Mathematics - 2014-06-18 (page 1 of 6)

Pedro Tamaroff

12:35 AM

@robjohn

@seaturtles !!!

Hello.

sea turtles

hello

Pedro Tamaroff

What's up?

Com Truise

well

I must go for coffee , back in 15

lol wut

ey yo

can some buddy help me understand continued fractions? i kno tha def'n and i am comfy with it n all. yet i still don't get what info about a number its continued fraction conveys

besides obvious ones like the ability to determine whether it is rational

robjohn

12:58 AM

@PedroTamaroff yes?

Pedro Tamaroff

@robjohn Still getting those daily downvotes.

=/

robjohn

@PedroTamaroff oops.. I have to take my dog to the park... I will look when I get back. If I don't see anything, you should contact the community team. I'll be back in a bit.

Ted Shifrin

rehi mr @pedro

hi @robjohn ... I just got some revenge downvotes, I do believe :P ... a few hours ago

Pedro Tamaroff

@TedShifrin Hello.

So you won't be around July 28th to August the 8th?

Ted Shifrin

I'll be back from CA August 1st.

robjohn

1:01 AM

@TedShifrin we have a lot of that going around. For the most part, we have to bump these upstairs to the community team. I will take a look when I get back.

Ted Shifrin

I don't recognize mr @seaturtles's new look.

Have a good walk with the dog, @robjohn :)

Pedro Tamaroff

@TedShifrin What does that mean? Back in Georgia?

Ted Shifrin

yes, @Pedro

Pedro Tamaroff

Well, I'll be in NJ by that time, so I can go to Georgia, if you want.

Ted Shifrin

oh, I thought you had ruled that out ... I was pondering flying up north, but I just have too much to do and too much traveling -- have to go to DC a month later.

Pedro Tamaroff

1:05 AM

So... is that a good plan for you, that I buy a ticket and go there say August the 2nd? Or do you prefer some more slack time? I was thinking about staying three days or so.

Mike Miller

@PedroTamaroff You realize NJ and GA are nowhere near each other, yes?

Ted Shifrin

Heya @Mike

Pedro Tamaroff

@MikeMiller Yeah, it is a 4h fly or something of the sort... not that much.

Ted Shifrin

no, it's only 2.25 or so hours by plane ...

But airfares are totally ridiculous now. And I don't know if the train is much better.

Com Truise

I want to prove something cool and be famous

Ted Shifrin

1:08 AM

Famous, mr @Com?

Com Truise

yeah thats why I do math

lol wut

fame is overrated (speaking from experience)

Ted Shifrin

I've done a bit of good math, but I'm totally NOT famous.

Com Truise

but it is not easy

Pedro Tamaroff

@TedShifrin Do you think they'll simmer down a little, or should I buy the ticket now...?

Ted Shifrin

1:09 AM

I dunno, @Pedro. The worse things get in the Middle East, the worse fuel prices will get. I honestly don't know.

Mike Miller

@PedroTamaroff I didn't realize you could afford to take long distance flights on a whim :P

Ted Shifrin

It's whimsy, @Mike.

I thought you were in NJ until August 20 or so, @Pedro.

lol wut

yea send me sum money @PedroTamaroff

Pedro Tamaroff

@MikeMiller On a whim? What do you mean? I've been saving money for this trip.

Mike Miller

That sentence is perfectly valid, @Ted

Pedro Tamaroff

1:10 AM

@TedShifrin I'm leaving on August 20.

I arrive on July 28th.

Ted Shifrin

See, my memory is not totally shot :P

I know, @Mike ... I was editing for humor.

Com Truise

maybe Math needs to start over again. It was once easier to be famous I think, but now all the major foundational theorems are proven. If you can solve any new problem today, it seems it must be a very obscure, highly technical problem

Mike Miller

@TedShifrin Ah, we won't have to fight about it then

Ted Shifrin

We are no longer at the time of Archimedes and Euclid, @Com

Are you in a pugnacious mood again, @Mike? Just 'cuz you graduated?

@Mike: I saw someone else I've talked math with a bunch here (mostly through answers and comments) is starting his Ph.D. at UCLA in the fall (after masters at NYU).

Mike Miller

Name?

Ted Shifrin

1:13 AM

Oh oh, @AWertheim hath returneth.

@Mike: Eric Auld.

AWertheim

Hello, @TedShifrin!

lol wut

@ComTruise just invent a new field

Mike Miller

@TedShifrin No, I'm always in a fighting mood.

Ted Shifrin

Um .... great.

Mike Miller

@TedShifrin I'm pretty sure I recognize him from the visit day. If he's who I'm thinking, he was a cool guy.

Com Truise

1:15 AM

you are right, if I make up a new area, then I can prove the foundational theorems and be famous

Ted Shifrin

We've mostly discussed multivariable analysis and geometry/topology stuff ...

Famous provided the area and the results are interesting, @Com

Mike Miller

I don't understand the interest in being famous. Do math because it's interesting.

Ted Shifrin

It is?!

lol wut

@ComTruise yep, the kicker is that the new field needs to add insight to something mathematical that already exists

Mike Miller

There are better ways to become famous...

lol wut

1:16 AM

@MikeMiller wait, wtf?

Ted Shifrin

I was so furious 5 hours ago ... The offender finally yanked his sketch of a solution of someone's takehome exam question.

Mike Miller

@lolwut i don't understand wanting to do math for reasons of fame. is that rephrasing better?

lol wut

@MikeMiller c gbe.poyrre

Pedro Tamaroff

@TedShifrin Can we agree on something? =P

Ted Shifrin

@Pedro: What do you want to agree on?

Com Truise

1:17 AM

Well, that person should not have posted their takehome problem here anyway

Mike Miller

idgi, @lolwut

Pedro Tamaroff

@TedShifrin On we meeting.

Ted Shifrin

Of course, @Com, but that doesn't make it right.

AWertheim

@TedShifrin: were those downvotes reversed after all?

Ted Shifrin

Oh, sure, @Pedro. I'd prefer some days to recuperate from CA ...

lol wut

1:18 AM

@MikeMiller your foolishness makes me type in tongues

Ted Shifrin

No, @AWertheim

Pedro Tamaroff

@TedShifrin OK. We can do something like 4th to 7th.

AWertheim

Hmm, that's not cool. :(

Ted Shifrin

I can afford the 10 downvotes, @AWertheim; it just pisses me off.

Com Truise

it seems like Graph Theory is still a hot field, but frankly I am just not interested in it

AWertheim

1:19 AM

Sure, it's not so much about the rep, it's just really childish and petty. Sad to see from a contributor whose posts I ordinarily very much enjoy.

Ted Shifrin

Sure, @Pedro, that's fine. Communicate with me about times, though, because ATL rush hour traffic is horrendous, and it's 85 miles from my house to the airport.

Pedro Tamaroff

@TedShifrin 85 MILES!!!!!!!!!!!!!

Shouldn't I choose a better arrival spot?

Ted Shifrin

Well, @AWertheim, I'm just suspecting he did it because of the timing. But it could be totally unrelated. (Hmm.)

lol wut

that's the size of a block in the us

Ted Shifrin

There isn't one, @Pedro. The US is huge.

Mike Miller

1:20 AM

a few more exclamation marks and that sentence might be 85 miles long, @PedroTamaroff

Ted Shifrin

LOL

There used to be flights into Athens on US Air, but those stopped 10 years ago.

Pedro Tamaroff

@TedShifrin Woah. OK. I'll try to give you all the info.

Com Truise

I have been to Athens, GA

small world

Ted Shifrin

Oh yeah? @Com ... And you didn't come say hi?

Com Truise

hehe, it has been several years

Ted Shifrin

1:22 AM

I've been here 33 years so far ...

But not planning on being here too much longer ...

Com Truise

you are professor at the university?

Ted Shifrin

Yuppers.

AWertheim

@TedShifrin: where to next?

Com Truise

in what area?

Ted Shifrin

I'll decide this summer, @AWertheim, but I'm seriously thinking of retiring to San Diego, where I have some very good friends.

@Com: Differential and complex differential geometry

AWertheim

1:23 AM

Ah, San Diego... lovely!

Ted Shifrin

I'm tired of the South, to be honest ... although the whole country sucks rocks, if you ask me. ...

Com Truise

oh I was interested in diff. geometry at one time, working through general relativity. I did not make it as far as I wanted because it seemed to be heading into differential equations

AWertheim

Heh, I can understand that. I loved Duke, but the south in general... a different story, sometimes.

Ted Shifrin

There's a lot of hard analysis/PDE in parts of diff geo, but that isn't the sort of stuff I did, @Com ...

Yup, @AWertheim. I spent 18 years in Berkeley and 10 in Boston, so after 34 in GA, I'm ready for a change :D

AWertheim

:) How were your years in Berkeley?

Com Truise

1:27 AM

I wanted to prove this en.wikipedia.org/wiki/Sphere_theorem

it seemed like a beautiful theorem to me

Ted Shifrin

@AWertheim: kidhood and then grad school ...

Yes, @Com: I actually have not read Brendle's proof.

That's very deep stuff ...

AWertheim

Happy times. It seems like a great place to be.

Ted Shifrin

Things have changed a lot over the years, @AWertheim. I'll be back visiting the Bay Area for a week this trip, so I can report back to you.

AWertheim

Haha, I'll be waiting! :D

Com Truise

its one of those odd things... why 1/4? mysteries of the universe

Ted Shifrin

1:31 AM

Because $\Bbb CP^n$ has sectional curvature between $1/4$ and $1$ (suitably renormalized). @Com

Com Truise

well

Ted Shifrin

well?

Mike Miller

1:46 AM

well well well

:-)

Well, fuck.

jumps down the well

Pedro Tamaroff

Ted Shifrin

1:49 AM

Do we need to resuscitate you, @Pedro?

Pedro Tamaroff

Rules stop Peter from posting the third picture.

lol wut

rules are meaningless

thats why i just ignore them

Com Truise

Ted Shifrin

I don't have vertigo, but that picture gives me it.

lol wut

it looks like there's a path on the mountain to the left

that is obscured from view

Pedro Tamaroff

1:52 AM

@lolwut You do look both ways right?

Ted Shifrin

Cagey, putting it at the back to sucker you into thinking that ...

That looks like Buenos Aires driving, @Pedro.

lol wut

@PedroTamaroff i only look to da righ

Com Truise

its the car's fault

shoulda swerved left

lol wut

@PedroTamaroff a shoe flies off, but also something white, not sure what that is

Com Truise

did that person live?

Pedro Tamaroff

1:56 AM

I don't know.

robjohn

@PedroTamaroff There was enough evidence that I've kicked the case upstairs.

Pedro Tamaroff

@robjohn Mine too?

Thanksies.

robjohn

@PedroTamaroff That was mistakenly sent to Ted

Ram

Hi all, is intersection of open affine set and closed subvariety is closed?

robjohn

@PedroTamaroff I don't think they will reverse the downvotes, but they are keeping an eye on the people responsible. The thing is, that people are allowed to vote as they see fit, and it is hard to tell them they are acting inappropriately. However, some people have a downvote/upvote ratio that is greater than 1, when the average ratio is quite a bit smaller than 1.

Pedro Tamaroff

2:01 AM

@robjohn Well, I do have a complaint to make, while we're at.

There is a group of people in the site that happens to have a "buddie upvoting" kind of mechanism, i.e. one in the group posts stuff and the others compulsively upvote and leave comments such as "+1 great answer" religiously. I don't know how far that goes or what other behaviour they endorse, but I don't like it at all.

robjohn

Those people whose downvote/upvote ratio is greater than one must see this place as below their standards. I suggest they either leave, as this site obviously is not helping them, or leave helpful comments along with or in place of their downvotes to help improve the site.

@PedroTamaroff The moderators have been complaining about these people to the community team as well, but for the same reasons, it is hard for them to act. However, they do act on the directed voting that happens in these groups, but it does not seem to be enough.

Pedro Tamaroff

@robjohn Have they thought of tougher measures?

To be honest, their contributions are usually on low level questions anyone can handle.

robjohn

@PedroTamaroff I have noticed this as well.

AWertheim

@PedroTamaroff: worse yet, some of these contributions seem to be redundant, verging on plagiarism.

Pedro Tamaroff

Yes.

robjohn

2:08 AM

@AWertheim I'd agree, but that might give away whom I am talking about :-)

AWertheim

@robjohn: I have a pretty good idea myself. :)

Pedro Tamaroff

We all know who we're talking about!

robjohn

It is dinner time... gotta go for a while... BBL

AWertheim

Have a nice dinner, @robjohn.

Pedro Tamaroff

@DemCodeLines How's your calculus going?

Mike Miller

2:17 AM

I hope he's seeing a dentist for it

DemCodeLines

@PedroTamaroff It's going...

@MikeMiller idgi

calculus = plaque

never knew dat

i think I need a break from math, and to then be somehow reinspired

lol wut

2:22 AM

somehow

DemCodeLines

lim x -> pi/2 ((2sec x + 1)/(tan x))

how would i do it?

Com Truise

Try writing as 2 fractions

see what happens

lol wut

don't. the world falls apart if you do

DemCodeLines

lim x -> pi/2 ((2sec x)/(tan x)) + lim x -> pi/2 ((1)/(tan x)) ?

Com Truise

yes now rewrite the trig functions

DemCodeLines

2:25 AM

i suck at trig

like really bad

and trig identities seem to be a serious weakness

Com Truise

just use the definition of sec and tan

DemCodeLines

1/sin and tan

lol wut

nah

Com Truise

sec is 1/cos

tan is sin/cos

DemCodeLines

what's csc?

Com Truise

2:27 AM

1/sin

lol wut

one of the meanings of $sin^{-1}$

DemCodeLines

csc, sec, cotan. so it's 1 over (sin, cos, tan) the appropriate position.

So csc = 1/sin

sec = 1/cos

cotan = 1/tan

Com Truise

yes. what does the limit look like after replacing sec and tan

DemCodeLines

(2(1) / cos x * (sin x / cos x)) + (cos x / sin x) ?

= ( 2 / sin x) + (cos x / sin x) ?

Com Truise

yes

now take limit as x to pi/2

DemCodeLines

2:32 AM

= (2 + cos x / sin x)

= 2 + 0 / 1 = 2

?

Com Truise

yes

done!

DemCodeLines

So it's not that hard after all. I really just need to know the identities and the unit circle.

Com Truise

yes sometimes the trick to finding limits is playing around with the function

lol wut

that's about all there is to trig

Pedro Tamaroff

@seaturtles Hey! I've heard there was a massive tornado in Nebraska. =/

sea turtles

2:37 AM

two

perfectly fine weather in omaha

Pedro Tamaroff

Oh, OK. I was worried. =P

lol wut

makes divide by zero joke

DemCodeLines

Here's another one:

Com Truise

fire away!

DemCodeLines

"Use analytical methods to evaluate the following limit."

lim x -> infinity (sqrt(x+2) - sqrt(x + 7))

Com Truise

2:46 AM

do you know the epsilon delta definition of limit?

DemCodeLines

Do i start with separating them again?

Com Truise

not sure what is meant by analytical methods

DemCodeLines

Well forget the "analytical part". How would you "evaluate that limit"?

sea turtles

multiply/divide by conjugate

DemCodeLines

@seaturtles You gotta speak to me as if I don't know anything, since...I don't know anything. :D

Com Truise

2:48 AM

that seems reasonable

sea turtles

@DemCodeLines how would you simplify 1/(1+sqrt(2)) ?

you would multiply and divide by the denominator's conjugate, 1-sqrt(2)

Com Truise

You should be able to graph the functions sqrt(x+2) and sqrt(x + 7). This will give you an ideal of what the differences approaches as x to infinity

sea turtles

what is the conjugate of sqrt(x+2)-sqrt(x+7) in this case?

DemCodeLines

sqrt(x+2) + sqrt(x+7)?

sea turtles

yes

so multiply/divide by that

the denominator is simply that sum

the numerator is sqrt(x+2)-sqrt(x+7) times sqrt(x+2)+sqrt(x+7)

what does that equal?

you should have the formula (a-b)(a+b)=a^2-b^2 ingrained in your skull permanently

DemCodeLines

2:53 AM

I did ((sqrt(x+2)-sqrt(x+7)) / 1) * ((sqrt(x+2) + sqrt(x+7))/(sqrt(x+2) + sqrt(x+7)))

and got 9 / (sqrt(x+2) + sqrt(x+7))

sea turtles

(x+2)-(x+7) is -5 not 9

but otherwise yes

what does 9/(blah) go to in the limit?

DemCodeLines

I thought (sqrt(x+2) - sqrt(x+7)) * (sqrt(x+2) + sqrt(x+7)) would take out the square roots and yield x + 2 - x + 7?

sea turtles

(x+2)-(x+7)

DemCodeLines

oh right

x + 2 - x - 7

so -5

how would i get the limit of (-5 / sqrt(x+2) + sqrt(x+7)) if x approached infinity?

sea turtles

-5 / (thing that goes to infinity), hmmm

DemCodeLines

3:00 AM

It's apparently 0.

But I don't get it

sea turtles

you don't get how dividing -5 by arbitrarily big numbers gets you arbitrarily close to 0?

or by "I don't get it" do you actually mean "how do I translate that into formal proofstuff"?

DemCodeLines

Yes, my brain, right now, is going step by step and proof by proof

Com Truise

you have to notice that the square root functions go to infinity as x does

DemCodeLines

But I guess it does make sense that as the denominator increases, the number approaches 0.

sea turtles

a blind person taking a hike step-by-step will not get to a destination very quickly, or even at all; you need to be able to see where you're going

DemCodeLines

3:04 AM

Here's another one. Ready?

A little more tricky.

lim x -> -8+ ((1/(x+8)) - (1/sqrt(x+8)))

Com Truise

common denominator maybe?

sea turtles

is that 1/x+8 or 1/(x+8)?

please use parentheses

Com Truise

you gotta play around with the functions a little

DemCodeLines

Sorry, corrected.

sea turtles

if f(x) diverges and g(x) converges to a nonzero constant, then f(x)g(x) diverges

ah, nevermind

if f(x) and g(x) both go to one of the two infinities then so does f(x)g(x)

factor out sqrt(x+8)

(that's just my thinking)

Com Truise

3:14 AM

you got it?

sea turtles

yes

Com Truise

@DemCodeLines

sea turtles

oh, mixed you up with him/her

slinks into corner

Com Truise

hehe its ok

DemCodeLines

No, didn't get it. The answer is infinity, but I don't know how it's solved.

Com Truise

3:17 AM

try this: (1/(x+8)) - (1/sqrt(x+8)) = (1/(x+8)) - (sqrt(x+8)/(x+8))

Pedro Tamaroff

@DemCodeLines What are you trying to do?

sea turtles

shun the nonscroller

Pedro Tamaroff

scrolls

Com Truise

do you see what to do now @DemCodeLines

Pedro Tamaroff

Dam son that's a long scroll.

@DemCodeLines Do you have ChatJAX?

Com Truise

3:19 AM

what is scroll

sea turtles

not sure if nonnative of English or of internet

Pedro Tamaroff

Not schur.

sea turtles

heh heh

Pedro Tamaroff

@seaturtles I don't learn from my mistakes.

I should be studying combinatorics, not algebra. Heh.

But Lang is too cool.

skullpatrol

@Com Truise scroll is to look further up the chat transcript.

Com Truise

3:22 AM

I just finished Algebra

Galois is a sick dude

DemCodeLines

I am doing a test review by the way.

So I have the option to do "Help me solve this"

Com Truise

did you get the last problem?

DemCodeLines

Well I hit on it and it made me arrive at the equation: (1 - sqrt(x+8))/(x+8)

The one that @ComTruise gave above.

Com Truise

yes use that

sea turtles

expression (equations equate things with equal signs)

DemCodeLines

3:24 AM

Then it me that 1 + sqrt(x+8) approaches 1 (1 + sqrt(-8 + 8) = 1) and (x+8) approaches infinity (or undefined since -8 + 8 = 0).

Com Truise

so the top goes to 1 and the bottom goes to 0 (from above). So the limit is ininity

DemCodeLines

So since the denominator approaches infinity, the limit as a whole is infinity.

Pedro Tamaroff

@DemCodeLines In general, use that sqrt(a)-sqrt(b)= a-b/(sqrt(a)+sqrt(b))

Com Truise

no the demoninator goes to 0

you are letting x to 8+

DemCodeLines

Oh right, it goes to 0 and since it's undefined, the limit becomes infinite.

Com Truise

3:25 AM

no

the top is approaching positive constant 1

DemCodeLines

Where'd I go wrong?

Com Truise

and the denom is going to 0 from above

so the limit is infinity

DemCodeLines

1/0 -> infinity?

Pedro Tamaroff

NOT THIS AGAIN.

Com Truise

do not think of it that way

this is a common problem for calculus students

skullpatrol

3:27 AM

YES THIS AGAIN :-)

DemCodeLines

$2^2$

Com Truise

there is a little finesse required with limits

DemCodeLines

Works!

lim x->0 (sin x)/x

THat would be 0, I think.

Pedro Tamaroff

No.

Com Truise

which side is x going to 0 from?

Pedro Tamaroff

3:32 AM

What is the derivative of $\sin x$ at $x=0$; @DemCodeLines?

DemCodeLines

1?

Com Truise

ignore my comment

Pedro Tamaroff

@DemCodeLines Yes.

There you go.

DemCodeLines

SO, undefined then is the answer.

Com Truise

undefined is never the answer on a limit problem

real number, +/- infinity, or does not exist

DemCodeLines

3:37 AM

What if the multiple choice is 1, 0 or undefined?

Com Truise

well on this problem it is 1

Pedro Tamaroff

@DemCodeLines sin x / x = (sin x - sin 0)/(x - 0)

DemCodeLines

"Draw a graph to match the description given."

"F(x) has a negative derivative over (- infinity, 1) and (6,9) and a positive derivative over 1,6) and (9, infinity)."

How would I go about graphing this?

Com Truise

negative derivative corresp. to negative slope

sea turtles

replace "negative derivative" with "is going down" and "positive derivative" with "is going up"

Com Truise

3:45 AM

your calculus teacher should have made this clear

DemCodeLines

Sadly, my calculus teacher is awful. That's why I am here reviewing for my test with you guys.

Not that I wouldn't be here otherwise. I'd still be here, but I wouldn't be asking to teach me every single thing.

Com Truise

any super tough questions for me?

DemCodeLines

Find the intervals on which f is increasing and decreasing. Superimpose the graphs of f and f' to verify your work. f(x) = 10 - x^2

Pedro Tamaroff

@ComTruise Suppose $A$ is a ring such that for every $n$ there exists a surjection $A\to \Bbb C[x_1,\ldots,x_n]$. Can $A$ be Noetherian?

@seaturtles $\uparrow$

@DemCodeLines Well, did you do it?

DemCodeLines

@PedroTamaroff I thought he was talking to me. So I gave him the question I was currently on.

Com Truise

3:54 AM

A Noetherian iff every submodule of A is finitely generated

Pedro Tamaroff

Did you find the intervals?

DemCodeLines

don't know how to

Com Truise

oh you are calling the ring A

A Noetherian iff every ideal of A is finitely generated

Pedro Tamaroff

A differentiable function is increasing on an interval if it's derivative is positive there, @DemCodeLines

@DemCodeLines Review your theorems =)

Com Truise

lol

Pedro Tamaroff

3:55 AM

@ComTruise Ideals are the submodules of $A$, yes.

Com Truise

hmm

Pedro Tamaroff

It's an open problem. Don't waste your time. =P

Com Truise

seriously?

Pedro Tamaroff

Yes.

Com Truise

LOL

I would have tried

to prove "no"

Transcript for

$Mathematics$ Mathematics