Mathematics - 2015-05-09 (page 1 of 4)

anon

00:02

you need to compute the components of one force, using the other force's direction as an axis. well, if the angle is bigger than 90, to compute the component in the other force's direction you need to cosine that angle, or you could cosine that angle's supplement and then negate the resulting value, either way works

Maximilian

so only if it is over 90 I do 180-angle?

the problems i did in the homework seem like i always just did it that way unless it was worded. Very confused:(

I got the same number though, at least for cos120 and cos60, but cos120 was negative and that made me add the number since the formula is subtract

anon

you shouldn't be trying to memorize rules you don't understand

figure out why you're computing whatever. have geometric understanding.

Maximilian

I don't know why

Book doesn't really say why either, I have no idea how i even figured it out before

Im like freaking out for this test, and feel like I've forgotten everything

:/

robjohn

00:33

I haven't seen Chris's sis around for a while.

user147690

yesterday, by Chris's sis

@robjohn The form you got is nice.

user147690

They talked to you yesterday haha

robjohn

@AlexClark Yes, and that is the last time I saw her. That is a long time for her not to be here.

user147690

@robjohn Fair enough. Wait how did you change your picture to inactive?

robjohn

@AlexClark pardon? which picture?

user147690

00:45

@robjohn Your gravatar(or whatever it is called) top right grayed out when it was the first on the list, I have never seen this happen before

robjohn

@AlexClark I edited a deleted chat comment, just because it seemed possible. It is marked as edited in the history, but is still deleted.

user147690

@robjohn And that set you to inactive?

robjohn

@AlexClark Perhaps it had something to do with that. The software may not be able to handle it.

SpawnKilleR

Hey guys, can you actually talk about questions in this room ?

robjohn

:21543779 no, it was one of mine that I up-arrowed to.

user147690

00:48

Oh okay

user147690

@SpawnKilleR Sure?

SpawnKilleR

Anyone familiar with Fisher information I am trying to solve something but I cant quite understand it :S

user147690

I am not sorry

robjohn

:21543779 yep, that's what did it.

user147690

@robjohn Did you ever find out what caused all of the people to remain in the chat page after they had exited the browser?

robjohn

00:51

@AlexClark obviously a bug, but I don't know the nature of it

Maximilian

Anyone good with trig?

robjohn

@Maximilian what kind of trig?

Maximilian

vectors right now

Teacher gave us questions which he says is the test, and already first one I got stuck

I think i overcomplicated it. did an entire page without an answer

I don't think it would be that hard

"Use the parallelogram method to find the resultant of u and w", u=<2,-5>, w=<3,2>

I found the angles and the magnitudes

magnitude of u was $\sqrt{29}$

and magnitude of w was $\sqrt{13}$

robjohn

Doesn't the parallelogram method give you $\langle5,-3\rangle$

Maximilian

-_- I was overthinking it

you are correct

I drew that, and then continued on to find something else.. oops

Thank you

Paul Plummer

02:07

@AlexClark Saw you blogroll, including me there is a little premature!

user147690

@PaulPlummer Oh you view my page haha

Paul Plummer

Will you still be using that when you "abandon" the challange? @AlexClark

user147690

@PaulPlummer I will continue to use that page. Although I guess I wouldn't be committingtothatchallenge :P

user147690

@PaulPlummer I think I will rewrite the challenge to a 6 month form

user147690

@PaulPlummer Perhaps a 3 month form, but I haven't had time to plan anything out yet

Paul Plummer

02:10

maybe you should by the domain notcommittingtoachallenge and have you site redirect to there. @AlexClark

user147690

Hahaha perhaps, or maybe Concernedaboutdyinginthefire.com

Paul Plummer

Mike will be so proud of you

user147690

@PaulPlummer I think I will keep my current one, and just make smaller projects

user147690

And actually commit to them :)

Paul Plummer

I actually have a site up, but at the moment it is just documentation of the themes and things like that. And an about page

user147690

02:15

I want to start writing posts on actual math that will interest people, but I am still a few months off that I imagine

Owatch

Hello all.

Have any of you spotted the elusive Tee Dog lately?

Paul Plummer

No

Owatch

-_-

I'll get him someday.

Paul Plummer

@AlexClark Here it is so far mathsalad.com

Karim Mansour

02:34

back

Karim Mansour

02:45

mathsalad

I want one of those math salad

Karim Mansour

02:59

any finite group can we always find set of generators for it ?

I guess there is always trivial one

Ted Shifrin

Trivial one, @Karim?

Karim Mansour

I mean all set G @TedShifrin

Ted Shifrin

Oh ... Rather overkill :)

Toooooo many relations!

Karim Mansour

yeah

Cbjork

hey @Ted

Karim Mansour

03:07

I was thinking how far can we shrink set G so it can generate G ?

Mike Miller

morning

Karim Mansour

for finite groups

Ted Shifrin

Hi @cbjork

Cbjork

68?

Karim Mansour

I guess there is no really algorithmic way of doing this

Ted Shifrin

03:08

Nope, you blew it ...

Cbjork

ouch...

Karim Mansour

:D

Ted Shifrin

Not that way.

Cbjork

:D What's the number?

Karim Mansour

what way ? can we do it I haven't read about free groups yet

rubito

03:09

From 2 men and 2 women, 2 people are selected at random. What is the probability that both people selected are the
same sex?

Can someone explain me why the answer is 0.333 and not 1/2?

Karim Mansour

which is dummit trying to explain that he will make this rigorous at section of free groups

Ted Shifrin

I don't remember. Something like 75.

Cbjork

Well that's a great way to end (compared to 63-68)!

Ted Shifrin

yup. In general, I was disappointed, but not by you. You made me happier. :)

Mike Miller

@rubito: How many ways can you get MM? How many ways can you get FF? How many ways can you get MF? How many total combinations are there?

Karim Mansour

03:11

is he talking about the age?

of retiring or what

@Cbjork

Ted Shifrin

regoodnight @Mike

Mike Miller

@Karim Average grade.

Karim Mansour

oh

Cbjork

Great! @MikeMiller not quite

Mike Miller

I WAS CLOSE

Cbjork

03:12

@KarimMansour grade on the final. I have a history of consistency on Ted's exams.

Karim Mansour

@Cbjork oh I see

Ted Shifrin

I remember now why Chrome drives me nuts :(

Karim Mansour

why

rubito

@MikeMiller I might be wrong but you can only get MM one way and same with FF, but there's a total of 4 combinations

Mike Miller

@rubito: There are not a total of four combinations.

Ted Shifrin

03:14

The bar to type in moves all over and disappears ... On the iPad

Mike Miller

You've got four people, and you're choosing two. What's 4 choose 2?

rubito

6?

Karim Mansour

yeha

Mike Miller

Aye. There are six possible combinations.

Karim Mansour

24/2 * (4 - 2)

which is 24/2 = 12/2 = 6

yaay

just kdding

Mike Miller

03:15

More down to earth: if it's Alex and Bart on one side, and Clarice and Danielle on the other, here are your possible combinations:

AB (MM)
AC, AD, BC, BD (MF)
CD (FF)

Karim Mansour

damn I wish I could open my brain and put bunch of books there

instead of taking sometime reading them

Ted Shifrin

It doesn't work, @Karim .... Just like memorization rarely works for learning math.

Karim Mansour

yeah I guess if you open it up and put the book there

then it is memorization

one gotta make connections and intuition in his head too I guess

Ted Shifrin

Yup, understanding is different from RAM access

rubito

@MikeMiller So, the probability of both people being of the same sex is 2/6 because the other 4 combos are not

Mike Miller

03:18

Yeah

there are 2 combos where both are the same sex, out of six combos total

rubito

great! thanks man!

Mike Miller

Sure, sure.

Karim Mansour

yeah

Seth Kitchen

$\int _0^1\:f\left(x\right)\left(a-x\right)^2dx=0$

Haha first time to chat... guess LateX doesn't work

Mike Miller

@SethKitchen See LaTeX in chat on the right.

Seth Kitchen

03:23

start ChatJax

I'm such a noob :)

Mike Miller

It's what it links to, not the text itself. Bookmark the link and then click the bookmark in this room.

Michael Albanese

Hello all.

Mike Miller

Hi @MichaelA.

Seth Kitchen

Thanks! Can anyone explain why that has no solutions for f(x)

Michael Albanese

@MikeMiller Hi Mike.

Mike Miller

03:25

How's things?

Michael Albanese

Semester's over, so pretty great. How about you?

Mike Miller

Still in the quarter here. I was sick this week so fell a bit behind on reading, doing some catchup this weekend.

Seth Kitchen

Where do you guys go?

Mike Miller

I'm a graduate student at UCLA.

Ted Shifrin

Hi @MichaelA

Michael Albanese

03:28

@TedShifrin Hi Ted.

Seth Kitchen

Impressive

Michael Albanese

I go to Stony Brook.

Seth Kitchen

Where's that?

Michael Albanese

Long Island, New York.

Seth Kitchen

Sounds expensive

Mike Miller

03:28

Home to some of the best geometers alive...

Karim Mansour

yeah

stony brook nice uni

Ted Shifrin

Seth, your question certainly has $f$ that work .... What's $a$, btw?

Seth Kitchen

f=0 works

oh and it has to be nonnegative

Mike Miller

@Seth: It shouldn't be expensive; any reputable PhD program provides their students with stipends that cover both tuition and living expenses.

Seth Kitchen

a is any number i think... not mentioned in the problem

Ted Shifrin

03:30

Well, duh. You need to put that in there. Does it have to be continuous too?

Seth Kitchen

Yes :)

Ted Shifrin

When you ask questions, hypotheses are part of math :D

Seth Kitchen

@MikeMiller Wow. Im an undergrad so excuse my ignorance.

Mike Miller

No need for apologetics, I understand.

Ted Shifrin

@Mike just makes me apologize :)

Mike Miller

03:32

With you it's fun, @Ted

Oh-oh... could probably have phrased that better.

Ted Shifrin

Hmm ...

Mike Miller

Is main down for anyone else?

Antonio Vargas

no

Michael Albanese

Not for me.

Ted Shifrin

So, Seth, what happens if your $f$ isn't always zero?

Mike Miller

03:34

aw man, people get so snarky with you when you comment without reading their question.

Ted Shifrin

I get snarky too ...

When people don't read my answer and tell me to post as a separate question.

rubito

Toss a fair coin 3 times. What is the probability that all three tosses turn up the same?

Is the answer to this 0.125?

Mike Miller

I told someone about the unit-speed parameterization, which he mentioned he knew about in the second sentence of his question.

Ted Shifrin

No.

Mike Miller

I mean yeesh, people these days, expecting me to read more than the first sentence? :P

Ted Shifrin

03:36

@rubito: does it matter whether the first toss is heads or tails?

rubito

ohh!!!!

Seth Kitchen

Let me make f(x)=1... I get $-(a-1)^3/3 + (a^3)/3$.. which isn't zero, but I don't know how you can check every answer

Antonio Vargas

@SethKitchen $$f(x) = \frac{6 a^2-8 a+3}{12 a^2-12 a+4} - x$$ works.

Ted Shifrin

Don't do it by trying to integrate, Seth. Draw a general picture.

Antonio Vargas

There must be some more restrictions on $f$ in order to say that it doesn't have any solutions.

Michael Albanese

03:38

imgur.com/gallery/eJfGoOV

Seth Kitchen

math-cs.ucmo.edu/~curtisc/contest/2014/smomaa14.pdf is the link to the solution... I am just too noob to understand

Ted Shifrin

Nonnegative @Antonio, and continuous!

Antonio Vargas

@TedShifrin Oh I didn't see the nonnegative part.

Seth Kitchen

but like how did you come up with that

Mike Miller

@MichaelAlbanese lol

Antonio Vargas

03:39

@SethKitchen Plug in $f(x) = b-x$, solve for $b$.

Karim Mansour

hm

what does group presentation really help us in

Seth Kitchen

@TedShifrin What do you mean by general picture?

Karim Mansour

it seems it doesn't really extract information about a group

Ted Shifrin

@Seth. Forget the $(x-a)^2$. It is nonnegative. Think about the general continuous nonneg. fn. what course are you in?

Karim Mansour

just some abstract thing

Seth Kitchen

03:41

Calc 3... i'm just a freshmen :( .. But I want to be like you guys

Ted Shifrin

Calc 3? Really?

this is like single variable ....

Seth Kitchen

I don't understand how you can check all functions at one time

Ted Shifrin

draw me a positive function with zero area, Seth.

user147690

@Paul How much time did you spend writing the about section haha

Ted Shifrin

You can't.

pjs36

03:43

@KarimMansour Group representations are extremely concrete. What would you rather have, an abstract group, or a group of matrices?

Seth Kitchen

Right, but how do we know a is not 0?

user147690

@Paul Also why the Github section?

Seth Kitchen

And that does make it easy to understnad Ted. Thanks!

Karim Mansour

I see

user147690

@SethKitchen I haven't been following, but it sounds like you want to think of the absolute value of a function?

Seth Kitchen

03:44

I mean how do we know a is not 1

Karim Mansour

I see @pjs36

Ted Shifrin

$a$ is irrelevant.

Karim Mansour

I am just reading just introduction so I will not be over my head yet until I read everything on free groups later on and discuss it with you guys @pjs36

Seth Kitchen

How do you know though?

Mike Miller

@pjs36: Depends.

Seth Kitchen

03:45

@AlexClark Just trying to learn some math stuffs

Ted Shifrin

All that matters is that both $f$ and $(x-a)^2$ are nonnegative.

pjs36

@KarimMansour No worries! They're also nice for other reasons. For me, I'd prefer to have characters, rather than representations, but that's just because I never learned representation theory :P

@MikeMiller Well, of course! But I'm just pointing out that representations are, in many cases, less abstract than being handed a generic group.

Seth Kitchen

Ok, let's say there is a solution and @AntonioVargas plugs in that $f(x)=b-x$, how do I know the answer that comes out is nonnegative and continuous? I guess I know it is continuous if the denominator is never 0

Karim Mansour

I should also learn some representation theory this summer too

Seth Kitchen

I guess what I'm really asking is how do I check if it is nonnegative

Antonio Vargas

03:48

@SethKitchen ?

Mike Miller

representation theory has historically been a weak point of mine

Antonio Vargas

My answer was wrong. $f(x) = b-x$ isn't necessarily nonnegative.

Seth Kitchen

how do you know?

Antonio Vargas

well if $b=1/2$ then $b-x$ is negative for $x > 1/2$

pjs36

Yeah, I don't know any of it, @MikeMiller. I just learned character theory (traces of irreducible representations) from those group theorists that taught me all my algebra

Seth Kitchen

03:50

Ok so the only thing I would be able to plug in is some power of x or a positive integer?

Karim Mansour

lol

group theorists

Mike Miller

I claim to have once known something about the representation theory of $S_n$

Karim Mansour

you say it in funny way @pjs36

Antonio Vargas

@SethKitchen No. Please think more about what Ted is telling you.

Seth Kitchen

I understand that there is no answer. I am just wondering if there was an answer

how i would solve

Antonio Vargas

03:51

Reread that sentence.

there's no answer. How could there be an answer if there's no answer?

pjs36

I do try, Karim :P

I know for $S_n$, integer partitions just roam freely, but I only ever got the Spark Notes version

Seth Kitchen

I want to be able to apply this to other problems. That's all I'm trying to say.

Kaj Hansen

Sup everyone

Mike Miller

h

user147690

h

Samuel Yusim

03:52

h

Antonio Vargas

@SethKitchen I see. Well there's a wealth of theory regarding solving integral equations - there's no one method.

Kaj Hansen

@AlexClark, you're committing right? Just making sure

user147690

@KajHansen Indeed

user147690

@KajHansen I won't change it again haha

Kaj Hansen

@AlexClark, I'm going to be away from the gym for a little over 2 weeks :(

user147690

03:54

@KajHansen Ahh shit man, those gains :(

Kaj Hansen

Went home, 3 hours away from my top-tier university weight room.

user147690

Do you have $100 you can just buy a barbell and some weights?

user147690

Did you go home by car?

Kaj Hansen

To be fair, I might need it because my shoulder and elbow joints were starting to feel a little strained from going every day. Nothing serious of course.

Seth Kitchen

I used to know an Alex Clark. He went to Westpoint

rubito

03:56

Given that in 4 flips of a fair coin there are at least two "heads", what is the probability that there are two "tails"?

Sorry about all the probability questions, I'm studying for a final and I really don't get this stuff

user147690

@KajHansen Do you do overhead press or incline bench dumbbell press?

Kaj Hansen

So maybe it's for the better. I just know I'll be hit with DOMS when I start up again, and it'll be hard to get back into it at first.

Ted Shifrin

@rubito: Stop giving us all your homework.

user147690

@rubito There are either two heads, three heads or four heads, so that means there are so many tails, you have a few cases, and you should know how to consider them

Kaj Hansen

@AlexClark, I do both. I know they put a good bit of strain on the rotator cuff, so I'm always pretty careful with my form

Seth Kitchen

03:57

We could troll him :) @rubito 50 %

Ted Shifrin

Well, @Kaj, I'm done done ...

rubito

@TedShifrin Is not homework, I'm going over our review problems and I'm okay with the later stuff but the early probability is what I don't get

user147690

@KajHansen Loading up the incline dumbbell is where I always got injured haha, I quit based on that

Antonio Vargas

@SethKitchen I think I came off harsh in the last message. Sorry about that. I shouldn't be doing something else while chatting :)

Ted Shifrin

Use conditional probability, @rubito.

user147690

03:59

@SethKitchen I don't know what that is sorry. I am in Straya'

rubito

@TedShifrin Okay I'm gonna give it a shot

Seth Kitchen

@AntonioVargas You're fine :) You're helping!

Kaj Hansen

@TedShifrin, that's kind of depressing to think about. I'll miss interrupting your office hours :)

Ted Shifrin

Not really, @Antonio. I Said the same thing three times.

Seth Kitchen

@AlexClark It's a military academy in the US

Antonio Vargas

03:59

@TedShifrin Well it's true.

user147690

@TedShifrin But we all know you are harsh :P

user147690

@TedShifrin You are done done now, congratulations! Heaps of time to dedicate to mathematics without having to deal with distracting students

Mike Miller

@Ted: "A smooth map $f: M \to M$ which is $C^1$ sufficiently close to the identity is a diffeomorphism." $M$ is closed. Why should this be true?

Kaj Hansen

@AlexClark, I actually go rather light on the dumbbells and save the heavy lifting for the barbell. For one, it's hard just getting into the starting position on DB presses safely.

Seth Kitchen

Lifting < Running

Kaj Hansen

04:01

@SethKitchen, depends on what you're going for IMO. Of course, my cardio is nowhere near where it should be, and running would help with that.

Ted Shifrin

When you don't have compact, @Mike, what does this mean?

user147690

@KajHansen Exactly hahaha. I would grab one with both hands while sitting and pull it onto my knee, and then grab the other with my stronger arm and put it on my other knee, but getting from sitting with that to lying down(on the incline) is where I hurt my shoulder for days on two occassions

Mike Miller

Fair enough, @Ted.

user147690

I need a coffee/redbull hmmmm

Ted Shifrin

Can you prove it for compact?

Kaj Hansen

04:03

@AlexClark, to get from knee to starting position, I'd do this weird "kick" from a sitting upright position to get one DB up, and take advantage of the momentum to get the other one up. Kind of dangerous when you think about it.

user147690

@KajHansen Yep that's the stuff that kills my back xD. I have been just doing bench/DL/OH and nothing else for a month and a half, and it's been pretty great for some reason

Mike Miller

Wait, @Ted, of course I can. Nevermind.

Ted Shifrin

Ok

user147690

Well I better go get a coffee and get back to work

user147690

Cya guys later

Seth Kitchen

04:05

Well I think more than just cardio, losing BMI, stress relief, leg muscle, and thinking time that comes from running far outweighs the nut bursting, constipation, and aneurism that is weight lifting.

Ted Shifrin

What do you mean in general?

Kaj Hansen

That's truly not bad at all @AlexClark. If I did that, I might throw in some forearm stuff for the grip strength. Especially since my DL is getting too heavy for me to maintain grip. Anyways, see you around!

user147690

@SethKitchen I do 5 minutes a day, every day, just three sets atm a day, and its been great and so little time/effort

user147690

@KajHansen I'm using straps now :)

user147690

Bye

Mike Miller

04:06

sufficiently close on something compact means you can bound the derivatives away from being nonsingular; local diffeomorphisms of closed manifolds are surjective, and thus are covering maps; I can't possibly homotope this diffeomorphism to be a nontrivial covering map.

Seth Kitchen

@AlexClark Haha I'm just messing with you.

Ted Shifrin

Night all ...

Kaj Hansen

@SethKitchen, there is some major stress relief that I get from weightlifting. The endorphin release from deadlifting alone is enough to keep my depression and anxious thoughts at bay for the next few hours.

Karim Mansour

nights @TedShifrin

Mike Miller

@Ted: I don't, the question is only posed for closed things. I guess with the right definition of $C^1$ topology on the space of smooth maps of something noncompact you can use the same argument to show that it's a local diffeo; I'm not sure if I should buy that it's still a diffeo.

Seth Kitchen

04:07

@TedShifrin night thanks for the help

Kaj Hansen

See you @Ted!

Mike Miller

bye

Seth Kitchen

Let $T_o$ be an isosceles triangle with base b and base angles a. Define a sequence ${T_n}$ n from 0 to infinity of triangles recursively as follows. The base of each triangle $T_n$ is b, and the base angles of triangle $T_n+1$ have half the measure of the base angles of triangle $T_n$. Evaluate lim n->infinity $2^n*area(T_n)/area(T_o)$

how do I know base angles are $a/2^n$ ?

pjs36

Because $a/2^n = \frac{1}{2}a/2^{n-1}$ is half of $a/2^{n-1}$, which is half of... which is half of $a$

Paul Plummer

@AlexClark Because I took the template from someone, and the template linked to their github. I spent like a minute on the about page

user147690

04:24

@PaulPlummer What sort of statistics do you get to collect?

Paul Plummer

I don't plan on setting up any sort of statistics

And not sure

I think it could be a bit, I would just have to set it up

user147690

@PaulPlummer Not even view counts??

Paul Plummer

Not sure what I would use it for, maybe if I want to get depressed I would set it up :D

Maximilian

Does this digram look correct?

Paul Plummer

I know I could set up google analytics @AlexClark

Mike Miller

04:27

wordpress seems to come with analytics

wow, someone went through and clicked all the links on my blogroll

user147690

@PaulPlummer I think it is nice to see it build up over time(although mine has done the opposite for obvious reasons)

Paul Plummer

@MikeMiller I think that was me

A couple hours ago

Maximilian

and would I start it as $cos^2(A+B)-2cos(A+b)+1+sin^2(A+B)=cos^2A+2cosAcosB-cos^2B-Sin^2A+2sinAsinB-sin^‌2B$

Mike Miller

only one person did it, so it must have been

Paul Plummer

Actually I don't think I clicked on the whats new, terry tao blog

Not sure why I clicked on the rest though, I had been to all of them but the floer homology

Mike Miller

04:32

floer homology isn't really for anyone but me

i only put it there to remind myself of it later

Maximilian

?

Paul Plummer

Haha, I saw a talk at JMM of someone doing some interesting stuff with floer homology and knots or links or braids (don't remember), I didn't really understand the floer homology, but it seemed like it had a nice geometric interpretation

Mike Miller

i'm trying to understand floer homology now

Paul Plummer

It was actually one of my favourite talks, seemed like really cool stuff

Mike Miller

well, heegaard floer; floer homology in general is absurdly broad

it just means "morse theory on infinite dimensional manifolds"; when one uses it on a 4-manifold, say, they associate an infinite dimensional manifold and a Morse functional on it and then do Morse homology on that. oftentimes this infinite dimensional manifold is something like the space of solutions to a certain PDE

Paul Plummer

04:35

"it just means..."

Mike Miller

morse theory = studying a function whose critical points don't suck

given a morse function on a smooth manifold you can reconstruct the manifold from it.

there's a notion of Morse homology, which ends up spitting out singular homology in the finite dimensional case; that's no longer true in infinite dimensions, which is why it's nice

eg here's an example of how it might be useful. if I give you a smooth manifold and a function on it that has exactly two nondegenerate (not messed up) critical points, then the manifold must be homeomorphic to $S^n$

this is how Milnor proved that his exotic 7-spheres were actually homeomorphic to $S^7$

user147690

@MikeMiller Are these $C^n, S^n$ things inaccessible to me? I keep reading them and they are bugging me

Owatch

@Maximilian Can't help you there myself at this time Max, but I'm sure other people in this room know Trig and can help out. :)

Mike Miller

$C^n$ function = function that's $n$ times differentiable, and whose $n$th derivative is continuous

user147690

Ahhh I have seen this in normal contexts

Paul Plummer

04:39

$S^n$ is just an $n$ dimensional sphere

Mike Miller

$S^n$ = n-dimensional sphere, $\{(x_1, \dots, x_{n+1}) \in \Bbb R^{n+1} | x_1^2 + \dots + x_{n+1}^2 = 1\}$

user147690

Ahhh alright, easy enough

user147690

But you have equal there, so it is the surface of the sphere

Mike Miller

no, the terminology is that that's the sphere

user147690

Or the shell of t he sphere so to speak

Mike Miller

04:40

what you're thinking of is called the unit ball

user147690

But the sphere is hollow correct?

Mike Miller

yes

Paul Plummer

I think I got 99 votes @AlexClark

user147690

That's what I meant

Mike Miller

I don't understand what you mean then

Paul Plummer

04:42

That is the definition of a sphere, if it wasn't "hollow" then it wouldn't be a sphere

user147690

@PaulPlummer Wow, you are in a tie with Yes for the week, nice!

Mike Miller

what I was talking to Ted about is the notion of two smooth maps being "$C^1$ close"; you can define a norm on $C^1$ functions on a compact smooth manifold (concretely, on $[0,1]$), and two $C^1$ functions are $C^1$ close if both them and their derivatives are close; if you learn about the sup norm I mean that $\|f\|_{C^1} = \|f\|_{sup} + \|f'\|_{sup}$

user147690

Yes the sup norm is the $p=\infty$ norm

Mike Miller

yes

also known as the $C^0$ norm

user147690

Oh I haven't heard that before

Mike Miller

04:44

different name, same thing

user147690

What does $C^1$ close mean?

user147690

Oh you define it immediately

Mike Miller

$f$ is $C^1$ close to $g$ if $\|f-g\|_{C^1}$ is small

how small 'small' is depends on the situation

user147690

Oh okay, that makes 'some' sense

Mike Miller

54 points away from delete votes lol

Paul Plummer

04:47

Nice, I will have to recruit for my ring of thugs that delete things

Mike Miller

you've got to catch up

user147690

@PaulPlummer I am out of that game lmao, I can't even cast downvotes

Paul Plummer

:D yah

Mike Miller

where do you find the questions that need to be pushed over by a vote or two for community

deleting that afterwards lest we sound like the mob

actually no

user147690

@MikeMiller Well the easiest place is the front page haha, otherwise page 24000 arranged by votes

Mike Miller

04:49

lol

Paul Plummer

@MikeMiller Read here

Too many bad questions have answers with a lot of votes

Then you can use advance search, to for example search for questions with no answers and zero votes, or something close to that

For example

answers:0 isanswered:no hasaccepted:no closed:no score:0 created:2014-09

Mike Miller

I see

Paul Plummer

Or you could search for closed questions, although I will have to see if there is a way to filter out questions with high voted answers

Transcript for

$Mathematics$ Mathematics