x,0)$ both come in from the right with the same direction, however, they give totally different results.

Matt N.

6:35 AM

Apparently I was invited to a chat room by masfenix last night.

Morning, btw.

Bleh, there it is again: I thought we'd had enough sun yesterday : /

@robjohn How was the proctoring?

Dan Brumleve

hmm i lost 100 reps in the last couple days but no downvotes in my recent history

Matt N.

Removed upvotes, maybe? Is that possible?

Ragib Zaman

Removed upvotes, a deleted answer, unaccepted answers, or system error in initial count.

Dan Brumleve

maybe dunno. must have offended someone for 10-20 upvotes to be removed

Matt N.

Oh, you're assuming it's the same person. I assumed it was a coincidence. Did you offend someone?

Dan Brumleve

6:43 AM

nope havent logged on in over a week even but ive beem checking my page sometimes

yesterday or the day before i had 2940-something im pretty sure

Matt N.

I wonder if the site keeps track of rep movements.

Dan Brumleve

what would happen if someone who had upvoted 10 of my answers deleted their own account or was banished?

i checked meta for similar complaints but nothing

Matt N.

Good question. I don't know.

Matt N.

7:00 AM

@tb I just realised that Wim Wenders made Wings of Desire. That was one boring torture of a film! Well, except for the bit where Columbo plays Columbo... : )

I assume you were talking about this.

Yay. And by coincidence I found this. Looks good.

Ragib Zaman

@DanBrumleve There's a notification on the (meta)[meta.math.stackexchange.com/] that you might find relevant.

anon

245

Q: Upcoming Reputation History Changes

Update: This has been rolled out to all sites in the network. Behind the scenes we've been hard at work making some changes to how we track reputation. Here are some of the issues we're aiming to address with these changes: Reputation Skew (your actual reputation doesn't match what's shown)...

discussion featured reputation rep-recalc

robjohn

7:46 AM

@MattN It was okay, but in general, boring

@anon I was mentioning this to Asaf :-)

7 hours ago, by robjohn

@AsafKaragila :-p read this

Dan Brumleve

thx anon

robjohn

@anon There had been some weirdness with my reputation, as I mentioned before that quote

Matt N.

@robjohn I thought so.

N3buchadnezzar

Man =(

I have been robbed

Matt N.

I have to go now, see you later.

robjohn

7:54 AM

@N3buchadnezzar howso?

@MattN buhbye

N3buchadnezzar

@robjohn -they robbed my wallet, and took the key to the appartment

anon

It's "fuuuuu"

robjohn

@N3buchadnezzar who did that? Did you get mugged?

N3buchadnezzar

crap

anon

Talk to landlord posthaste.

N3buchadnezzar

7:55 AM

I already did talk to the landlord

anon

how much $ did you lose?

ID, security cards?

That would screw me over.

N3buchadnezzar

@anon Someone "broke" in and cleaned out my jacket, ID, cash and some other card is gone.

robjohn

@N3buchadnezzar Oh, crap. That is so violating on top of it all :-(

N3buchadnezzar

@robjohn I dont give a shit about losing money, it is just crap somebody did it. Losing the keys is also a bummer, need to change the locks now...

anon

Wow. Could it be personal?

N3buchadnezzar

7:57 AM

Nah

No cell, no monkey, no keys

anon

atm/credit/debit cards?

robjohn

@N3buchadnezzar They didn't get your computer?

anon

lol

N3buchadnezzar

Whoever broke in just cleaned out the hallway, I ahve another lock on my room...

I see why the need for the second lock now.

anon

Did you talk to your neighbors?

N3buchadnezzar

7:59 AM

Not yet, will talk to my roomates first

Although they are still sleeping

I am seriously thinking about moving now

I dont give squats about losing money, I just want to feel safe =(

Kannappan Sampath

@N3buchadnezzar If I may ask, what had happened? Were you robbed/ beaten up?

: |

N3buchadnezzar

@KannappanSampath I just woke up, went outside my room, and all the stuff in my wallet had been cleaned out

Kannappan Sampath

@N3buchadnezzar Oh, so you think some of your friends must have done that?

N3buchadnezzar

@KannappanSampath I doubt that, but ... maybe

Kannappan Sampath

@N3buchadnezzar You can try and shift over to a new apartment, cant you? (Feelings like this upset a lot.) Also, why don't you stay at the university? Don't they provide you housing and stuff?

N3buchadnezzar

8:13 AM

@KannappanSampath They do not provide housing and stuff, and also... how cn I leave, when my keys are gone?

Kannappan Sampath

@N3buchadnezzar Holy crap.... Contact people responsible for the house, Is it so serious you must call a cop for assistance? Don't reply to this, but Swing into action. I am not joking, quite serious!

N3buchadnezzar

@KannappanSampath I am just waiting for the landlords response through mail... We firstly need to change our locks though

Kannappan Sampath

:-)

Gigili

What will happen at 1k rep?

Other than my laptop will explode.

I'll find out soon.

Kannappan Sampath

8:28 AM

FWIW none of our laptops burst, when we had made 1k rep.

anon

Mine evaporated

I had to wait for the next round of precipitation and go find it in the woods

Kannappan Sampath

@anon Really? You must have told this before I jumped the gun!

Kannappan Sampath

8:49 AM

"It means whatever it says it means in the place where you found it."- G.M

anon

9:04 AM

I lol'd when I read his answer. It's true though: it annoys me when OPs simply assume something they saw is completely standard and therefore deign to provide no context.

N3buchadnezzar

Should I wake my roomie?

anon

Dunno what your timezone is, what his/her sleep schedule is, etc. If it's about theft though I would be inclined to wake them.

robjohn

@N3buchadnezzar If it looks as if something of theirs might have been stolen, I would.

N3buchadnezzar

@robjohn Well he has a friend over, and did not go to bed to untill after 4am. And I think he had a few beers.

And it is 10 am now

robjohn

@N3buchadnezzar Ah, then the situation might be a bit more delicate. Use judgement.

N3buchadnezzar

9:10 AM

@robjohn I guess my main motivation for waking him, would be to not feel so alone right now.. Mmm. =( =( =(

robjohn

@N3buchadnezzar we're all here, so in a sense, you're not alone. Perhaps it's not the same thing :-)

N3buchadnezzar

@robjohn Just to let you know, I really appreciate you all being here. You guys rock... =)

I just feel so alone, anxious and vulnerable.

robjohn

anything for an ancient Babylonian king ;-)

N3buchadnezzar

I guess I will procastinate in Latex...

I really want to move though

First my cell and then a few days later my money, and keys.

Eric Gregor

9:32 AM

Can someone explain to me what Mariano means here. I don't see how he is defining a smooth vector field on the sphere minus the north pole: math.stackexchange.com/a/71597/21725

It seems that his definition is not well defined, since each great circle passing through the north pole has two differently oriented vector fields

anon

You're right, Mariano's field doesn't seem to be well-defined. Why don't you post a comment on his answer though?

Also, I think he means $xy$ plane, not $yz$...

Skullpatrol

9:48 AM

@N3buchadnezzar My personal advice to you would be to first call the cops and make out a report of the facts immediately.

N3buchadnezzar

@Skullpatrol they took my cell

Skullpatrol

@N3buchadnezzar Then go to a phone booth.

N3buchadnezzar

@Skullpatrol They took the keys to my appartment

anon

You can file police reports online.

N3buchadnezzar

@anon I know

I think I will talk with my roomates first though

Skullpatrol

9:51 AM

@N3buchadnezzar Then knock on the nearest door you can find and ask them to call the police.

N3buchadnezzar

@anon What is the point in filing a report?

Skullpatrol

The point is you were robbed of your belongings and you need to tell someone.

anon

Unless insurance or retribution is going to be involved somehow I don't think there is a point, I just wanted to point out it could be done online.

Police aren't going to do anything and filing a report might turn out to be a bereaucratic hassle.

Eric Gregor

I am not able to post a comment, anon

N3buchadnezzar

Well i just lost 65-70 dollars, and those keys

The problem is I do not feel safe, and ironically enough calling the police will not change that.

anon

9:54 AM

@Eric: I'm sorry, I forgot about the threshold. I'll post one :)

Eric Gregor

Thanks, anon. I appreciate it.

Skullpatrol

@N3buchadnezzar True enough calling the police may not change how you feel, but at least you will have a record of what and when this happened.

In case it happens AGAIN in the near future.

N3buchadnezzar

It sort of happened twice already :/

Skullpatrol

Oh?

anon

@Eric: Actually, I figured it out while typing up the comment!

Skullpatrol

9:59 AM

@N3buchadnezzar Then treat this time as if it were the first and report it, in my opinion.

anon

There are indeed two orientations for each circle, but as long as you choose one consistent on all of the circles the resulting field is smooth. I'll do an mspaint quickie

Eric Gregor

I don't see how that's possible, but I may just be really tired.

anon

I didn't see at first, but that's because I was defining the planes' orientation in space incorrectly

how do you redo an action in mspaint? :P

Eric Gregor

cntr+R?

anon

Up is positive $z$ direction, right is positive $y$ direction, and into the screen is positive $x$ direction. @EricGregor

Eric Gregor

10:07 AM

ahh. that actually makes a bit more sense. but he said perpindicular to the xy plane

anon

No, he said perpendicular to the yz plane.

I thought he meant xy plane, but I was incorrect.

Eric Gregor

i see

thank you, this makes sense

anon

Here a yz plane is parallel to the screen itself. No problem.

lol, I reloaded the page and was going to upvote @Mariano's answer, but then LaTeX kicked in and I ended up downvoting

N3buchadnezzar

@anon Are you familiar with tikz?

Eric Gregor

i just upvoted it, so we cancelled it out

anon

10:13 AM

I know of it, I don't know it though.

I undid my downV and made it an upV.

N3buchadnezzar

\documentclass{article}
\usepackage{tikz,pgfplots}

\begin{document}
\begin{tikzpicture}
\filldraw [color=black,fill=gray!30!white,draw opacity=0.5,thick] (-2.356,-1) rectangle (3.9269,1)
\draw[fill=gray!30!white,color=blue,smooth,thick,domain=-2.356:0.7854] plot (\x,{sin(\x r)});
\draw[fill=red,color=green,smooth,thick,domain=-2.356:0.7854] plot (\x,{cos(\x r)});
\draw[fill=gray!30!white,color=green,smooth,thick,domain=0.78545:3.9269] plot (\x,{cos(\x r)});
\draw[fill=red,color=blue,smooth,thick,domain=0.78545:3.9269] plot (\x,{sin(\x r)});

@anon Could you test that codesnip? Mine seems to crash

Just to see wheter it compiles or not.

Kannappan Sampath

Something in me tells Aryabhata is an Indian! Anyone disagreeing?

anon

I know @Kanna is familiar with tikz. I don't have the package though, do you want me to download, install and all that jazz?

N3buchadnezzar

Kannappan can do it =)

anon

Good job, Sherlock. :) @Kanna

Kannappan Sampath

10:16 AM

@N3buchadnezzar I am doin' it!

anon

Hmm. Could it be sensible to allow commutative diagrams to include arrows pointing to and from other arrows?

Kannappan Sampath

My TeXmaker seems to give me a sarcastic look!

anon

\sarcasticlook

Kannappan Sampath

The process began a few minutes ago and still on.....

N3buchadnezzar

@KannappanSampath AprilFools!

Skullpatrol

10:19 AM

April?

Kannappan Sampath

@N3buchadnezzar Why!

N3buchadnezzar

\documentclass{article}
\usepackage{tikz,pgfplots}

\begin{document}

\begin{tikzpicture}
\filldraw [color=black,fill=gray!30!white,draw opacity=0.5,thick] (-2.356,-1) rectangle (3.9269,1);
\draw[color=red,fill=white,smooth,thick,domain=-2.356:0.7854] plot (\x,{cos(\x r)});
\draw[color=blue,fill=white,smooth,thick,domain=-2.356:0.7854] plot (\x,{sin(\x r)});

\draw[color=blue,fill=white,smooth,thick,domain=0.7854:3.9269] plot (\x,{sin(\x r)});
\draw[color=red,fill=white,smooth,thick,domain=0.7854:3.9269] plot (\x,{cos(\x r)});

This one should compile, this is although a very strange way to solve this problem (filling the area between two functions.)

anon

N3buchadnezzar

I call it the moustache function!

Kannappan Sampath

What is this $f^t$?

anon

10:22 AM

This is my idea of how to define the transpose $\cdot^t:\mathrm{Hom}(V,W)\to \mathrm{Hom}(W^\vee,V^\vee)$ with arrows pointing to arrows in the category $\mathrm{Vect}_k$

Kannappan Sampath

TeXmaker died. His father sent me a note :/

anon

the transpose precomposes a functional $W\to k$ with a linear map $f:V\to W$ to create a functional $V\to k$

N3buchadnezzar

I think the problem lies in the closed cycle, although I have no idea why it fails

@KannappanSampath I was able to create a tikz file to easilly make problems, with automatic link to the solutions =) both short and long solution-.

Kannappan Sampath

@N3buchadnezzar Oh, I see!

My laptop shows signs of feverishness. It's heating more than ususal. A realistic solution would be helpful! Please..

N3buchadnezzar

@KannappanSampath Actually I have no idea why the first tikzpicture fails :p

ctrl + alt + delete
Then find the texmaker program, and annihilate the process.

anon

10:27 AM

@Kanna: I prescribe chicken noodle soup.

Kannappan Sampath

@anon I know you're mocking me. Please tell me something realistic! I'll send you chocolates if you did solve my problem, really!

Gigili

Are you on Windows 7 @anon?

anon

I can't think of a solution that keeps in you the chatroom the entire time.

More or less unfortunately, yes. @Gigili

Kannappan Sampath

@anon What do you mean?

anon

I mean holding down the power button will disconnect you until you get back on. :P

Gigili

10:30 AM

@anon Um, I thought Linux might be the problem but failed =\

anon

the problem but failed? what are you referring to?

Kannappan Sampath

@anon This is again a mockery: I spend all my time in the chat room is not true! I keep me logged in though!

anon

heh heh

Gigili

@anon Oh I thought you were the one having the problem, sorry for being silly =\

anon

I figured that.

Kannappan Sampath

10:33 AM

:----------------)

anon

But thanks for trying to help me over Kanna :)

\runsaway

Kannappan Sampath

\runsaway

\runsback

\runslikeadog

\...

Gigili

@anon I live to please! :P

anon

Better than pleasing to live, I say.

Gigili

Yes, I am the bestest, I'd say.

anon

10:38 AM

I saw The Artist recently. Didn't think I'd like it cause it was silent and black-and-white, but I was impressed.

Gigili

Silent and black&white is impressing indeed.

Ilya

10:56 AM

@Kan: don't shout on him! :D

Kannappan Sampath

@Ilya I am now writing an answer for that chap. :-)

Ilya

@KannappanSampath nice :)

anon

"We already have hamburgers and hot dogs, so after all why do we need pizza?" – Pete L. Clark

2

Kannappan Sampath

@anon A link to catch up with the whole story would be appreciated, dear brother.

anon

see the first link Willie posted on the recent question math.stackexchange.com/questions/115630/…

Kannappan Sampath

11:04 AM

:-)

Thank you.

Ilya

@anon because pizza appeared earlier

Kannappan Sampath

@Ilya What do you think about how how far it has gone? Any mistakes? Please let me know!

anon

11:21 AM

$$\mathbb{E}(X)=P(T)\;\mathbb{E}(X \;|\;
T)+P(\text{not } T)\; \mathbb{E}(X \;|\; \text{not }T)$$ is a valid formula, right?

Kannappan Sampath

Haven't come across!

anon

Just consider that with $T$ being the statement $X>0.5$ and it's a matter of direct computation for all three parts.

I mean, it's obvious in the discrete case, and my gut says it's obvious, I just don't know the theory to phrase a justification

oh, nevermind, now I do

Kannappan Sampath

But, I am finding something wrong with my answer. Will you go through?

anon

Only after I finish typing my answer >:)

Kannappan Sampath

Sure!

anon

11:33 AM

Okay, I gave up on how to formally justify it. I'll look at yours.

Eh, not sure if looking at the distribution function is the best way to do it

Kannappan Sampath

11:50 AM

I'd like to get hold of density from there!

And, then the expectation, the most straight forward!

@anon

(Sorry for the late reply, I was having two Masala Dosas!)

anon

problem is, the density at x=1/2 isn't defined unless you use dirac deltas, I think. because $P(1/2 < X < 1/2+\epsilon)/\epsilon$ doesn't exist as $\epsilon\to0$

change the X with Z,Y, or W - my bad

Kannappan Sampath

Ah, not having a density at a few places is not a problem!

anon

plus the problem just screams out splitting into two cases, at least to me, so I feel finding an explicit density or cum. distribution function is superfluous calculation. there's symmetry that can be intuitively exploited.

Kannappan Sampath

But, my density does not integrate to $1$, noticed that?

Hi @tb I missed your entering the room!

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$Mathematics$ Mathematics