The h Bar

Anonymous

5:04 PM

@Tanuj There's a chat room named "The Periodic Table" on Chemistry SE.

Anonymous

Also, I'm a bit busy now. Not sure I can help you. You can ask nevertheless and hope someone comes by

bolbteppa

"The matter couplings of chiral multiplets are **conveniently** described in the language of Kahler geometry"
...

ACuriousMind

5:23 PM

@Blue Yes, all products of groups exist (and "are groups", but in some definitions that's already included in saying they exist) whether finite or infinite. Their order is completely irrelevant for the notion of the direct product.

0celo7

@Tanuj you mean you have a question?

ACuriousMind

And indeed taking the direct product of some A as often as the cardinality of some other B is isomorphic to the maps from B to A, which is why you can find $A^B$ as notation for all maps $B\to A $.

Anonymous

@ACuriousMind Woah, that's a good point

Anonymous

It's a pity that my Algebra textbooks - Gallian and Artin don't go into much depth when discussing direct products

0celo7

@Blue Exercise: the power set is $2^X$, where $2=\{0,1\}$

Anonymous

5:33 PM

@0celo7 I don't understand the notation $2=\{0,1\}$

Balarka Sen

It's a good notation.

Anonymous

I mean I don't know what it means

Anonymous

Are you labelling the set as 2 ?

Balarka Sen

Yes

0celo7

it's a generic set with two elements

Balarka Sen

5:34 PM

It's in accordance with the PA definition of natural numbers, or ZFC thereof

0celo7

but as Balarka says, in PA you define numbers as sets

and 2 is the set with 0 and 1

Anonymous

Ok, and what do I have to find? Power set of 2 ?

0celo7

power set of $X$

Anonymous

What is $X$ ?

0celo7

any set

Balarka Sen

5:36 PM

Any set

0celo7

@BalarkaSen do you gork the layer cake representation

Balarka Sen

idk what it is

John Rennie

gork?

0celo7

grok

I think it's actually super trivial but the proofs people give are all quite complicated

Tanuj

5:53 PM

@blue @JohnRennie are you guys avaialable? I just need 10 minutes of yours.

Abcd

@Tanuj JR is not available when he is offline.

bolbteppa

Turns out Kahler manifolds are easier than Riemannian ones on a basic level

Bernardo Meurer

@DrSatan1 @0celo7 On it

Slereah

6:22 PM

So if we take the empty set to be a Lorentzian manifold

What is its causal structure

I mean, it's true that $\forall p \in \varnothing, p \ll p$

Is the empty set a Lorentzian manifold

It's a $4$-manifold

With the coordinate chart $(\varnothing, \varnothing)$

Mapping to the subset $\varnothing \subset \Bbb R^4$

Balarka Sen

It admits a Lorentzian metric vacuously

Slereah

It has the vector bundle $\pi : \varnothing \to \varnothing$, with the local trivialization $\psi = \varnothing$

I wonder if everything works vacuously or if, at some point, you encounter an obstacle

Maybe I should make it a PSE question for fun

Anonymous

@0celo7 I didn't write it down formally. But here's the idea: Let $S$ be the set of functions from the set $X$ to $\{0,1\}$. Say we have a set $X=\{a,b\}$. The possible functions are $f_1(a)=0,f_1(b)=0$, $f_2(a)=0, f_2(b)=1$, $f_3(a)=1, f_3(b)=0$ and $f_4(a)=1, f_4(b)=1$. I can always make an one-one onto correspondence between these functions and the elements of power set of $X$.

Anonymous

For example, here the function $f_1$ can be mapped to the element $\{\}$ of the power set, $f_2$ to $\{b\}$, $f_3$ to $\{a\}$ and $f_4$ to $\{a,b\}$.

Slereah

Hm

0celo7

6:37 PM

@Blue that's the idea

a formal proof goes along these lines

Balarka Sen

If $Y$ is a subset of $X$, define $f : X \to \{0, 1\}$ as $f(x) = 1$ if $x \in Y$ and $f(x) = 0$ otherwise.

This is a bijection (check)

0celo7

If $A\in \mathcal P(X)$, then define $f_A\in 2^X$ by $f(x)=1$ if $x\in A$, and $f(x)=0$ if not

Anonymous

Uh, yeah. Gotcha

0celo7

For the other way, assign to $f\in 2^X$ the set $A_f=\{x\in X:f(x)=1\}$

CooperCape

Boo

0celo7

6:46 PM

@CooperCape oh, you're a Klansman?

CooperCape

Ahh yes I am very pleased it's another burn tonight :)))))

0celo7

@ACuriousMind ^ my god

CooperCape

Although once I did make a cross out of two splints and burn it in a chem class

I mean if I can't convince you away from it I may as well be so outrageous that you refuse to mention anything near it it again.

Balarka Sen

did you also sing violent black metal while doing it

0celo7

@CooperCape you have completely misjudged me if you think that's a valid stategy

CooperCape

6:48 PM

Ehh I'm trying a few methods

Apparently "Hey ocelo I am not racist" doesn't work either so like whatevs

0celo7

you've been banned multiple times for racism

CooperCape

Once, I called you a whatsit. The next time I joked and said "I can't even call you a wotsit"

wow I have no continuity

0celo7

turns out I am jewish

Slereah

Oy vey

Anonymous

@0celo7 I thought most Ungers are Germans...

CooperCape

6:50 PM

@0celo7 Were you offended by it?

Balarka Sen

I have been banned for saying something unintentionally racist and I think it's well-deserved.

Anonymous

There could have been inter-mixing though

0celo7

@Blue Germans can't be Jewish?

Slereah

German jews disappeared a lot in the 40's

CooperCape

I didn't think getting banned for what I said wasn't well-deserved. I think this is 6 months later and ocelos suggesting I am a member of the kkk for it.

Slereah

6:51 PM

Not sure why

Balarka Sen

@0celo7 According to you know whom

0celo7

@Slereah holocaust denial is probably the worst thing to do in this chat

Anonymous

@0celo7 I mean that's quite rare. And you know why

Slereah

I ain't denying no holocaust

0celo7

@Blue No, I don't know why. There's lots of Jews in Germany.

Hitler didn't get all of them

Balarka Sen

6:53 PM

It's not rare I do not think.

CooperCape

How has this discussion started from me saying 'boo'

like for real

Emilio Pisanty

hey @JohnRennie is there a better dupe for this one? physics.stackexchange.com/questions/384139/…

Anonymous

@BalarkaSen That's a double negative :P

0celo7

@BalarkaSen We've established Blue's ignorance of Western society often enough

Balarka Sen

@Blue A missing comma, not a double negative

0celo7

6:54 PM

@Blue My great-great (great?) grandfather was an orphaned Jew who was adopted by Germans

and my great-grandfather came to America before WW1

CooperCape

You want a sticker/

Anonymous

@0celo7 Well, I'm at least learning new things from you guys. I already admitted long ago that my knowledge of Western history is quite shallow (mostly because of my hate for history classes during school :p)

CooperCape

Oooh how about a sta... w..waaa...wait.

0celo7

you want me to put a Jude patch on my arm?

@ACuriousMind I'm triggered

Balarka Sen

According to wikipedia the core Jewish population in Germany is 0.9% of the total population

Not bad

It's less than Russia though

Which is 1.4%

Soviet Russia also gave Jews a hell of a hard time though (this sentence is not correlated with the data I wrote above)

CooperCape

6:57 PM

I swear 50% of the time I'm here a discussion on some kind of 20th century history involving some sort of genocide takes place.

Balarka Sen

Talking about something is not necessarily a bad thing.

0celo7

@CooperCape wonder why, david duke

CooperCape

@BalarkaSen Yeah well it's how it begins is the issue

Balarka Sen

How it begins is how people get freaked out about conversations like you're being now

CooperCape

@BalarkaSen scroll up bb

0celo7

6:59 PM

@BalarkaSen ok measure theory time

@Blue

Anonymous

@0celo7 ?

0celo7

Let $f$ be a nonnegative measurable function on some measure space (doesn't matter which)

Anonymous

I solving weird circuits now

0celo7

Define $\mu_f(t)=\mu\{x\in X:f(x)>t\}$

the distribution function of $f$

Balarka Sen

okie

0celo7

7:01 PM

uh hold on

@BalarkaSen I'm trying to write a proof of something tautological that has taken me hours to think about correctly

I'm trying to make it more clear but don't know if I can

Balarka Sen

Write it up once you get it; I'll have a look once I wake up

Going to sleep now

0celo7

I do get it, I just don't know how to write it down

Balarka Sen

Gotcha

0celo7

Layer cake representation

In mathematics, the layer cake representation of a non-negative, real-valued measurable function f defined on n-dimensional Euclidean space R n {\displaystyle \mathbb {R} ^{n}} is the formula f ( x ) = ∫ 0 ∞ 1 L ( f , t ) ...

read this before you sleep

Anonymous

@BalarkaSen Unusually early for you. Guess you are awake for >24 hrs?

0celo7

7:07 PM

wonder if Reed and Simon have a picture I can emulate

@BalarkaSen the layer cake formula is really trivial

it just says that if $f$ is nonnegative, one can obtain $f(x)$ by going to $0$ above $x$ and then going up to the graph

like, completely tautological

but very useful

bolbteppa

8:15 PM

The dow, thanks Trump

Bernardo Meurer

9:17 PM

Number theory

Donald Trump Counts To The Biggest Number Ever

►

0celo7

10:17 PM

proof that ZFC is incorrect i.redditmedia.com/…

@BernardoMeurer please evaluate

DanielSank

10:44 PM

@dmckee

2

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