Mathematics - 2015-05-07 (page 2 of 6)

Paul Plummer

4:00 AM

:D

Okay

Or not

user147690

I thought this was directed at me haha

user147690

2 hours ago, by Mike Miller

@Alex: I wrote the first part of the talk as a blog post

user147690

About my presentation and discussing it with Mike - looked a little harder :P

Paul Plummer

Hahah, Doing your homework

Remember me

Why do i get disconnected.....Aww

Horror

My physics test went horror

user147690

4:05 AM

@PaulPlummer Ummm not sure how to show you my latex hmmm

Paul Plummer

"Milnor was able to write down a few exact sequences that help us with our problem."

user147690

@PaulPlummer I saw that xD

user147690

@PaulPlummer Pretty sure it was directed at AlexWertheim

user147690

Wait I have it

Paul Plummer

@AlexClark Yah, that is why we always put your full name

user147690

4:07 AM

@PaulPlummer Indeed :P

Remember me

Lets go and play some games then i can restart my revision in chemistry

user147690

Oh man I just got that coffee.... I was so out of it(hence why I needed the coffee) I walked up and said "Can I just have a 16 inch cappuccino please" in place of 16 ounce....

Paul Plummer

Haha

user147690

@PaulPlummer Oh god, it's so long, you can just skim it lmao

Paul Plummer

Pretty good

user147690

4:14 AM

@PaulPlummer I'll probably be skipping straight to where the example starts, since the other guy wants to mainly do defining I think

Paul Plummer

That makes sense

No reason to define things twice

user147690

Yep

Paul Plummer

Unless the other person does a horrible job

....

user147690

Indeed, but he's a good student, so he'll do fine

Mike Miller

user147690

4:16 AM

Wut^

Paul Plummer

He is trying to write on the banana

user147690

@MikeMiller Nice blog entry btw, even though I don't understand much :P

Mike Miller

thanks

re: Wut: it is a combination of the covers of two classic albums, amalgamated in an amusing way; the resulting image looks as though david bowie is gently caressing a banana

hope this helps

user147690

@MikeMiller Hahaha it does, but I hadn't seen either album before

Mike Miller

for shame

user147690

4:18 AM

I knew you would say something like that :P

user147690

What is the non-david bowie one?

Mike Miller

the banana cover is canonical

user147690

My ex-ex had a weird crush on David Bowie, but I had never heard any of his music(knowingly atleast)

Mike Miller

you can peel off the sticker

user147690

:P

user147690

4:21 AM

Oh crap I meant to be studying topology

user147690

Damnit algebra is too good

Karim Mansour

topology also has its flavour

user147690

Is this an example of a discrete topology @Paul:

Karim Mansour

Is there discrete topology the power set ?

I don't remember

user147690

Goddamn rep limitations

Paul Plummer

4:22 AM

Rep limitations?

Oh couldn't post a pic

Karim Mansour

yeah

it is the power set

user147690

Yep no pictures from me

Karim Mansour

it is all subset of your set S

Mike Miller

what an awful picture of a topology

Paul Plummer

Yes it looks like it,

Karim Mansour

4:23 AM

yeah it is the discrete topology

that is from munkrees no @Incurrence?

Mike Miller

absolutely no intuition is gained by drawing the open sets on a finite set

Paul Plummer

Except to learn how godawfull general topological spaces are

pjs36

More like topowlogy, amirite? Beceause it looked like an owl.

2

user147690

Oh goddamnit lol

Paul Plummer

He was so ashamed of LOLing

he had to delete it

user147690

4:25 AM

No I was on the wrong window

Mike Miller

@pjs36 what a hoot!

user147690

So does the powerset give us the discrete topology, and the discrete topology is the power set?

Karim Mansour

yeah

user147690

So it is IFF

user147690

And doesn't break down atleast in the finite case?

Karim Mansour

4:27 AM

well what is the definition of the power set?

Paul Plummer

$(S, \mathcal{P}(S))$ is the discrete topology on $S$

Remember me

set of all subsets of some set X

user147690

And the trivial topology is called the indiscrete topology

Karim Mansour

discrete topology is collection of all subsets of X

Paul Plummer

I don't know what the trivial topology is

user147690

4:28 AM

Lol sorry I am so out of it for some reason

Karim Mansour

@AlexClark also discrete topology changes any group to a topological group btw

Paul Plummer

Guessing the indiscrete topology

user147690

@PaulPlummer Yeah see edit

Paul Plummer

Okay,

user147690

My bad homes'

Karim Mansour

4:29 AM

np it happens @AlexClark anyway I am off to sleep cya guys tomorrow algebra,physics day :D

pjs36

Have fun, @KarimMansour

Karim Mansour

cya tomorrow guys

Remember me

cya @KarimMansour

user147690

@KarimMansour Night!

Remember me

Yes I am getting Halo 4

user147690

4:31 AM

@Rememberme I haven't played games for 2 years or so

Remember me

I have just started with the halo series @AlexClark

Its amazing .... i have also found an emulator for Xbox360 @AlexClark

user147690

@Rememberme I was rank 48/50 on duo queue halo 3, almost masters league with my brother haha. That was 2008(?)

Remember me

wow....amzing....

Have you looked at Halo5....its about two spartans@AlexClark

user147690

@Rememberme Nah, I don't hear much about games these days, most of my friends stopped playing aswell

Remember me

I will stop once i finsh Halo.....WEll there is more imp stuff to do than games and more sensible stuff@AlexClark Maths!!!!!!!!!!

user147690

4:35 AM

@Rememberme Haha, only if you enjoy it enough to not game though :P

Remember me

I am so excited i will be able to start topology once i finish Linear algebra @AlexClark SO three to four months to go before toplogy!!!!

user147690

@Rememberme :P Linear algebra is something to enjoy, don't rush it

Remember me

Yes it is atleast it is not mechanical.....

Where on the other hand calculus is a lot mechanical

@AlexClark you have started algeb top

user147690

@Rememberme Not yet, next semester(in 2 months)

Remember me

I really hate when you find stuff and dont have a way to prove it...@AlexClark

Like the triangle conjecture which i found few days ago....No way to prove it

Paul Plummer

4:41 AM

Well then you will hate math

Remember me

:(

I dont but it is sometimes a lot tough

Real tough...

It feels so easy but no way to prove it

And i have no reason why i cant disprove it

Really in a huge dilemma

@PaulPlummer

ADG

can anyone form a riddle for me whose answer should be the catalan constant

Remember me

Hey @ADG Can you do me a small or big favour

ADG

@Rememberme firstl tell thenI'll decide

Remember me

Can you write some codes...i dont know how to write them.....for a question of mine

ADG

4:55 AM

OK

how'd you know I can?

Remember me

From your answers...and questions...I see that you provide a lot of codes so i felt that you might help me

ADG

ok

Remember me

So my question is : Can the cube of every perfect number be written as the sum of three distinct positive cubes...I want to check for as many perfect numbers I can ?@ADG

ADG

it's easy

Remember me

easy??

ADG

4:59 AM

have you asked it on main, I may put up the code there in some times

*time

Remember me

i have@ADG

ADG

perfect number = square

?

Remember me

No perfect number is a number whose divisors except itself add up to the number itself

ADG

6,24,...

Remember me

People please look at this question
http://math.stackexchange.com/questions/1270894/a-conjecture-about-triangles

Yup......

anon

5:04 AM

there is a conjecture that all perfect numbers are even

and a fun fake proof: write $2n=\sum_{d\mid n}d$, apply Moebius inversion, $n=\sum_{d\mid n}\mu(d)(2d)$, hence $n$ is even

Remember me

SO what do we get from here@Anon

anon

where's here?

Remember me

Ah i mean your proof

anon

so you mean "there"

that is the whole proof

observe $\sum_{d\mid n}\mu(d)\cdot 2d$ is even, as is any sum of multiples of two

Remember me

Forget about it i think i need some computer engineers help and @ADG might help me anyways have a look at this question which i ust posted@Anon

0

Q: A conjecture about triangles

I have found a conjecture that there is no triangle in this world which can have sides,medians,altitudes all rational. I thought that someone must have already found it and yes i saw this conjecture but no proof or hints. Is this still an open question? Also I feel that I cant prove it but how do...

this one

Any takes @anon

anon

5:11 AM

"how do i show that I can't prove it"?

Remember me

Yes

anon

are you suggesting the conjecture is independent of the standard assumptions of mathematics?

or else what does that even mean? I've been trying to revise your question to be more readable but I have no intelligible translation for that sentence.

Paul Plummer

Well you make an attempt and fail and fail until you die

ADG

@Rememberme solved it

Remember me

Solved what?@ADG

Mike Miller

5:13 AM

cute trick @anon

Remember me

How do i show that i cannot prove that there exists no triangle with sides medain,....all rational@Anon

anon

@Rememberme what do you mean by that? are you suggesting the conjecture is logically independent of standard assumptions of mathematics? or are you asking how to show that any proof of the conjecture would be beyond your personal, individual ability to comprehend? if the latter, that's an extremely odd request.

and not possible if the conjecture is still open anyway

Remember me

Is there a way that i can show that this is conjecture is impossible to prove

Paul Plummer

Well it would not be a conjecture then would it

Remember me

Well I can say it is possible to prove if and only if we develop a new field of mathematics @PaulP :p

anon

5:18 AM

@PaulPlummer the continuum hypothesis was proven independent of ZFC. a few have suggested that maybe the Riemann hypothesis is (although it's not the type of thing we have any precedent for expecting to be independent).

@Rememberme no, you can't say that

Mike Miller

i don't think i've ever seen any serious number theorists suggest RH is independent of ZFC

do you have any names?

anon

@MikeMiller definitely not any serious number theorists

Mike Miller

figured

anon

more like amateur fora

Mike Miller

someone notable or another suggested Collatz might be independent, but that also boggles the mind; it's not the type of thing I see any reason to be independent

Paul Plummer

5:20 AM

The continuum hypothesis isn't a conjecture

Mike Miller

oh, Knuth

but he's also Knuth

anon

I never really understood why CH and RH are called hypotheses instead of conjectures

Paul Plummer

I think the reason was that in general those types of problems are not decidable, although I think that was algorithmically decidable, not sure

Mike Miller

continuum conjecture doesn't ring quite right

i take that back, i like the sound now

anon

@MikeMiller maybe that's because we've been indoctrinated though!

@PaulPlummer so at the time CH was first looked at, it did not constitute "a conclusion or proposition which appears to be correct based on incomplete information, but for which no proof has been found"? what about the RH?

Remember me

5:24 AM

How would this sound.....
Riemann conjecture ....weird

I have found the answer to the "Riemann conjecture" Yay!!!!!!!

Paul Plummer

I am saying that if we knew how to show that problem $X$ is independent of the axioms or algorithmically undecidable, or whatever it wouldn't be a conjecture @anon

Remember me

@anon I think our current mathematics is not enough to prove these stuff

Paul Plummer

Generally asking how to solve open problems is not a great math.se, or mo question

Which I am sure you know

Remember me

I mean the Riemann hypothesis,CH

anon

asking about current state of the conjecture is more debatable

Remember me

5:26 AM

So should i edit the question??@paulp

Paul Plummer

That can be a fine questio

I have not looked at the edited quesiton yet

Remember me

let me edit it

anon

I already did edit it, and you have received two replies already

Remember me

Thanks!!!!

I think i should include area too that would make it better

anon

@Rememberme you said you saw this conjecture somewhere, do you have any source?

Remember me

5:30 AM

Yes i have wait let me show you

anon

also, don't overwrite the original question, just add onto it with the additional thought that adding rational area to the list might make the question more interesting. it's considered poor form to ask a question, receive replies, and then change the question, but it's alright to add a little more onto it in that form.

Remember me

@anon here ics.uci.edu/~eppstein/junkyard/open.html

see the rational triangles one

@ADG i have edited the question

anon

hmm, embedding the hyperbolic plane into higher-dimensional Euclidean space is an intriguing idea

Remember me

These are amazing questions @aron arent they?

Mike Miller

embedding into $\Bbb R^4$ is open? weird

anon

5:37 AM

4 does seem to be the hardest dimension

Mike Miller

for different reasons; there's no exotic structure in play here

Remember me

Why?@anon

@anon it is in physics but maths we have gone to n dimensions so 4 must be easy

Paul Plummer

@Rememberme Maybe you should take a look at Mikes blog

Remember me

link pls@paulp

anon

@MikeMiller so does a lot of the special phenomena in dimension four reduce to spherical stuff (which is what I assume you're referring to)?

Mike Miller

5:41 AM

not really, it's just that the bizarreness in 4 dimensions that people usually refer to is that there are often exotic smooth structures on 4-manifolds; for sufficiently big simply connected 4-manifolds we know that they support infinitely many pairwise non-diffeomorphic smooth structures

anon

I don't really know that much about differential geometry

Paul Plummer

2 hours ago, by Alex Clark

2 hours ago, by Mike Miller

@Alex: I wrote the first part of the talk as a blog post

Mike Miller

@anon: I'm talking here about differential topology, which is where the weird stuff happens. my impression is that differential geometry isn't particularly wacky, it just gets harder pretty much uniformly as dimensions go up

eg I think we've classified Einstein metrics on 3-manifolds now? on 4 it's a big important question, and 5 and up I think it's hopeless. I'm not very knowledgeable about this, if differential geometry is taken to mean Riemannian geometry

Remember me

Why are there so many exotic spheres in the 11 and 7 dimensions??

228 but on the other hand so less 12th dimension

user147690

@Rememberme Wait until you have done more math before stressing these questions

Remember me

5:50 AM

yes i think i should because the exotic spheres are increasing and decreasing such horribly

user147690

@Paul Can I exchange my $\Bbb Z$ for $\Bbb R$?

Paul Plummer

Pretty sure you can

user147690

Is it more interesting?

Mike Miller

group theoretically? no

user147690

Is my current case "a Lie subgroup"

Mike Miller

5:56 AM

in a trivial sense

if you want to think about Lie groups and such, you should do it after your presentation

user147690

I shall

Mike Miller

right now your focus should be understanding the case you already have, and once you do, presenting it coherently

good to hear

user147690

Next year I will have to fill in all of my units, so I will be doing 6 unit research two semesters in a row

user147690

2 units is a course in Australia, don't know if that is standard

user147690

I imagine you have both done a research paper before, where did you get the topic? Given by adviser?

Mike Miller

6:00 AM

@anon: there is an isometric $C^1$ embedding of the hyperbolic plane into $\Bbb R^3$; seems you can't get $C^2$

Samuel Yusim

earlier today I was thinking about automorphisms of graphs which fix some subgraph and I was thinking it would be cool if there was a sort of analogue to galois theory in this context

by fix a subgraph I mean that the automorphism restricted to that subgraph is the identity

surely this is something someone has thought of, does anyone know of any information?

Paul Plummer

That is an interesting idea, I would be surprised if you could say anything in general, because every group is the automorphism group of a graph, and I would be surprised if you could not arrange for there to be these fixed subgraphs for any subgroup of a group

Mike Miller

gromov proved that you can $C^\infty$ isometrically embed every surface into $\Bbb R^5$; and if your metric is real analytic, you can do so analytically. more reason to learn partial differential relations, i guess, though that stuff seems impenetrable

Paul Plummer

Although ever finite group is a Galois group

user147690

What do you think about me making my presentation topic more about split extensions, but using his central extension presentation as the build up to mine? @Paul

Paul Plummer

6:11 AM

Sure, do you have any central split extentions?

Mike Miller

@paul :p

user147690

I meant with focus on non-splitting extensions whoops

Samuel Yusim

I guess a more general idea is to consider the "galois group" of any object over some sub-object, which would be simply the group of automorphisms that object that restrict to the identity on the sub-object

Paul Plummer

@AlexClark I don't see a problem with that, no reason to go through all the definitions a second time, unless that is what the prof wants.

user147690

@PaulPlummer Well the problem is, he gave us 10 topics to choose from and everyone(16 people) must present, dafuq

Mike Miller

6:14 AM

@AlexC: i'll spoil the fun and let you know that the only split central extensions are ones of the form $1 \to N \to N \times H \to H \to 1$

Paul Plummer

@SamuelYusim That is a pretty cool idea

Mike Miller

i.e. the trivial extension

user147690

@MikeMiller That's boring

Samuel Yusim

yeah, and an interesting problem, I suppose, is to figure out what types of object extensions give a galois correspondence

Mike Miller

split extensions are classified by the action of $H$ on $N$, and the assumption that $N$ is contained in the center implies that this action is trivial

Samuel Yusim

6:26 AM

not that I've put a huge amount of thought into this but if $T$ is a topology on $X$ then is $\{\emptyset, X\} \cup \mathcal{P}(X) \setminus T$ a topology on $X$?

er

no

edited

probably still no

example?

but not universally false

cofinite topology

Samuel Yusim

6:28 AM

okay, sure

so when is it a topology on $X$?

Paul Plummer

Couldn't you take the reals with standard topology, then this new "topology" would not be closed

since you could union up the singletons

to get intervals

Mike Miller

@samuel one obstruction, abused above, is that you can never write an open set as a union of non-open sets for this to be a topology

Samuel Yusim

so then it's pretty uncommon of a phenomenon to have it be a topology

Mike Miller

this gets rid of any connected T1; T1 implies the singletons are closed; connected implies they're also not open, so they're in the 'complement topology'

but that would make the complement discrete, and thus your original space indiscrete, which is silly

Samuel Yusim

so is there something nontrivial for which it'll work that isn't a particular point or excluded point topology

I guess if you pick some subset instead of a point it's good

but yeah

Mike Miller

6:34 AM

I think probably it won't work for any non-discrete T1 space

Samuel Yusim

sure, but I'm happy to consider spaces other than those

Mike Miller

then sure; the complement of the Sierpinski space {{}, {a}, {a,b}} is just {{}, {b}, {a,b}}, aka itself

Samuel Yusim

sure but the first one is a fixed point topology with a fixed and the second is the excluded point topology with a excluded

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$Mathematics$ Mathematics