So is that something you can ask on the main site, rather than here in the chat room?

@DavidWallace @Gigili You're entitled to your opinions. Regards,

@DavidWheeler I am happy to have been called a blah synonymous with rowdy. Thanks for calling me that way.

And, if Jordan (or those who rant with well-defined plans.) could get away speaking whatever he wants in this room, I probably have other priorities than this room. Regards to all of you here, See you somewhere else.

@DavidWallace i could, but it seems so formal

umm, do you think that @KannappanSampath realized i was actually defending him?

I was looking back to see what you had actually said.

I'll have to be honest - I really don't understand Kannappan's remark that was directed at you.

i called him "rambunctious" as i recall. he took it to mean "rowdy" but i rather meant it as "youthful exuberance".

I think his first language is Tamil. He may have needed to look "rambunctious" up in a dictionary; and the translation may not have been a good one.

i suspect he had to look up the meaning, and unfortunately dictionaries do not do a good job of explaining the nuances

Jinx!

David Wheeler!

I have little sympathy for someone who dishes out insults, but appears to be unable to take what he hands out. I shan't be apologising to Kannappan.

when i was a kid, me and my sister played what is probably a common children's game: whenever we said the same thing at the same time, one would say:

Jinx! you owe me a Coke! and the other had to say their name before the first counted to 20

@DavidWallace On that note: my Oxford American Dictionary gives me "uncontrollably exuberant; boisterous." for rambunctious. This may not be very helpful but uncontrollably is already giving a bad impression. Then you look at "boisterous" and get "noisy, energetic, and cheerful; rowdy"

and see, i meant it in the sense of "cheerful, yet exuberant", and he probably took it as all the other things. i am so fugazi....

@DavidWheeler I think it's a peculiarly American thing; I have only learned of this game in the last couple of years.

yes, Americans are very peculiarly

@tb...in context, i was trying to argue people shouldn't be so judgmental of Kannappan

@tb And Kanna’s English is occasionally not entirely reliable; I think it almost certain that he misunderstood. The misunderstandings occasionally go the other way, too: he does not always mean things quite the way they at first sound.

@DavidWheeler Why don't you ping Kannappan just to tell him that "rambunctious" has a positive connotation, not a negative one? Of course, it's possible that he won't believe you.

Gigili's sudden exit makes me wonder if he hurt her feelings

I think Gigili is pretty resilient. In any case, Kannappan has said far worse things than that to her in the past.

ok, i SO don't want to know....sheesh

In any case, she's not active in any of the chat rooms that she normally hangs out in, so she's most likely off doing something else right now.

meh...it's not anything i can do aught about

Yeah, I'm not going to lose any sleep. Kannappan is not the first person whom I've managed to piss off in the SE chatrooms, and I doubt whether he'll be the last.

oh, i'm really good at pissing people off, and even better when i'm trying to

@BrianMScott I agree. I guess it's just too easy to forget that most of us here are not native speakers and that all sorts of colloquialisms and nuances are completely lost on us or misinterpreted by us (which leads to misinterpretations in the other direction, too). I observed quite a few situations where misunderstandings arose because people weren't quite clear on what they were saying or hearing (or writing and reading).

@tb We also get spoiled by folks like you, Matt, Henning, and even Asaf, who has an obvious written ‘accent’.

@DavidWallace i did ping Kanna once, i dunno if he noticed or not...

Well, if he wasn't around, it'll be in his SE inbox.

@DavidWheeler To be sure, do ping with the back arrow on the right, because for some people the manual @username thing does not work (this is the case for me and I know for sure that it is also the case for J. M.).

@tb I think you need at least three non-punctuation characters in your username for the pinging to work correctly.

Someone want to tell me what's going on here?

I don't know. I didn't see what was flagged.

But there's some tension in the room since early this UTC morning.

Guys, I have kannappan on skype. Let me speak to him.

What's going on with the convo with this statement here:

Hey @Ben I don't want to talk over this issue./

He's here in the room with us. He's just not talking.

@KannappanSampath What's going on

@casperOne It was a long time in the past.

@KannappanSampath He didn't mean it to you as an insult. Sometimes people accuse me of not being tactful (which is even worse than what someone called you above). Take it easy man.

13 minutes is an eternity in a chat room, I agree.

@casperOne That's not what I meant.

I would like the user to justify what I said was more worse than what Gigili had to say.

She would abuse my country and she would say what she wants.

@casperOne I don't know how many weeks ago there was a big clash between the two mentioned persons. They couldn't stand each other ever since.

@KannappanSampath No offense, but you can't make a user say something in chat that they don't want to. This is just not the way things work.

But I should not react.

It 's not that I want them to, but I would like them to.

@KannappanSampath I'm two years older than you, probably we have been in situations like that before. Common man whatever people say to you, just forgive and forget.

@KannappanSampath You can react, but just remember, the fundamental tenant of all SE sites still applies, BE NICE

And that applies to everyone on all SE sites, on the sites themselves, in meta, in chat.

@Kannappan - I didn't mean to bring up an old battle all over again. But I think you misunderstood some of Gigili's remarks in the earlier incident. Then it got out of hand. But it's a long time past now.

Yes, if this applies to every one, I am not sure, if Gigili's remark about my country men is nice

My only point was that today's argument was mild by comparison.

@KannappanSampath Then flag that message and someone will take a look at it. But don't go on a flagging spree, a) it's noise and b) it's chat.

@BrianMScott Well, I wouldn't take it serious anyway :-).

@KannappanSampath hey, i wasn't trying to insult you...we were having a conversation about Jordan, and i was trying to argue for more tolerance on the part of all concerned

That said, I don't see anything particularly egregious, yet. That said, everyone have a good day.

@casperOne I have not flagged in a spree. Is one flag considered that way?

@JonasTeuwen The gods/topology paper?

@Kannappan I would be genuinely sad if you chose to stop using this room. I think you often make a really good contribution here.

@KannappanSampath I'm commenting about possibly doing so in the future. Don't go back and flag a whole bunch of chat messages at once; it will more than likely be seen as retaliatory.

@JonasTeuwen Could you maybe take a look at leo's answer here if you have time? He's rewritten it and it looks quite okay to me, but I'm not terribly in the BV-mood.

@KannappanSampath If someone has made a remark about your countrymen, so what? Let them make such remarks! Remember, you can't control what other people say.

@MarianoSuárezAlvarez What was that about $A[x]$ being a left $A[x]$ module and a right $A$ - module? Aren't $A[x]$ and $A$ commutative so why the need for left and right?

I am in no mood for an argument--but one last thing to say: @David You have no right whatsoever to say something without defining what your conception of worst is... I have not reacted in a way that is more insulting than it was to the whole country where I come from.

@Kannappan - Also, can I stress David Wheeler's point again, and add that rambunctious isn't really a synonym of rowdy. Rambunctiousness is a good thing; rowdiness less so.

@KannappanSampath could you clarify that? i don't quite understand what you are trying to say

hmm...you were probably pinging Wallace, eh? nevermind

If it's not understandable, just flag that and I would be fine. After all, I am not going to use this room again.

@KannappanSampath Common man we need to tackle tensor products together!!

@KannappanSampath that would be rash

@DavidWheeler He has acted in a bit of a rash manner in the past. Especially that downvoting thing that happened.

@Kannappan - Gigili was trying to explain to you why she was offended by remarks of yours that she perceived as sexist. To show you why they might be considered offensive, she drew a parallel between racism and sexism. Her statement about Indians was part of a hypothetical example showing a parallel; I don't believe they truly reflect her views.

@KannappanSampath I really think that you’re being a bit hasty. Give it a rest for a while and then try it again.

@tb Will do!

Thanks, Jonas.

@DavidWallace What did Kannappan say to her that was sexist?

sigh i feel as if there are landmines lurking in every word

I think the problem here is this. When english is not your first language, you do use words that people who have english as their first language would find offensive.

@BenjaminLim Who cares? It was more than a month ago now. Sorry that I brought it up!

Conversely, if someone who has english as their first language says something to you that means something good, it may mean something bad due to the subtleties involved.

@DavidWallace yeah let's forget about it.

@BenjaminLim i'll drink to that

Could we forgo the post mortem? It seems more likely to harm than to help.

Can we maybe switch the topic? I don't think it will do anything good. It is bound to get people more irritated and irritable.

@DavidWheeler I have spoken to kannappan many times face to face on skype and he is an extremely intelligent person.

Brian beat me to it :)

Nah, I just reinforced you. Or vice versa.

Ok let's all forget about it. In a few days I'll talk to kanna on skype.

@tb Looks good.

Also nicely written. Maybe he forgot to mention "a.e.", but that doesn't really matter.

@BenjaminLim yes, he's very bright, and has a real talent for algebra, as far as i can see

@JonasTeuwen Great, thanks!

@DavidWheeler Him and I are supposed to be helping each other with commutative algebra

These are my favorite type of theorems.

@tb good idea

I was really looking forward to discussing tensor product with him..........

@JonasTeuwen every such theorem is a beauty in itself, yes.

Approximate units, some estimates, some implications on modes on convergence, in short everything the analyst needs to feel happy :)

Yes.

@Ben: do you happen to have some topology problem to think about?

@tb You have a topology problem for me?

Almost midnight here. Good night, everyone.

@tb Sigh, I got my knickers in a twist I used like a composition of 6 isomorphisms and now I have to compute something concrete from the isomorphism, gonna get ugly!!

@DavidWallace Forgot that kiwiland is 2 hours ahead of us!!

@tb analysts seem to feel like: well, i don't know what that really is, but it's smaller than something i do know what is, which i like much more.

Good night, David the down-underner

@BenjaminLim are you in Australia?

@DavidWallace yes i'm now in sydney

Do you like it there?

i'm australian.

6 isomorphisms? eeee!

That's not what I asked.

@DavidWallace Sorry, what did you mean then?

@DavidWallace Well it's a nice country but occasionally we have the problem of people getting maggot too much.

maggot?

Sydney is one of those places that people either love or hate. Not sure why.

@DavidWheeler to get drunk

@DavidWallace it's beautiful. I've been to london and I'm like naaah

@DavidWheeler I didn't understand him either.

oh yeah...they sell beer by the gallon there, amirite?

@BenjaminLim London’s a fascinating place, but I’d not want to live there.

I've enjoyed my visits to Sydney. I've never lived there. It just seems so ... big!

@DavidWheeler @DavidWheeler au.answers.yahoo.com/question/index?qid=20100627040603AAj9AuI

@DavidWallace where do you live, tauranga? hamilton?

@BrianMScott I know it's always like gloom and doom :(

Lower Hutt, just north of Welly.

@tb topology problem for me?

@DavidWallace My friend vince is now in VUW

@BenjaminLim Lots of bookshops!

@BrianMScott I know!!

That's where I studied.

They had one where there were a lot of springer UTM books!

@DavidWallace Never been to kiwiland

although virgin sometimes has cheap flights

Now after midnight and I really am going to bed. Good night everyone.

bye

It’s 0800 here, which is about time for this nightowl to go to bed. I’ll see you folks later.

@BrianMScott nite

See you, Brian! Sleep well!

@BrianMScott have a good sleep

@tb Hey Theo did you have a topology problem for me?

@DavidWheeler Yes I used like 6 isomorphisms

then realised I had to do a concrete calculation with them

fffffffuuuuuuuuuuu

@BenjaminLim Okay here's one: Let $X$ be a Hausdorff space and let $Y$ be arbitrary. A map $f: X \to Y$ is called proper (or sometimes perfect) if it is closed and $f^{-1}(\{y\})$ is compact for all $y \in Y$.

Yesterday we discussed that if $X$ is compact and $Y$ is Hausdorff then the projection $X \times Y \to Y$ is proper.

right

that came from the tube lemma

so we have that the preimage of every singleton set is compact?

Prove: If $f: X \to Y$ is proper and $C \subset Y$ is compact then $f^{-1}(C)$ is compact.

@BenjaminLim yes, because it is of the form $X \times \{y\}$, which is a product of two compact spaces.

@tb Right.

If you have two positive increasing sequences, $a_n$ and $b_n$, can you assume something like one increases faster than the other?

Can you give some context?

I'm thinking about this one.

I don't think such a reduction could possibly be justified.

Both take $n^{-1}$?

Uh, $n$.

Oh, wait.

:'). Should read.

@tb Any continuity assumptions here?

But each is increasing at some "rate". If I can assume something like $\frac{1}{b_n}$ goes to zero faster equals than $\frac{1}{a_n}$ then I'm done.

Never mind.

I'm interested in why nobody is taking my question about what a "variable" is seriously? I even included a link at the bottom...

@MattN It's a pretty tough problem, actually. See the solution to the duplicate

@tb Is $f$ a continuous function?

@BenjaminLim yes, the function is assumed to be continuous.

oh ok

Sorry, when talking about topology functions are continuous without explicit mention of the contrary (for me).

phew

@BenjaminLim lol i was just about to ask that myself

yeah

i tend to do that too

and maps always are at least continuous.

huh? This user's name means "meatloaf" in German :)

@tb Let's hope he's not in a sauer mood :-)

:)

@tb I

I will sleep over your problem

I have to go now

I stayed too long, I was only supposed to look at Mariano's comment

Good night!

night, thanks for the problem!!

@Rob well there are two different meanings one could ascribe to an equation $f(t) = a$. one is an equality of numbers, and in this view, $t$ is just an "unknown". another way is to see it as a set of intersection of the graphs of two functions, in which case $t$ is a "true variable".

@DavidWheeler Did you see the link at the bottom David?

the thing is, equations with numbers can often be generalized to equations with functions, but the equations look "just the same"

@BenjaminLim I should probably have emphasized that closed means that $f$ maps closed sets to closed sets, not that the graph is closed, of course (because that follows from continuity, provided $Y$ is Hausdorff).

@Rob i did, but so?

Okay, I have to go. BBL

@DavidWheeler Just wondering what you thought about it?

well sometimes you DO want to make the distinction...it's "context-sensitive"

Especially the line .. a rose is a rose is a rose only means something if you know what a rose is .. @DavidWheeler

@Rob there's that problem with almost all definitions

suppose i have an equation 2x - 5 = 3

it turns out that x = 4.

so why didn't i just write 2(4) - 5 = 3 to begin with?

because there are rules that apply to "expressions involving x" (even if we have no idea what x is) that are very similar to rules involving numbers (ordinary arithmetic)

and we can use that knowledge about the "more general thing" to later discover a fact about a number

Here x is a specific unknown.

let me give another example: suppose $x^2 - 16 = 0$

we want to solve this, so we factor $x^2 - 16$ as $(x + 4)(x - 4)$

that "factoring step" uses x as a complete variable, it is true no matter "what" x is

Here x is two specific unknowns.

more formally $x^2 - 16 = (x + 4)(x - 4)$ for all x

it is an equivalence of two functions $f$ and $g$, where $f(x) = x^2 - 16$ and $g(x) = (x + 4)(x - 4)$

after doing that "purely functional" step, we then "pull back" to numbers to conclude $x = \pm 4$

do you see what i'm getting at? we actually have two different meanings for x, but we're using the same symbol for both

in "higher math" (like linear algebra, or group theory) the situation becomes even more blurred, but a similar thing is going on.

the letter "v" might stand for a particular element of a vector space V, or a completely arbitrary one

Don't the phrases: "a particular element" and " a completely arbitrary one" have opposite meanings?

in other words, something like x+4 might mean: the function f(x) = x+4, or it might just mean x+4 for some x we have in mind

"opposite" might be too strong a word

they are dual concepts...two extremes of a range

in an expression like "ax^2 + bx + c$ the ambiguity is even more pronounced

is that a function of x, of a,b, and c or of all 4?

in all honesty, there's a world of difference between the function f(x) = x+4, and the number x+4, but it is a common abuse of notation to identitfy them, which leads to the type of confusion we are talking about now

What I'm trying to say is that at the particular end of the range the "vari-able" loses its ability to "vary."

another word which suffers from the same type of problem is "parameter"

yes, Rob, that is true...and perhaps it is unfortunate that people use "variable" when what they MEAN is "unknown" but language usage isn't always strictly logical

@DavidWheeler Thank you for the clarification.

@Rob if you look at systems of simultaneous equations, you can see "both things happening at once" often you get equations where x, and y might have to be particular numbers, but z can be anything.

but you can't tell that just from looking at the equations

and in this situation the term "free variable" is introduced to distinguish between the two

@DavidWheeler Indeed, and as you said it is all very "context-sensitive."

this same sort of thing can happen anytime you go from "concrete" to "abstract"

at the "concrete" extreme...you have "facts"....at the "abstract" extreme you have "rules"...but most of the time, we're somewhere in the middle, mixing and matching as it suits us

@JasperLoy so what options do i have for not doing that?

@Rob like this?

@DavidWheeler That works :-)

@DavidWheeler In a more particular and concrete way.

lol

To ping only me.

well i am going to sleep a bit..i'm seeing pink elephants

@DavidWheeler Bye and thanks again.

@DavidWheeler Feel free to leave an answer on the post.

here

@tb It's ok I knew you were talking about closed maps :D

@JasperLoy Thanks for the spell check.

@JasperLoy Or should I say "Thanks for the spelling correction?"

Thanks for the punctuation check also.

how is a derivative different from a slope at the point? seems the same to me

stewart really does a poor job of explaining concepts

According to stewart The tangent line is a line through a,f(a) whose slope is equal to the derivative of f at a

but that doesnt appear to be true

for example y = x^2 the derivative is 2x and at 2 the function will equal 4

I mean the derivative

but finding the tangent line $\frac{f(2) - f(a)}{x-a}$

that will not equal 2

@tb How "modern" is this Plateau's problem book? Apparently nobody still uses "varifolds".

so if I evaluate at f(3) I get 3.1 for the tangent line and the derivative is 6

Steward said that the tangent line is the same as the derivative

the derivative should equal the slop of the tangent line

according to stewart

yes, the instaneous rate of change at a point

wahts the problem?

I am just trying to find these mathematically

stewarts claims the the tangent line should equal the derivative

but it doesnt seem to be true

for y=3^2 I get 3.0001 for the tangent line and I get 6 for the derivaitve

whats a gradient? Stewart hasnt introduced that word

$\frac{f(a+h)-f(a)}{h}$

or actually I did $\frac {f(x) - f(a)}{x-a}$

$\frac{3^2 - .0001^2}{3-.0001}$

stewart tell me that lim as x approaches a is equal to to that

I am going through my book right now

so the tangent line is just a line but the slope of the tangent line is the derivative?

You don't have the right equation for the difference quotient, in your calculation.

It is from Stewart

What you want is $\frac{(3.0001)^2 - 3^2}{.0001}$

The tangent line to the durve y = f(x) at the point P(a,f(a)) is the line through p with slope $m = lim x approaches a \frac{f(x)-f(a)}{x-a}$

$f(a) = (3.0001)^2$

as far as i can tell

what is a tangent line then? just the slope?

The thing you said above, $\frac{3^2 - .0001^2}{3 - .0001}$ doesn't make sense

the tangent line is an equation of a line (y = mx+b)

the slope, m, is the derivative at the point, and the y-intercept, b, will depend on the curve and the point.

but what the hell is a tangent line? how do I figure out a tangent line?

Does anyone know how to put an arc over a pair of letters? \overarc{AB} doesn't work.

once you calculate the derivative you use the point-slope form of a line.

$y - y_0 = m(x - x_0)$

tangent line is $\frac{f(x)-f(a)}{x-a}$ so if I want to find x^2 at 3 $\frac{3^2 - .0001}{3-.0001}$

no no no no

that isn't the tangent line

So stewart is wrong?

@Jordan The tangent line is a line that can be moved along the curve.

the LIMIT of that as x -> a is the SLOPE of the tangent line

at the point a

Touching it at one point. @Jordan

I have to go get ready for class, etc. good luck.

@Jordan Can you picture a line segment moving along a curve touching it at only one point?

yes, the slope of the line?

So the slope of that line is given by the derivative evaluated at that point on both the line and the curve.

so what I am calculating is the tangent line

but the slope of the tangent line will give me the derivative?

Not quite.

I guess that is what m means, stewart keeps using m without defining it

according to this book those two equations are equal

Yes, m is the slope of the line but there must be some particular point along the curve to evaluate it at.

@JonasTeuwen It was written in the seventies. However, varifolds are still used or at least they were still used 10 years ago. In a course on geometric measure theory I had twelve years ago (following Leon Simon's lecture notes), we exclusively used varifolds. If you want a more modern thing then look at Frank Morgan's Beginner's guide but that one is more than twice as long.

@Jordan Go back to the picture of the line moving along the curve and touching it at only one point. Now fix that point on the curve.

@Jordan Let's say it has x-coordinate 2 and y coordinate 3.

@tb Oh, my advisor said it was old-fashioned wording :-). He read the book by Federer... I think. (btw, it is published in 1966)

@Jordan If you substitute those coordinates into your derivative, you will get the slope of that line.

the slope isnt 3/2

?

@Jordan It maybe, but that depends completely on what you get after substitution into the derivative.

say y=x^2

dy/dx=2x

@JasperLoy I know that one, but it is thick.

Or Federer.

@Jordan take the point (2,4)

@JasperLoy I'm not asking for easy. I'm asking for a short introduction.

I cant make it work

@Jordan The slope at that point is 4.

Atiyah-MacDonald is also short, but I wouldn't call it easy.

it isnt 2?

wahtever I give up this is too ahrd and people here are just going to laugh at me so thanks for the help but I am done. I have to go figure out how I can waste all my time and money in a community college

@Jordan 2 is the slope from the origin to (2,4)

@Jordan stick with me

I hear terrible things about Lang's books constantly. I took a look through his Complex Analysis book when I was in the library the other day though, and it didn't look THAT awful...

It didn't throw you into residues or several variables or anything like I'd come to expect, hearing some people talk.

then people need to quit fucking starring my comments

:o

@Jordan y=x^2 is a parabola right?

fuck you

Although one of the funniest things I've ever read in a math textbook did come from a Lang book

@Jordan me?

This one, in fact: mathoverflow.net/questions/10897/…

the people who think it is hilarious to keep tagging my comments

STOP

like I am sure it is just hilarious for evreryone that I have trouble grasping concepts that you slept through when you were 14

I must have an awful sense of humor then :p

@JonasTeuwen well, that Federer advocates currents is no surprise, is it? :) anyway, varifolds have their virtues: they capture the geometric intentions nicely, while currents are more abstract. It is (tautologically) a bit like the measures versus functionals philosophies in measure theory.

@JasperLoy I've never seen Cohn's books. Are they just called Algebra?

oh... what a bummer!

@Jordan Do you follow me so far?

Nice chatting with you all, bye

@Jordan Can you see the graphic I found on wiki under "derivative"?