Mathematics - 2014-12-23 (page 7 of 10)

Yea, not bad thanks, @Ted. ^_^
I've started some really basic Analysis (sequences, series and completeness), so that's started to eat away at my days. =P

Alexander Gruber

@JasperLoy 2 leaving, 3 new ones

Jasper Loy

@AlexanderGruber Ah, sometimes, I am right after all.

Ted Shifrin

Good, good, @Khallil.

Don Larynx

8:22 PM

I have the system $$2^a \equiv 7 \mod 27$$ and $$2^{18} \equiv 1 \mod 27$$

Ted Shifrin

@Studentmath: Have you taken over with @A.E? He forgot to ping you.

Mike Miller

What do you study, @Lord_Farin?

Khallil Benyattou

Does that symbol mean congruent to, @DonLarynx?

Alexander Gruber

@PedroTamaroff @JyrkiLahtonen @DanielFischer Y'all got your superpowers yet?

Don Larynx

Fixed @Khal

A.E

8:23 PM

Sorry, @stud

Pedro Tamaroff

@AlexanderGruber Yes.

A.E

@Studentmath
Given a subset S of P, the probability of some e in P appearing in S is (P - 1 choose |S| - 1) / (|P| choose |S|)

Khallil Benyattou

Ah, what was the symbol before the edit, @Don?

Alexander Gruber

@PedroTamaroff Can you enter mod chat?

Lord_Farin

@MikeMiller I graduated last year; my primary focus was on logic.

Don Larynx

8:23 PM

a congruent symbol

Pedro Tamaroff

@AlexanderGruber Link?

Daniel Fischer

@AlexanderGruber Let me first find my profile. An old man is not so fast.

Khallil Benyattou

It looks cool. What was it's $\LaTeX$ code, @DonLarynx?

^_^

Mike Miller

Are you still doing it, @Lord_Farin?

Don Larynx

\cong

Ted Shifrin

8:24 PM

LOL @Pedro @DanielF

Khallil Benyattou

Ah, nice!

Lord_Farin

@MikeMiller Occasionally; I'm in the IT business nowadays, so not too much time to spare for maths unfortunately :(.

Ted Shifrin

Now I feel like a very lesser person, @Alex @Pedro @DanielF @Jyrki

Khallil Benyattou

It looks cooler than \equiv, @DonLarynx. =P

Mike Miller

Ah, I see. Are you enjoying it?

Ted Shifrin

8:25 PM

Very different from your namesake when I was in grad school, @Lord

Studentmath

@A.E I think that looks right.

Lord_Farin

@MikeMiller Very much, my employer is aware of my abilities and gives me challenging tasks :).

Ted Shifrin

@Studentmath, @A.E: I'm no longer paying attention, so you'll have to let me know if I am needed.

Mike Miller

Great!

Ted Shifrin

Challenging tasks is wonderful @Lord

Lord_Farin

8:25 PM

@TedShifrin Sorry?

Don Larynx

I think $\leadsto$, short for \leadsto, is cooler

Ted Shifrin

My classmate named Farin was in a field very far from logic.

Lord_Farin

@TedShifrin Ah :).

Ted Shifrin

@DonL: I learned to write that for \mapsto because Mike Artin loves it so.

Jasper Loy

@TedShifrin That field is called delusion.

Studentmath

8:26 PM

@A.E that's considering the subset is chosen at random, i.e. uniformly - right?

Don Larynx

$\bigodot$.$\bigodot$

A.E

@Studentmath Yes

Ted Shifrin

logic? @Jasper

Jasper Loy

@TedShifrin I mean that delusion is far from logic, lol.

Ted Shifrin

Oh, well, no, I don't think of complex geometry as delusion, thank you.

Jasper Loy

8:28 PM

I think people in this room are quite bad at getting my jokes.

In the Eng room, I am quite bad at getting their jokes.

Mike Miller

I claim to get your jokes, and I also claim they're not very funny.

2

Ted Shifrin

There's symmetry to it, @Jasper.

Lord_Farin

Can anyone tell me who user Behaviour is?

Pedro Tamaroff

@AlexanderGruber

Lord_Farin

They apparently remember me, but have only joined 7 months ago.

Pedro Tamaroff

8:29 PM

Where's the chat?

@Lord_Farin Hello there.

Lord_Farin

@PedroTamaroff Hello, Pedro.

Studentmath

@A.E then you are right, and wrote it elegantly - now we want to think of the probability of an element not appearing in a given subset

Lord_Farin

It's been a while :).

Mike Miller

@Lord_Farin They've been around for a while. You might also know them under the past names of "Post No Bulls", "40 votes", and some other username I don't remember.

Alexander Gruber

@PedroTamaroff Your mod powers are still gettin' beamed down

Jyrki Lahtonen

8:30 PM

@Alexander: I did click the mod agreement. When and where is the hazing ritual?

Ted Shifrin

Now we're Star Trek, @Alex?

Lord_Farin

@PedroTamaroff How have you been doing? Quite fine, I presume, seeing that you have been elected as a moderator - for which I congratulate you.

Jasper Loy

An SE staff was concerned about me after reading the transcript, so decided to send me an email. I was surprised to get it.

A.E

@Studentmath The form I wrote simplifies to Q / P, so then the probability of a specific element not appearing in a given subset is just 1 - Q/P

Lord_Farin

@MikeMiller Ah, 40 votes rings a bell. That makes sense, thanks :).

Pedro Tamaroff

8:30 PM

@AlexanderGruber I think I just misclicked. Dang this buttons are too close, eh.

Ted Shifrin

@Pedro:

Mike Miller

@AlexanderGruber I am making the silly assumption that you're not already, but you might look at the comments on the mod election page.

Ted Shifrin

Are you going to misclick and eradicate me?

Mike Miller

I hope so, @Ted

Jasper Loy

User X once ignored me accidentally. It took him long to figure out how to undo it.

Studentmath

8:32 PM

@A.E right, for some reason I forgot the original question - we want to work in the complement, so while that's true it's not exactly what we care about. So you have the probability of specific element apearing in a given subset. What's the probability the given element appears in 2 different subsets?

Ted Shifrin

Concerned about you in what way, @Jasper? Not the recent comments, but some of your old ones?

Jasper Loy

@TedShifrin Well, I have been talking about my problems quite a lot the last few days in chat, so he got worried, I think.

Alexander Gruber

@MikeMiller Asaf's post?

A.E

@Studentmath Well those are independent, so it should just be the product (Q/P)^2

Mike Miller

Yes, @Alex

Alexander Gruber

8:33 PM

Ah, yeah, we're on it

Ted Shifrin

Ah, well, there's only so much (i.e., not much) we can do for you, @Jasper, but that makes me glad that he was concerned.

Jasper Loy

@TedShifrin Aha. I hope it was not someone who complained about me talking too much though.

Studentmath

Right, so for $N$ different subsets of $P$?

A.E

@Studentmath So this gives me the probability of a specific element appearing in all N subsets: (Q/P)^N.

Studentmath

Correct. But does it gives us the complement probability that we are looking for?

A.E

8:35 PM

No

Pedro Tamaroff

@AlexanderGruber Alex.

Link me to the mod chat.

Studentmath

What do we need, then?

Mike Miller

I am going to click the mod chat link.

I'm going to do it.

A.E

I would think we need a factor of P, to account for the P choices of a specific element appearing in all N subsets

Alexander Gruber

@PedroTamaroff I just pinged you from in there.

Mike Miller

8:36 PM

@Alex I can't click the link if you don't link it.

Alexander Gruber

:-D

Ted Shifrin

I gather user26857 is going to be a pleasure to deal with ...

Mike Miller

That's apparently YACP if you remember the name. I don't.

Studentmath

Right, and also we wouldn't mind if more than 1 element appears as @Ted said, so we need to account for the option they have 2, 3, ... P elements in common.

Ted Shifrin

You shouldn't need to worry about that if you've done it right, @Studentmath :P

Lord_Farin

8:38 PM

@MikeMiller I recall that name as regularly sparking tensions.

Pedro Tamaroff

@AlexanderGruber I didn't get the ping.

Lord_Farin

An uncompromising character.

Alexander Gruber

@PedroTamaroff rob's workin on it

Mike Miller

You'd better just link it, @Alexander

A.E

@TedShifrin mind giving your input? I have Pr{A specific element belongs to all N subsets}, and I want to calculate Pr{Any element belongs to all N subsets}

Ted Shifrin

8:39 PM

I don't either, @Mike.

Lord_Farin

@A.E Are the probabilities independent?

A.E

Pr{A specific element belongs to all N subsets} = (Q/P)^n

Yes, each subset is of size Q drawn uniformly from P elements

Ted Shifrin

Oh, I see ... Ugh, we are going to need inclusion/exclusion this way.

Studentmath

@Ted what way did you have in mind?

Jasper Loy

Another question on RH.

Ted Shifrin

8:41 PM

I should go back to avoiding all probability questions, now that I'm done teaching :)

I guess we can alternatively add up terms for exactly one overlap, exactly two, etc., @Studentmath ...

Jasper Loy

@TedShifrin If you are very free, you can look at my article and tell me what you think, though I forgot what I had written ten years ago. I hope it will at least help me get into grad school.

Studentmath

@Ted ah yeah, that might be nicer

Probably will be

Lord_Farin

@Studentmath "Nice" is not the word that comes to my mind in this context...

It'll probably be a messy, messy expression.

Jasper Loy

@Lord_Farin I remember you. I think you are a girl, iirc.

Ted Shifrin

@Jasper, thanks for reminding me. I will try to look at it over break. I have to read 15 teaching award nomination dossiers, each 25 pages long.

Lord_Farin

8:44 PM

@JasperLoy You recalled wrong.

Ted Shifrin

Well, @Lord, inclusion/exclusion isn't exactly elegant :D

Studentmath

@Lord messier than the inclusion/exclusion we gonna need here otherwise?

Jasper Loy

@TedShifrin Wow, 25 pages is too long. Should be at most 2.5 pages.

Ted Shifrin

LOL ... in some cases, yes, @Jasper, but in most cases not.

What is absurd is that someone would include a 12-page research CV for a teaching award nomination. Drove me nuts last year, too.

Lord_Farin

@Studentmath I'm not sure. I just want to make sure I'm not the one writing everything up in the end :P.

Studentmath

8:45 PM

@Lord oh yes, certainly. Though I don't think we are helping @A.E this way :P

A.E

:)

Lord_Farin

@Studentmath True, true. But there might be more virtue in thinking out a more elegant approach :).

Studentmath

@Lord true

A.E

I have to go, I will keep thinking about it. Thanks for the help, guys.

In case you feel like writing something down, I made a post here: math.stackexchange.com/questions/1078342/…

Ted Shifrin

I thought I suggested doing the complement in the first place ? Of course, now I've forgotten. :)

Lord_Farin

8:47 PM

@A.E Thanks for handing me a nice problem to think about :).

Jasper Loy

@TedShifrin Wait, who submits these nominations? They nominate others and then include others' CV?

Ted Shifrin

Well, the candidate helps in preparing the nomination, @Jasper. But someone is supposed to collect all the stuff, all the letters written by colleagues/students, and write a narrative for it.

Studentmath

@A.E same as Lord said, if I think of something elegant I will let you know.

@Ted we were working on the complement :P

Ted Shifrin

No, we weren't. His question is for subsets with nontrivial overall intersection, @Studentmath. But the complement is likewise yucky. I forgot he changed the question after I started thinking.

Jasper Loy

@TedShifrin That is extremely weird. I think the candidate should not have any hand in it.

Ted Shifrin

8:50 PM

Well, @Jasper, I tend to agree, but the candidate has to provide a CV and a list of students to contact. In some cases over the years, it has looked almost totally self-prepared, which I find disgusting. I have prepared a number of these dossiers, and I take it seriously.