Mathematics - 2011-10-20 (page 1 of 2)

Asaf Karagila

00:07

@JM: Congrats. You pass me on flag weight now.

I got a declined flag, which dropped me to 633. I'm really tired of this, and it pisses me off. I'm gonna stop flagging for a while.

J. M.

I have? I haven't flagged in days...

Asaf Karagila

You have 634... I have 633

J. M.

(On the other hand, I apparently now have a 45 flag allowance per day.)

Asaf Karagila

Yeah, that's crazy :D

J. M.

Considering I only use three or four on a busy day...

(because it seems either Zev or Mariano are also online when spammers are poking about)

Asaf Karagila

00:11

Yeah, I'm gonna stop altogether.

Maybe flat out spam, but not CW/comment-answers/account merging/whatnot.

J. M.

Oh...

Asaf Karagila

I'm completely pissed at the -10 for declined flags.

I mean, at this stage 10 points worth like 15 helpful flags.

For me it's like the system says "Hey, you're doing an awesome work. But this declined flag? It is worth as much as the last 15 helpful ones..."

J. M.

I'd tell you to bitch at meta.SO, but I remember you're lazy... on the other hand, it does sound off from their stance on up/downvoting, no?

Asaf Karagila

In that thread I wrote about flag comments Grace Note replied to me about this bitching, I wrote her a comment now stating that while it sounds pissy and immaturely whiny I am stopping all my flags until they fix this.

J. M.

I mean, for voting on questions, the weight for "helpful" ones is higher in magnitude than the penalty for piss-poor ones.

Asaf Karagila

00:14

Yeah, exactly.

J. M.

and yet it's all backwards for flagging. I mean, who designs these things?

Asaf Karagila

And while it's fine at the early stage where you win and lose the same amounts, and it's even fine at the lower part of the reputation where you seem to be more inclined towards bad flags and whatnot...

At the pinnacle of flag weight they just make it unreasonable.

The decline comment even began with "sorry for the weight-hit"

J. M.

This software's weird.

Asaf Karagila

Yeah...

Well. I'm going to bed now. Be seeing you.

robjohn

@AsafKaragila sleep well

J. M.

00:25

Have a good one, Asaf.

robjohn

:-)

what flags are you talking about above?

J. M.

Oh, flags for bugging moderators...

robjohn

Are these things you only get when you have 10 or 20K?

J. M.

for things like "this is spam", "please set CW", that sort of thing.

robjohn

oh

J. M.

00:27

No, everybody with rep > 20 can flag.

robjohn

those flags.

yes, now I understand.

Jack Schmidt

i've never seen any spam on math.se

J. M.

@Jack: Thank the promptness of the mods for that. :)

robjohn

@JackSchmidt have you looked at any of my answers? ;)

I just get back from UCLA, and now I need to take the dog for a walk. BBL

J. M.

Good grief, the world would be way lot better if spambots can write mathematical proofs...

( on that note...)

robjohn

00:42

Have you considered that perhaps I am just such a spambot?

J. M.

As long as you post helpful and interesting stuff, you could be single-celled for all I care.

robjohn

Thanks, I'll put in my agar order now.

Snug down in my petri dish and watch TV...

J. M.

=))

robjohn

Now I really need to walk my amoeba or it will absorb me.

J. M.

Yeah, those buggers can get nasty when hungry. They'll engulf without warning...

First you think they're affectionately touching you with their pseudopods. Next thing you know, you're inside them.

J. M.

01:17

Argh!

Whoops, never mind. It was a hiccup on m.SE.

t.b.

01:29

@JM ah, you had that hiccup as well? strange. Didn't happen in a long while :) Meanwhile, they seem to have fixed the imgur-thing

J. M.

Yes, I was dreading an hour without m.SE... :D

t.b.

same here :)

robjohn

01:53

Huh... I edited one of my answers before my walk, and upon arrival home, it has disappeared.

Perhaps the fix involved a restore from backup.

from just before my walk.

J. M.

Probably the hiccup. Was a lot undone?

robjohn

I have the change backed up locally, so I will redo it. I was confused until I saw about the hiccough.

Hiccup

A hiccup or hiccough ( or ) is a myoclonus of the diaphragm that repeats several times per minute. In humans, the abrupt rush of air into the lungs causes the vocal cords to close, creating a "hic" sound. In medicine it is known as synchronous diaphragmatic flutter (SDF), or singultus, from the Latin singult, "the act of catching one's breath while sobbing". The hiccup is an involuntary action involving a reflex arc. A bout of hiccups, in general, resolves itself without intervention, although many home remedies shorten the duration. Medical treatment is occasionally necessary in cas...

I guess I am old.

J. M.

Nah, I just write "hiccup" because it's shorter. :)

(I'm lazy that way.)

robjohn

Wikipedia spells it the same way

I used to regard that spelling the same way as twilite and hilite

midnite

but it is now more accepted than hiccough

J. M.

Oh, those remain the visual equivalent of nails-on-chalkboard for me...

I'm lazy, but not that lazy.

robjohn

02:38

Odd. The comment I made after I edited the answer was still there.

J. M.

I have to step out. See you.

Gortaur

06:16

I dreamed I met a Galilean, a most amazing man.

robjohn

08:16

J.M. is steppin' out and Gortaur has found religion.

Gortaur

@robjohn good early morning, 1am?

He had that look you very rarely find

robjohn

It is just after 1 AM, indeed.

J.M. looked rare?

Gortaur

if he is Galilean - maybe

(though I was told that 'maybe' is from XV cent and I shouldn't use it)

robjohn

Ah...

Gortaur

I remember some time ago my friend were willing to enter the university of arts

and there he had to sing a couple of songs at the enter exams

robjohn

08:21

In Galilee?

Gortaur

I advised him Pilat's song and accompanied it with a piano - I liked to play this sogn that time

his voice was cool

@robjohn a bit to North from Galilee

Asaf Karagila

Mornin'

robjohn

what's happening?

Gortaur

@AsafKaragila it is indeed

robjohn

For both of you it is 10:24 AM?

Gortaur

08:24

yeah

robjohn

Since J.M. has stepped out, it is morning for all of us.

early morning for me.

Gortaur

after Einstein it seems like everybody thinks that everything is relative

we lost determinacy and objectivity

people even think that beauty is relative (

robjohn

in a cyclic time system, I am tempted to normalize 24h = 2 pi...

It is 0.379609112308767 here

Gortaur

where is 0 then?

I thought in Greenwich

and time is not cyclic, it's spiral more likely

robjohn

Ah.. then it is 2.21947703211945

Gortaur

08:29

I will grab a crappy coffee

but I want to grab a cool one, poor me

robjohn

If I kept a log, then I could see making a Riemann surface of the time...

Gortaur

oh! we have a coffee plus! some cakes will be there, see ya

robjohn

Great, now I am hungry at 1:30 AM.

:-p

wow, usually there is some residual rep trickling in, but nothing at all today. I'd better get to writing some answers :-)

Asaf Karagila

Drats.

I asked a question on MO, and it seems that the basis for my question was a misguided idea and since I cannot find it written where I thought it was written, it means only one thing.

Once again my mind is playing tricks on me and I remember things from dreams.

Gortaur

my mind is playing tricks on me, I am not as stable as I used to be

robjohn

08:44

@Gortaur you are at a saddle point?

or on top of a sphere?

Gortaur

relatively yes, if we assume that the Earth is the sphere - then I'm on its top

w.r.t. the saddle point I would say that bifuraction fits better here )

Alexei Averchenko

09:22

hi all

Gortaur

hi Alex

Gortaur

13:44

that what the phase I found this chat in when first time appear here

nobody here and the last message was for 17 hrs ago

Willie Wong

14:19

Can someone (maybe @JM if he is not too busy, since he has been keeping an eye on these things before) add the "tail of normal distribution" questions to our list of commonly asked questions on Meta? Some examples include math.stackexchange.com/questions/74151/… and math.stackexchange.com/questions/28751/… (I'm a bit busy at the mo' or else I'd myself.)

Asaf Karagila

Hi @Willie

By the apology on the declined flag, I'd take that it was you?

Willie Wong

@AsafKaragila Not really here. Just here to leave a message / some work for volunteers. (See my previous post.) Need to head back to work soon.

@AsafKaragila yes.

Asaf Karagila

Figured you'd have this kind of courtesy :-)

Willie Wong

/me Bows. -- In any case, need to run. Sorry couldn't stay.

Asaf Karagila

Ciao.

Gortaur

14:46

@Sasha: hi

J. M.

15:02

@Willie: done. I added only one since the answer there looked more elaborate to me...

Gortaur

15:17

@JM: could you tell me please, what is the flag weight?

@JackSchmidt: hi

J. M.

16:02

@Gortaur: see this.

Gortaur

@JM: thanks, reading

Ramana Venkata

16:39

Can anyone explain me this statement "every metric space X is opensubset to itself and is closed subset to itself"

Gortaur

@RamanaVenkata: opennes and closedness are relative notions

robjohn

The whole set and the empty set are both considered open sets in a topology

Gortaur

e.g. (0,1) is open as a subset of R but not closed there. On the other hand, it is closed as a subset of itself

robjohn

so the whole set and the empty set are both closed and open sets.

Gortaur

@RamanaVenkata If you don't study topology, you can easily check this statement by the definition of open and closed set in metric space

the same for [0,1) - it's not open nor closed in R but it's an open as well as closed in [0,1)

Ramana Venkata

16:43

I am actually a begginer so things are a bit confusing

Gortaur

@robjohn hi, how are you? )

@RamanaVenkata did you understand our comments?

robjohn

@Gortaur: doing well, been busy the last couple of days with midterms at UCLA.

this topic, considered by itself, is closed, but still open for discussion ;-)

Ramana Venkata

@Gortaur No My notions of closed set and open set on R are the ones due to which my confusion arises

Gortaur

what is your notion of an open set?

what is for closed?

robjohn

Closed sets contain all of their limit points; open sets contain a neighborhood of each of its points?

Ramana Venkata

16:47

Set is open if every point is a interior point of the set

Set is closed if every limit point is point of set

robjohn

@RamanaVenkata how do you define interior point?

Ramana Venkata

p is a interior point of E if there is a neighborhood of p N such that N is subset to E

robjohn

Ah, so my assessment was correct.

So consider [0,1)

can you see that considered as a metric space, it is open and closed?

is there a limit point that it doesn't contain?

is there a point that is not contained in a neighborhood?

are these trick questions? :D

Ramana Venkata

actually I am reading some theorems on metric spaces there they use the fact that if a set is not open then it is closed so I am wondering how they be simultaneously

be tru

Gortaur

if a set is not open then it is closed

completely wrong and dangerous statement

be aware

the set is open iff its complement is closed

i.e. A is open iff X \ A is closed

robjohn

16:58

@RamanaVenkata either you are misinterpreting the book, or the book is wrong.

Ramana Venkata

Okay I got my mistake My interpretation is wrong thank you

robjohn

open and closed sets are complementary.

the open set said to the closed set, "my don't you look sharp!"

the closed set said to the open set, "you are surrounded by your loveliness"

Ramana Venkata

:) in [0,1) i am not able to see which open set contains 0?

robjohn

the whole set contains 0

Gortaur

@robjohn we don;t know that [0,1) is open yet

@RamanaVenkata listen

B(x,r,A) = {y\in A: d(x,y)<r} - this is an open ball in the set A

robjohn

17:04

find a point in [0,1) that is not contained in the ball of size epsilon around 0

Gortaur

here d(x,y) is a metric/distance function

Ramana Venkata

i know that

Gortaur

when you put A = R, then any B(0,r,R) contain negative values, right?

Ramana Venkata

Yeah

Gortaur

so it does not lie inside [0,1)

Ramana Venkata

17:05

Yes

Gortaur

but now, if you consider B(0,r,[0,1) ) then it will not include negative values

because by our definition, B(0,r,[0,1) ) = {y\in[0,1): |y|<r}

did I confuse you?

robjohn

@RamanaVenkata: find a point in [0,1) that is not contained in the ball of size r around 0

That point will not be in [0,1) so it is not on the table for consideration.

Ramana Venkata

@robjohn okay then

@Gortaur can we call that ball open??

Gortaur

@RamanaVenkata: the trick is that some balls open in A are not open in R

you can immediately see it from the definition of on open ball B(x,r,A). E.g. let A = x. Then any ball open in A contain just one point: x itself

and certainly x is not open as a subset of R

robjohn

@RamanaVenkata: it is open by the definition of open in a metric space, a point x is interior if there is a ball of radius r around x so that the ball is contained in the set

Gortaur

17:11

@robjohn I think that it's hard for Ramana to listen to both of us ) I need to go in 5 minutes, so the floor is yours, sir

robjohn

The ball of radius r around x is a subset of the metric space, so the ball of radius 1/2 around 0 is [0,1/2)

@RamanaVenkata: sorry for the noise.

Ramana Venkata

@Gortaur @robjohn Thank you guys for taking pains to clear my doubts

robjohn

@Gortaur: sorry to be interference.

@RamanaVenkata: are you clear, or do you still have doubts?

Gortaur

@robjohn that's relative who is intereference here )

Ramana Venkata

just wait a second i am thinking

Yes I am able to understand

Gortaur

17:15

@RamanaVenkata: if you can give me a pleasure and right what is B(1/3, 1/2, [0,1) ), i.e. x=1/3, r=1/2, A=[0,1) I will read it later and will be very happy

robjohn

@Ramana: the open ball of radius r about the point x is defined as
B(x,r)={y in X:|x-y|<r}

I switched my x and r to match Gortaur's

Gortaur

@robjohn my pleasure )

@RamanaVenkata: and note please that the notation B(x,r,A) is not usual - I just use it here to underline in which space we are working because it matters. Usually one write B(x,r) keeping A in his/her mind

robjohn

@Mike: Curse you! :-)

Mike Spivey

@robjohn: Did you notice the OP accepted your answer on the binomial inversion identity question? So maybe you should be thanking me! :P

robjohn

I hadn't gone back yet. Thank you! :-)

Ramana Venkata

17:18

@Gortaur think it will be [0,1/2)

robjohn

@RamanaVenkata: really?

Mike Spivey

@robjohn: I'm always glad to mess up somebody's attempt at a post so that they can write a better second attempt. :)

robjohn

@MikeSpivey All three answers are really the same thing in disguise anyway.

@RamanaVenkata: remember it is about the point 1/3

Ramana Venkata

@robjohn okay

Mike Spivey

@robjohn: Sure.

Gortaur

17:21

silence almost all the day

and now I'm going home. that's all about time zones ))

robjohn

@Gortaur: is there a connection? ;-)

@Mike: what time is it there? We can confirm Gortaur's conjecture.

Gortaur

@RamanaVenkata almost right, but not the 1/2 on the right end

@robjohn Gortaur's conjecture ) I like it - should ask G. Perelman to prove it

Ramana Venkata

@Gortaur I excluded 1/2 from the ball

robjohn

Gortaur's conjecture: One commutative Ring can rule them all. It was proved false by F. Baggins.

@Mike: in any case, it didn't stop me from upvoting yours. It was my first choice, after all.

@Ramana: let me know if you still have any questions. I will be about for a while.

Mike Spivey

17:40

It's 10:40 a.m. here. I'm in Tacoma, WA.

robjohn

Ah, so the same zone, I am in L.A., CA

nice to finally see some people from this continent :-)

Mike Spivey

@robjohn: So where do the folks who hang out in chat tend to be from?

robjohn

All over, J.M. is in the Philippines, Gortaur is in the Netherlands, and Asaf is in Israel

t.b. is in Switzerland

Mike Spivey

That is all over. Wow. You know, that's one of my favorite things about math.SE - getting to interact with math folks from all over the world, rather than just those down the hallway.

robjohn

Other than us, those are all of the locations that people have divulged.

It is interesting especially listening into the discussions about food.

Mike Spivey

17:46

Food?? Math.SE chat is about food?

robjohn

It moves around, sometimes there is talk about food, customs, language, but then there is math, too.

Ramana Venkata

I have seen people talking about food recipies

robjohn

those involve fractions...

@Ramana: 1/2 is in the ball. it is around the point 1/3.

Good early morning, @J.M.

or is it late night?

1:50 AM could be either.

Ramana Venkata

@robjohn @Gortaur Ok I did a mistake the answer is [0,5/6)

robjohn

@Ramana: that's it!

Gortaur

17:50

hooray

I m from the phone, can read not write

J. M.

Hi @rob. just checking. I'm about to sleep; it's hard to do math with droopy eyes...

So, quoting your governor: Hasta la vista.

robjohn

@J.M.: pleasant dreams.

Gortaur

good night, JM

Mike Spivey

@robjohn: He's not governor anymore, is he?

robjohn

Not still.

Brown is governor again.

But Arnie is still the Governator!

Mike Spivey

17:55

When Arnold left did he say, "I'll be back"? And wasn't Brown governor a few decades ago, too?

robjohn

I don't think Arnold gave that line, but yes, Brown was the governor from 75-83

Ramana Venkata

@robjohn Can you give an example of a bounded set on R with exactly three limit ponts

Gortaur

take three distinct points

robjohn

@RamanaVenkata: can you think of a bounded set with exactly one limit point?

If so, then you can translate it and make a couple of copies.

Ramana Venkata

Okay I got Your point guys

Mike Spivey

18:00

@J.M.: If you're still here, good idea changing the "Moron" reference on that old binomial identity post from last year. I imagine it would have made no sense at all to new readers now that Moron has changed usernames.

robjohn

@Mike: ouch. I remember seeing references to Moron, and since it was capitalized, I figured it was an avatar name.

Gortaur

@Ramana which book are u readibg

damn. re-a-ding

Ramana Venkata

Principles of Mathematical Analysis - walter Rudin

robjohn

Great book!

Gortaur

cool book they say

robjohn

18:04

I used that in my first year analysis.

Gortaur

you see, again

Ramana Venkata

What do you mean they say??

robjohn

@RamanaVenkata: I assume he has not read it.

Gortaur

like, a lot of people say like this

yeah, I have not. studied analysis from Numenor manuscripts

robjohn

@Gortaur: before the flood?

Asaf Karagila

18:06

Hooray. I'm baking another loaf of bread!

robjohn

@Asaf: what goes into backing bread?

Gortaur

they wete quite old, without category theory, topology and axiom of choice

Ramana Venkata

I don't i saw that it contained a topic called Basic Topology So I started reading it

Asaf Karagila

@rob: backing bread? :P

robjohn

@Asaf: sorry, I couldn't resist.

Mike Spivey

18:07

@robjohn: Moron was one of the top users on the site from almost its inception until sometime around April when Moron changed username to Aryabhata. But there are still references in many old posts addressed to "Moron," which I imagine appears inexplicably insulting.

Gortaur

do you pur the bread in shower like chiken?

Mike Spivey

@robjohn: And there's the food you were talking about...

Asaf Karagila

I only bathe my chick, not my chicken :-)

What food?

robjohn

@Gortaur: touché

Asaf Karagila

Hello Mike.

Mike Spivey

18:08

Hi Asaf. My first extended time in chat.

Gortaur

@Ramana you don't what?

Asaf Karagila

I know, it is not without reason I generate about a quarter of the traffic in this chat... :-)

How do you like it so far?

robjohn

@Mike: yes, it comes up at some point most every day. I don't know about yesterday since I was overseeing a midterm at UCLA.

Gortaur

@Mike if bathing chicken for you is about food, then yes

Ramana Venkata

its just a mistake I just typed something while thinking something else I think

Mike Spivey

18:10

@Gortaur: I meant the bread. Although when I bathe my nine-month-old twins they do kind of look like chickens...

Gortaur

icic

robjohn

The showering chicken quote has been moved off the starred list.

Gortaur

@Mike 0_o7

Asaf Karagila

Anyway, I'm gonna make JM soooooo jealous.

Although this time we only have a good pesto, not awesome. Oh well. :P

Gortaur

how

Asaf Karagila

18:13

He lives in a place where olive oil is expensive, so he cannot use it often. Unlike moi who lives in Israel where olive oil is good, common and used for almost everything.

Mike Spivey

@Asaf: Chat's a lot more active than it used to be - There was hardly anybody on it a year ago, but it seems pretty active now.

Asaf Karagila

@Mike: Sure is, my part of the chat went down to a fifth! >:[

robjohn

@Asaf: I didn't think olive oil was very expensive anywhere. There must be a decent substitute there.

Mike Spivey

@Gortaur: "Gortaur" is a Tolkien reference, isn't it?

robjohn

@Mike: indeed

Gorthaur in the books

Sauron more commonly

Asaf Karagila

18:18

He uses butter.

And where there are no olives, there is no cheap olive oil.

robjohn

@Asaf: a substitute, but not quite as healthy.

Asaf Karagila

Indeed.

So in this bread there are chopped black olives, tomato and garlic.

robjohn

@Gortaur: Is the name Gorthaur mentioned in LotR or just in the later books (Silmarillion, etc)

Ramana Venkata

@robjohn Can you answer my last question once since I think I did some mistake ??

robjohn

@Mike: just after you joined this morning, I stated Gortaur's conjecture: One commutative Ring can rule them all. It was proved false by F. Baggins.

Asaf Karagila

18:23

I don't think it was commutative.

Frodo was just in the center.

robjohn

@Asaf: it sure moved around a lot

Asaf Karagila

Does that imply commutativity? I don't think so!

robjohn

It sure shows that it commutes.

Asaf Karagila

Not between everyone, though.

robjohn

Aha.

Asaf Karagila

18:25

Just the few people in the center...

Well. I'm going to preheat and finish preparing the bread.

robjohn

Thus, why the conjecture was proved false, it was annihilated by a member of its center

Ramana Venkata

@robjohn Can you answer my last question once since I think I did some mistake?

robjohn

@Ramana: you mean the limit point question?

Ramana Venkata

@robjohn Yes

Mike Spivey

@robjohn: Very nice. And I think you're right about Gorthaur being in The Silmarillion. I rember that Sauron had another name originally, but I didn't remember what it was.

robjohn

18:35

@Ramana: (2cos(2k\pi/3)+1)+(4cos(2(k+2)\pi/3)+2)+(6cos(2(k+1)\pi/3)+3)+1/k

now that is sneaky

(2cos(2k\pi/3)+1) is 1 for k=0 mod 3

and 0 for k = 1 or 2 mod 3

so the sequence for k=0 mod 3 converges to 1, for k=1 mod 3 it converges to 2, and for k=2 mod3 it converges to 3

so add 1, 2, and 3 to the set and you have a set with three limit points.

Ramana Venkata

can we prove that only 1, 2, 3 are the limit points of the set??

robjohn

what you can also do is just take the union of the sets 1/n and 1+1/n and 2+1/n

Asaf Karagila

The bread is in the oven.

robjohn

@Ramana: you can show that all the other points are isolated.

Ramana Venkata

yeah I agree

robjohn

18:42

That is they have a small ball around them that has no other points of the set

so those are the only limit points of the set

Ramana Venkata

@robjohn Are you a graduate student??

Asaf Karagila

lol :-)

robjohn

@Ramana: no, I was about 25 years ago.

The Chaz

:D

Ramana Venkata

Okay so what is your profession?

Asaf Karagila

18:50

A chatter... :-)

He sits here all day to chat with folks.

Mike Spivey

Nice chatting with you folks... I'm off to play some tennis. I'll have to drop by again sometime.

robjohn

@Ramana: I currently write software to teach logic to students at UCLA, and it is also used in about a dozen other schools.

@Mike: have fun!

@Ramana: I did teach math at UCLA for a couple of years a long time ago, though.

Asaf Karagila

@rob: You do? Interesting, what sort of software and how does it work?

The Chaz

@rob (ditto)

robjohn

@Asaf: the students use the software to do their homework and exams. It gives instant feedback as to whether the answer is correct and, if not, in most cases why it is incorrect.

Asaf Karagila

18:54

Interesting. CAS based?

That is they build proofs and it tells them what is wrong, or is it some multiple choice kind of thing?

robjohn

It knows the rules used for justification and as they enter their proofs it can tell whether it is right, and if not, it can often tell them why.

It parses the WFEs into its internal format and knows the rules (modus ponens, double negation, etc) and how to apply them

it can also match a WFE and tell whether it is an instance of another WFE and return the substitution used

in most cases.

Asaf Karagila

Nice!

robjohn

some cases it needs to get some information about the substitution from the user (in the form of a multiple choice question about which is the proper form they were thinking of)

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$Mathematics$ Mathematics