Mathematics - 2012-07-22 (page 2 of 4)

David Wheeler

5:26 AM

la la la

Peter Tamaroff

@DavidWheeler Dude

Ragib Zaman

@PeterTamaroff Sorry I didn't reply to your pings yesterday, I was out all day, came home and fell straight asleep lol.

Peter Tamaroff

@RagibZaman That is a healthy thing to do.

Ragib Zaman

@PeterTamaroff Did you need me for any particular reason?

Peter Tamaroff

@RagibZaman I don't really remember what the pinging was for now.

David Wheeler

5:31 AM

@PeterTamaroff hmm?

Peter Tamaroff

@DavidWheeler Ahammm?

David Wheeler

u said "Dude"

Peter Tamaroff

@DavidWheeler Oh, I just started with the chapter on topological spaces.

David Wheeler

now things will get...bizarre....

Peter Tamaroff

I have to prove that given $(X,\mathfrak I)$ a metrizable topological space, then for $a,b$ distinct points of $X$, there exist open sets $O_a$ and $O_b$ such that $O_a\cap O_b=\varnothing$.

Ragib Zaman

5:34 AM

So it's basically like you are working in a metric space but you don't know the metric.

David Wheeler

yes, that is what is called a "separation property"

Peter Tamaroff

Subsequently I have to prove that the topological space $(\Bbb N,\mathfrak I)$ with $\mathfrak I=\{\varnothing,O_1,\dots,O_n,\dots\}$ such that for each $n$, $O_n=\{n,n+1,\dots\}$ is not metrizable.

@DavidWheeler I'll jot that down.

Ragib Zaman

More specifically, it is probably the most important of the separation properties, it is the Hausdorff property.

The name makes it easy to remember the definition and vice versa - A topological space is "Hausdorff" if every 2 points can be "Housed off".

Peter Tamaroff

@RagibZaman The definition of the Hausdorff axiom here is that there exist neighborhoods that are disjoint.

Basically the same, right?

I know:

Ragib Zaman

Yup, precisely the same, when I say two points are "Housed off" I imagine I can put them in two houses and their houses don't go over each other lol.

Peter Tamaroff

5:38 AM

In turning a metric into a topology, the open sets are preserved.

Thus the open balls are open sets of the topology.

David Wheeler

no

Ragib Zaman

There are more open sets than just open balls

David Wheeler

open balls are open sets, but not "the" open sets

Peter Tamaroff

Well, the open sets of metric spaces arent open balls?

@DavidWheeler Sorry.

Ragib Zaman

(1,3) U (5,7)

David Wheeler

5:39 AM

also true

Ragib Zaman

is an open set.

David Wheeler

open sets are unions of open balls

Peter Tamaroff

Well, because it is a union of open balls

@DavidWheeler Yes, precisely.

David Wheeler

the exact term is: the open balls form a base

Peter Tamaroff

@DavidWheeler I proved that before: A set is open $\iff$ it is the union of open balls.

@DavidWheeler for the system of nbhds

=P

David Wheeler

5:41 AM

a base for the topology

the open balls ARE a system of neighborhoods

Peter Tamaroff

So I should start with "The open sets in the metric space are union of open balls, and conversely, so the topology of $X$,$\mathfrak I$, consists of open sets taht are the union of open balls"

@DavidWheeler Yes.

$\mathfrak N_x$ is the notation Mendelson uses.

David Wheeler

the notations for topology vary, i have seen the notation $(X,\tau)$ for example

Peter Tamaroff

$\mathfrak I$ is over 9000 times cooler.

And is appropriedly upper case.

$\tau$ is lowercase. It shall be left for insignificant concepts.

Ragib Zaman

Why are we talking about unions of open balls and stuff? Aren't we doing the question about why the topological space Peter mentioned before is not metrizable?

David Wheeler

he has a number of different problems he is working through, i believe

Ragib Zaman

5:45 AM

O I see.

Peter Tamaroff

@RagibZaman First I have to prove a metrizable space is Hausdorff as you guys call it.

=)

Ragib Zaman

Oh ok!

Draw a picture!

Peter Tamaroff

@RagibZaman LAWL

@RagibZaman No, but really. I can just choose $\epsilon<d(a,b)$, right?

Ragib Zaman

Whenever you have a chance, draw a picture, things are much clearer. This proof becomes almost trivial once you've drawn the right picture.

Peter Tamaroff

@RagibZaman I know.

Ragib Zaman

5:47 AM

Yes you can choose an $\epsilon < d(a,b)$

Peter Tamaroff

I mean, let $O_a=\bigcup_{x \in O_a}B(x;\epsilon_x)$ and $O_b=\bigcup_{y \in O_b}B(y;\epsilon_y)$.

David Wheeler

i would choose $\epsilon$ < (1/2)d(a,b)

Peter Tamaroff

@DavidWheeler You play it safe. And I'm not a physicist. Leave to them the ugly $\dfrac 1 2$

David Wheeler

no, imagine we are in the euclidean plane, and our two points are (1,0), (2,0)

then d((1,0),(2,0)) = 1

Peter Tamaroff

@DavidWheeler Hhehe sorry, in this case you're right.

David Wheeler

5:50 AM

the two disks of radius 1 centered at those 2 points will intersect

Peter Tamaroff

In fact there was an exercise I had to make the same picking.

Let me see if it relates to this.

Here it is

David Wheeler

there's no need to pick a "maximal" epsilon, but you can try to do so, if it pleases you

Peter Tamaroff

Let $a$ and $b$ be distinct point of a metric space. Prove there are nbhds $N_a$ $N_b$ such that $N_a\cap N_b=\varnothing$.

I chose $\epsilon <d(a,b)/2$ as you point.

@DavidWheeler Nah, I'm OK. I was just joking.

David Wheeler

you'll need to invoke the triangle inequality at some point

Peter Tamaroff

@DavidWheeler To prove disjointness?

David Wheeler

5:55 AM

yes

do you see why?

well, you'll have to tell me what "x" is

Peter Tamaroff

@DavidWheeler Can't I just choose two open balls? They are open sets after all....

David Wheeler

yes, but you need to prove they can be chosen to be disjoint.

Peter Tamaroff

@DavidWheeler OK.

I'm on it

David Wheeler

how do you show two sets are disjoint?

Peter Tamaroff

I'm just sketching the proof out

I hate having to rewrite stuff.

David Wheeler

6:03 AM

one way (the way stated by your problem) is to show the intersection is null

you could proceed one of two ways (well, 3, but two are "the same")

pick a point in $N_a$ and show it is NOT in $N_b$ (or vice versa)

you'll have to pick an "arbitrary point"

or...assume the intersection is NOT empty, and get a contradiction

Peter Tamaroff

@DavidWheeler Yes, I'm doing that.

OK

I have that for any $x$ in $O_a$

$$\eqalign{
& d\left( {a,x} \right) < \frac{{d\left( {a,b} \right)}}{2} \cr
& d\left( {a,x} \right) + d\left( {a,x} \right) < d\left( {a,b} \right) \cr
& d\left( {a,x} \right) + d\left( {a,x} \right) \leqslant d\left( {a,x} \right) + d\left( {x,b} \right) \cr} $$

So

$$d\left( {a,x} \right) \leqslant d\left( {x,b} \right)$$

I should arrive at the same

That is

$$d\left( {a,x} \right) \geqslant d\left( {x,b} \right)$$

Then it can only be that for every $x$ in both balls $$d\left( {a,x} \right) = d\left( {x,b} \right)$$

Sorry I was naivly thinking about $\Bbb R$.

David Wheeler

no, it stands to reason that x would be closer to a than to b

Peter Tamaroff

@DavidWheeler Could you rephrase that?

David Wheeler

what you want to show is that d(x,b) > (1/2)d(a,b)

which puts x outside of $N_b$

Peter Tamaroff

OK.

Wait.

Ragib Zaman

6:16 AM

@PeterTamaroff What have you picked to be your open sets around a and b?

Peter Tamaroff

@RagibZaman Open balls.

Ragib Zaman

With radius what?

David Wheeler

half the distance between their centers

Peter Tamaroff

@RagibZaman $\epsilon <d(a,b)/2$

Ragib Zaman

Instead of less than, just pick equal.

user19161

6:17 AM

@PeterTamaroff Note that there are also different non-equivalent definitions of the same term when it comes to the different separation properties you will study later on like $T_1$ and $T_2$.

Ragib Zaman

radius for both balls: $d(a,b)/2$

Peter Tamaroff

@RagibZaman OK

Ragib Zaman

Now suppose they intersect. You get a $t$ in both balls.

By definition of being in those balls, we have $d(a,t) < d(a,b)/2$ and $d(b,t) < d(a,b)/2$

Do you see a contradiction about to happen?

user19161

You are up early today @jonas!

Peter Tamaroff

$$\eqalign{
& d\left( {a,x} \right) + d\left( {a,x} \right) < d\left( {a,b} \right) \leqslant d\left( {a,x} \right) + d\left( {b,x} \right) \cr
& d\left( {b,x} \right) + d\left( {b,x} \right) < d\left( {a,b} \right) \leqslant d\left( {a,x} \right) + d\left( {b,x} \right) \cr} $$

Ragib Zaman

6:20 AM

That is too complicated

Hint: Add the two inequalities I wrote.

Peter Tamaroff

Barf

OK

So you see it?

Yep

Cool =].

we have d(a,b) ≤ d(a,t) + d(b,t) < d(a,b)/2 + d(a,b)/2 = d(a,b)

Peter Tamaroff

6:22 AM

@RagibZaman So I have to state open balls in the metric space are open sets in the topology, for starters

David Wheeler

which is why "open" is important, we NEED the strict inequality

Ragib Zaman

@PeterTamaroff Yes, that should have been one of the first things proved when you defined these terms.

David Wheeler

what the book is trying to show you, by the way, is that the hausdorff property can be used as a "weak substitute" for the triangle inequality

Peter Tamaroff

@RagibZaman I have that result is true because of a THEOREM I have on open sets in Metric Spaces.

They precsiely have the properties a topology should have

@DavidWheeler Good!

Ragib Zaman

@PeterTamaroff Well there are no "open balls" in a general topology, you need the metric for the defining condition to make any sense.

user19161

6:26 AM

@PeterTamaroff Yes, and also there is no need to capitalize "theorem" or "metric" in such sentences.

David Wheeler

that even if we have no notion of "distance" we can still separate using neighborhoods to tell "near" from "far"

Peter Tamaroff

@RagibZaman I'm talking about metrizable spaces here.

@DavidWheeler ;)

Ragib Zaman

@PeterTamaroff Yes whenever I see metrizable space I just think of a metric space where we don't know the metric.

The moral here is, metrics induce a topology that is fine enough to "separate" two points, there will exist members of the topology that contain each of the two points but not intersect. In this sense the topology can "tell" the two points apart.

Imagine you can see open sets as a whole, but you can't see
inside" them. If your open sets are such that there exists two points are always "together" - if one of those is in an open set then so is the other, then there is no way for the topology to distinguish between those two points.

David Wheeler

for example, in the indiscrete toplogy, you just have one big "blob", whose individual points remain a mystery to you

Peter Tamaroff

Thanks for the insights!

You're awesome.

David Wheeler

6:31 AM

because your only neighborhood is X.

Peter Tamaroff

@DavidWheeler I have only been introduced to the discrete topology $\mathfrak I=\mathcal P(X)$

Ragib Zaman

While with the discrete topology, everything is an open set so the topology is very "fine", it can see every little thing as different.

Peter Tamaroff

but just told it has that name

David Wheeler

you can also go to the other extreme...the neighborhoods are "chopped so fine" they never interact with each other

Ragib Zaman

Often for your purposes you want something in between these two.

Peter Tamaroff

6:32 AM

and that it is the "largest" one

David Wheeler

each point is a neighborhood unto itself

and sometimes that's the best you can hope for, with a totally disconnected space, like the integers in the relative topology

Peter Tamaroff

Oh! Right. Every singleton of $X$ is part of the topology, right?

David Wheeler

right, what is the intersection of an open interval containing k, with [k,k] (where k is an integer)?

Old John

Good morning

Peter Tamaroff

@DavidWheeler what is $[k,k]$ here?

David Wheeler

6:38 AM

a closed real interval

Peter Tamaroff

But doesn't that vanish?

Old John

Not quite :)

David Wheeler

no, it contains the single point {k}

Peter Tamaroff

@DavidWheeler DERP

Well, vanishes to a point. =D

David Wheeler

i'm just giving you an example where you get a discrete topology "naturally"

Peter Tamaroff

6:39 AM

Or more dramatically, collapses into a point.

David Wheeler

by considering the integers embedded as a subset of the reals, and using the subspace topology

Peter Tamaroff

@DavidWheeler I haven gotten there yet =P

David Wheeler

you were doing the subspace topology of the reals (well, a metric space, in fact) yesterday

when we were doing the "intersect Y" business

Peter Tamaroff

@DavidWheeler Yes, I know about subspaces ofmetric spaces but not subspaces of topologies.

David Wheeler

well topologies are very simple: they're the collection of open sets

in a metric space, you use the metric to DEFINE what "open" means

Peter Tamaroff

6:43 AM

@DavidWheeler RIght

@DavidWheeler But now I define a topology and call tis elements open sets

David Wheeler

but you don't actually need a metric...you can axiomitize what open means

Peter Tamaroff

@DavidWheeler Open means being a member of the topology!

David Wheeler

and then metric spaces become a "special case"

right..but a topology has to satisfy certain rules

Peter Tamaroff

@DavidWheeler Yes, yes, sure.

David Wheeler

the null set and the whole space must be open

arbitrary unions of open sets must be open

and finite intersections of open sets must be open

any subset of the power set of X which conforms to these rules, qualifies as a topology for X

{Ø,X} is the "coarsest one", the indiscrete topology

P(X) is the "finest one", the discrete topology

Peter Tamaroff

6:49 AM

@DavidWheeler Oh, that is mentioned as an example, but don't tell it is called that.

David Wheeler

the "standard topology" for $\Bbb{R}^n$, which is the one that serves as the "intuitive" example, can be constructed in different ways...one of these is as a metric space

Peter Tamaroff

@DavidWheeler I assume you're talking about the union of open balls in it.

David Wheeler

in particular, the one inherited from the euclidean metric

d(x,y) = |x-y| (where this is a vector norm, |v| = √(v.v), that comes from the "dot product")

Peter Tamaroff

I am being told to prove that $(X,\mathcal P(X))$ is metrizable by using the binary metric $d(x,x)=0$,$d(x,y)=1$

I undertand now!

$0\Rightarrow$ the topology says "Dude, that element is in this set"
$1\Rightarrow$ the topology says "Dude, that element is not in this set"

David Wheeler

yes, that is often called "the discrete metric", only x is near x, everything else is "away"

you can use any positive real number instead of 1, but 1 is "convenient" (simple, easy to grasp).

Peter Tamaroff

6:56 AM

I'll go to sleep now.

It is 4am

I end up oversleeping then.

David Wheeler

somewhere, you probably have a theorem that says: if d is a metric, then so is d', where d'(x,y) = r(d(x,y)), for any real r > 0.

Peter Tamaroff

@DavidWheeler I don't have it but it is immediate.

David Wheeler

in other words, we can "scale the space" it doesn't affect the metric properties

because the actual numbers we get aren't that interesting...we just want a way to say "nearer"/"farther"

Peter Tamaroff

@DavidWheeler You have a way to interpret anything!

David Wheeler

topology is very "geometrical", we're interested in "spatial" properties

Peter Tamaroff

7:02 AM

@DavidWheeler So, how do I describe the metrizaation of $(X,2^X)$?

by means of the discrete metric.

David Wheeler

when calculus is taught...you learn to do all sorts of cool things with limits and stuff

Jonas Teuwen

@JasperLoy Yep.

David Wheeler

and it's the open sets that make it all work

Peter Tamaroff

@DavidWheeler Should I define open balls by means of $d$?

David Wheeler

they gloss over that...a theorem will start with suppose f is differentiable on (a,b) blah blah blah

sure...using that binary metric, what is an epsilon ball centered at x of radius 1/2?

Peter Tamaroff

7:05 AM

@DavidWheeler Yes, yes!

David Wheeler

and that shows that for every x in X, {x} is an epsilon-ball

Peter Tamaroff

Every singleton of $X$ is open

and its union is a subset of $X$

and so is any finite intersection

David Wheeler

so therefore, every element of P(X) is a union of epsilon-balls

Jonas Teuwen

I, Sir, am also a union of balls.

David Wheeler

so when you use "the same construction" as any metric space, you get that the collection of all open sets is the power set of X, under that binary metric

this is topology, not tea-bagging

Old John

7:09 AM

@JonasTeuwen Good morning, your ball-ness :)

David Wheeler

you have to admit, though, as a topology...it's not very "interesting"

we just throw in every set we can think of, sort of unfair

Jonas Teuwen

@OldJohn :-. Hi.

@DavidWheeler It is very fair: no discrimination. All balls are welcome!

Old John

Topologies tend to be most interesting when they have "enough" open sets but not "too many" (in some sense)

Jonas Teuwen

@OldJohn Ahh! Weak topologies. Spoken as a true analyst.

David Wheeler

yes...when they are "warm and fuzzy" (advanced technical terms i prefer not to define)

Jonas Teuwen

7:13 AM

I need to study some category theory.

Old John

@JonasTeuwen Yep - I had a love-hate relationship with fine topology in potential theory

Peter Tamaroff

Bye byes peoples of the math.

Old John

now forgotten most of it

Peter Tamaroff

Have a good one.

Old John

@PeterTamaroff Bye Peter

Peter Tamaroff

7:14 AM

@DavidWheeler Special thanks to you and @RagibZaman for the enlightment!!

David Wheeler

universal properties still seem like cheating to me, somehow

like this is "the that", because it does just what we want it to

Matt N.

Please vote to close as exact dupe. Thx.

Old John

@DavidWheeler Agreed

Breakfast beckons - back later

Jonas Teuwen

@MattN. Sup!

@OldJohn Perhaps true love. Involves hate sometimes.

Old John

7:30 AM

@JonasTeuwen Yes indeed - sometimes these mathematical mysteries keep us frustrated for ages, and then suddenly open them selves up to our advances and we make progress ...

Jonas Teuwen

@OldJohn :-).

user19161

7:42 AM

@OldJohn How was breakfast?

Old John

@JasperLoy Great, thanks - my wife does the best scrambled eggs :)

user19161

@OldJohn Oh I love scrambled eggs too, but I usually take soft-boiled eggs nowadays. Do you know what that is?

Old John

@JasperLoy Yes, we have tnem too

user19161

@JonasTeuwen Indeed. Sometimes love turns into hate. There is a thin line separating the two. Unless you are talking about that Buddha guy's universal compassion.

Jonas Teuwen

@JasperLoy You know what the last thing (I believe it was the last) Bertrand Russell said on TV? :-).

user19161

7:45 AM

@JonasTeuwen No, I don't know.

Jonas Teuwen

@JasperLoy "Hatred is foolish, love is wise."

user19161

@JonasTeuwen When people talk like that, either they are truly wise and know what they are talking, or they are truly foolish and just parroting others.

Jonas Teuwen

@JasperLoy Russell was truely wise. Here it is: io9.com/5827117/…

Apparently not his last. He looked really old there though 8-).

user19161

@JonasTeuwen Hah, maybe I was Bertrand Russell in my previous life. :-)

Jonas Teuwen

@JasperLoy Hmm... well... start being very profound then! Or is that now how it works?

user19161

7:48 AM

@OldJohn I usually take it with soya sauce. Is that what you do too?

Old John

@JasperLoy Nah - I prefer a bit of fresh chopped chilli :)

Russell was a great guy - but have you ever looked at his Principia book? (Along with Whitehead)

user19161

@OldJohn That is unheard of here. Soya sauce is the norm.

user19161

@OldJohn Nope, never seen it.

Jonas Teuwen

@JasperLoy Russell's message to the future.

Old John

@JasperLoy Interesting - where are you? I'm in the UK, but chilli is not the norm here - I am unusual :_

Matt N.

7:55 AM

@JonasTeuwen Hey there. Just doing commutative algebra. What about you?

user19161

@OldJohn I am in Singapore, your ex-colony. :-)

user19161

@JonasTeuwen After watching that video, there was one girl in bra video that was advertised. Weird!

Old John

@JasperLoy Ah - sorry about that - being British means I often apologise for my ancestors behaviour

Jonas Teuwen

@JasperLoy Mm, it remembers your preferences.

user19161

@OldJohn I think they are good. Perhaps life would be better if we were still a colony. :-)

Jonas Teuwen

7:57 AM

@OldJohn At least you're not German... 8-). (sorry, bad joke)

user19161

@JonasTeuwen Ah, the GND...

Old John

@JonasTeuwen :)))

Jonas Teuwen

@MattN. Working on Puzzles.pdf :-).

Zhen Lin

@OldJohn I find it a somewhat irritating habit. Colonisations has its ups and downs, but I'd rather not be living in a tropical backwater.

Old John

Hmm my reputation has gone static, I must see if there are any questions I can understand enough to provide an answer

Matt N.

8:00 AM

bbl

Old John

@ZhenLin What is the annoying habit? If it is "apologising", then I am sorry :)))

Jonas Teuwen

@OldJohn So what? :-). Write cool stuff.

Old John

@JonasTeuwen :)

Jonas Teuwen

Or maybe colonisation is the annoying habit?

user19161

@JonasTeuwen Or write hot stuff.

Jonas Teuwen

8:01 AM

@JasperLoy Are you Donna Summer?

Old John

@JasperLoy Maybe not enough hot stuff on main?!

Jonas Teuwen

Almost all West-European countries have a colonial history.

I seriously wonder if the current generation has to feel guilty about that.

user19161

@JonasTeuwen No, I had to google her.

Jonas Teuwen

Not even their parents could have been involved.

Zhen Lin

Precisely!

Old John

8:02 AM

@JonasTeuwen True

user19161

@JonasTeuwen It's not necessarily a bad thing. In fact it is often a good thing.

Zhen Lin

The way people feel obliged to apologise about it, you'd think each country perpetrated its own Holocaust on its colonies...

Jonas Teuwen

@ZhenLin Well, for Belgium that is basically true.

Zhen Lin

shrug

Jonas Teuwen

If mass murder qualifies :-).

user19161

8:05 AM

@JonasTeuwen Never studied European history to know. But I think we should not think of whether we belong to this or that ethnicity for identity. We should just be true to ourselves.

Zhen Lin

I don't really know the history elsewhere in the world. But we got off lightly enough.

Jonas Teuwen

Hmm, it is so long ago... don't forget history, don't make the same mistakes again. Done?

user19161

QED.

Zhen Lin

In fact, as far as I know, any lingering resentment here is usually directed toward the Japanese.

user19161

@ZhenLin Did you know that "Jap" is considered offensive? I didn't.

Zhen Lin

8:08 AM

Well, historically, it was used as an ethnic slur during WWII...

nowadays youngsters use it because they're lazy

user19161

I only learnt about it a few months ago. I mean we do shorten lots of words in speech.

Jonas Teuwen

I love this bird.

user19161

@JonasTeuwen Looks a bit like you bro.

Jonas Teuwen

A baby chick.

@JasperLoy Thanks!

user19161

There is a stupid user on ELU who created over 60 sockpuppet accounts to override suspension.

Jonas Teuwen

8:14 AM

@JasperLoy Subnet ban...?

user19161

He has started posting offensive things about other users as well.

user19161

@JonasTeuwen IP ban not feasible. I think TPTB are looking into what can be done.

Jonas Teuwen

@JasperLoy 60...? Then you have to make like 60 e-mailaccounts?

@JasperLoy If you keep banning his IPs he will run out of them eventually.

Zhen Lin

There are websites that let you make emails easily.

user19161

@JonasTeuwen Yes. At first I thought he is just a troubled kid, but now I think he is actually an evil thing.

Jonas Teuwen

8:16 AM

@ZhenLin Yes, but there are only finitely many of these.

@ZhenLin Or... you mean real ones and not redirects?

Old John

Pardon my ignorance, but what is ELU?

user19161

@OldJohn English language and usage SE.

Old John

Ah - thanks

Zhen Lin

@JonasTeuwen $10^{10^{10^{10}}}$ is a finite number too!

user19161

@OldJohn We also have CLU, GLU, FLU for Chinese German French.

user19161

8:18 AM

@ZhenLin I have difficulty parsing this expression.

Old John

@JasperLoy I must get round to looking at some of these - but not enough time for everything

Jonas Teuwen

@JasperLoy Overflow?

@ZhenLin Hmm... perhaps enforce the use of OpenID?

user19161

@JonasTeuwen Yeah, I know a googol is 10^100 and a googolplex is 10^googol.

Jonas Teuwen

@JasperLoy It think the idea is: like really really big.

user19161

@JonasTeuwen Yeah, but not as big as my balls.

Jonas Teuwen

8:20 AM

Mm...

user19161

Convergence is making smaller balls, divergence to infinity is making bigger balls.

user19161

I like the blue theme of MSE. Some sites have a red theme which is too bright for me. I think it would be nice if SE lets us choose from a set of themes for each site when we log in.

Old John

@JasperLoy Excellent idea

Jonas Teuwen

@JasperLoy Massage the CSS, bro, massage the CSS...

Old John

I must go and do some work in the garden - back in a few hours

Jonas Teuwen

8:28 AM

@OldJohn Have fun!

user19161

@JonasTeuwen Oh, that's what the programmer guys in the other room told me, but it should work OOTB instead of hacking!

Old John