The h Bar

At least in the sense in which I would use the word - you can check continuity on an arbitrarility small neighbourhood around the point at which it's supposed to be continuous.

0celo7

correct

@ACuriousMind ok, I have three options

(i) continue reading Hatcher

(ii) read Kreyszig to help Balarka with 2D geometry

(iii) play Fallout

Bernard Meurer

I meant that it is countinuous at a point $a$ as opposed to continuous for every point

0celo7

@ACuriousMind @BernardMeurer @Obliv decide what I should do

user218912

why don't you ask me too? :(

user218912

#leftout

0celo7

7:21 PM

@BernardMeurer That just means continuous at $a$ as opposed to continuous on the dokain

@bl00 Didn't know you were here

@ACuriousMind I'm gonna play Fallout :3

user218912

@0celo7 play fallout.

Obliv

@0celo7 balarka needs help with 2d geometry?

Bernard Meurer

@0celo7 Teach me how to multiply matrices

Obliv

what's that wallpaper from @acuriousmind

user218912

@BernardMeurer seriously?

user218912

7:30 PM

I wrote some notes on how to multiply matrices a year ago for a presentation I did to my class.

Bernard Meurer

@bl00 No, unless you know how to do it without wanting to commit suicide in the process

user218912

want to see?

Bernard Meurer

It's simple, it's just a pain in the ass

I'd like your notes, yeah

they can always be helpful

user218912

here's the exact section

user218912

user218912

7:32 PM

idk if I made any mistakes

0celo7

@Obliv not in the strict sense

Bernard Meurer

Nah that's correct

Obliv

going to see if i remember how to write matrices in latex. $\begin{bmatrix} a & b & c \\ d & e & f \end{bmatrix}$

oh nice.

Bernard Meurer

but it's still the same method that makes you want to die

user218912

lol

Bernard Meurer

7:32 PM

There's a linear algebra method, but it's even worse

i think, I gotta read my notes

0celo7

As @ACuriousMind knows I can't multiply matrices

user218912

right because you're missing the part of your brain that does linear algebra.

user218912

yet ur still better than me at linear algebra.

user218912

life sucks.

0celo7

@BernardMeurer via tensor products/universal properties?

Obliv

7:35 PM

$\begin{bmatrix} a & b & c \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{bmatrix} \cdot \begin{bmatrix} d & e & f \\ d_2 & e_2 & f_2 \\ d_3 & e_3 & f_3 \end{bmatrix} = \begin{bmatrix} ad + bd_2 + cd_3 & ae + be_2 + ce_3 & af + bf_2 + cf_3 \\ ... & ... & ... \\ ... & ... & ... \end{bmatrix}$

there that's not so hard

@bernard just follow that and you'll be fine 8^]

user218912

what if I'm too dumb to fill in the blanks.

user218912

you should have included all of it like in my notes.

Obliv

nah he's smart and I'm lazy so

0celo7

rekt

user218912

who got rekt?

0celo7

7:37 PM

you

user218912

how?

0celo7

he called you dumb

user218912

no he didn't.

Bernard Meurer

@Obliv It's not that it's hard, it's that it's boring as fuck

0celo7

that's what she said

Obliv

7:37 PM

yea well would u rather get a poor grade on a test

@0celo7 are you like 5

user218912

@0celo7 I said what if... and he said bernard isn't dumb.

Bernard Meurer

Who's missing a part of the brain?

user218912

I don't see who got rekt there.

Bernard Meurer

What is happening?

0celo7

nothing of interest

starting windows

Bernard Meurer

7:39 PM

@JohnDuffield Hello darkness my old friend

The Sound of Silence (Original Version from 1964)

►

Obliv

@0celo7 do you want to try a new and fun game

0celo7

Nope

Literally zero interest

Bernard Meurer

You guys changed pics again

It's confusing af

0celo7

we should just block them @BernardMeurer

they're basically the same person

Bernard Meurer

@0celo7 I need @Obliv b/c he drops some nice programming challenges every once in a while

Obliv

7:43 PM

it's the latest and greatest videogame

user218912

well me and @Obliv are really similar in ways.

Bernard Meurer

@Obliv That is the dumbest thing I have ever seen

user218912

@BernardMeurer wow so you don't need me? </3

0celo7

my computer is broken

Bernard Meurer

@bl00 Well, no, but I also don't need my mother which doesn't mean I dislike her

Obliv

7:44 PM

lol i'm just gonna delete that in case..

user218912

what's bad about it?

Bernard Meurer

@Obliv Which school do you go to again?

Obliv

idk i saw a mod walk in tho

@bernard trump university

Bernard Meurer

@Obliv ¬¬

Obliv

he's my dad so i get free admission

Bernard Meurer

7:45 PM

Sigh

Obliv

whats ur favorite drinks guys

user218912

blue koolaid.

Keshav Srinivasan

@ACuriousMind "The algebra of infinitesimal rotations is the algebra of angular momentum, which is not commutative in 3D. What is that comment supposed to mean?" Infinitesimals do commute to first order. That's why angular velocities add vectorially.

ACuriousMind

@Obliv Beer.

Bernard Meurer

You guys are all insane

@Obliv Beer

0celo7

7:48 PM

ok fixed my computer

Obliv

any favorite beer?

@0celo7 welcome back

Bernard Meurer

@Obliv Hard question

user218912

are there any blue beers?

Keshav Srinivasan

@ACuriousMind Here's a proof from Taylor's Classical Mechanics textbook that angular velocities add vectorially:

Bernard Meurer

Flens is good for just drinking a lot, I like Duvel and Colorado for savouring

Keshav Srinivasan

7:48 PM

Bernard Meurer

@bl00 Probably

Obliv

@bl00 there's blue moon but i don't think the actual beer is blue :\

ACuriousMind

@KeshavSrinivasan To what order? The infinitesimal rotations are the three generators of rotation with commutation relation $[L_i,L_j] = \epsilon_{ijk}L_k$. You must be using "inifnitesimal" in a non-standard sense.

Bernard Meurer

@ACuriousMind LOVE ME

0celo7

@BernardMeurer wtf

user218912

7:50 PM

gonna read cya guys

Obliv

@bl00 good luck cya

Bernard Meurer

This exam is stressing me out

0celo7

@ACuriousMind Some grad student tried to say the commutation relations were wrong for that

ACuriousMind

@Obliv Many. I don't have any I'd put above all others

0celo7

he got laughed at by everyone

ACuriousMind

7:50 PM

@BernardMeurer <3

Bernard Meurer

@ACuriousMind <3

Obliv

@acuriousmind so what was your wallpaper?

ACuriousMind

@KeshavSrinivasan I don't see what adding angular velocities is supposed to have to do with infinitesimal rotations.

@Obliv Player character at a bonfire in Dark Souls.

Obliv

REALLY? I had no idea the game was that pretty..

the original dark souls?

ACuriousMind

I don't think it's a screenshot :P

Bernard Meurer

7:53 PM

Dank souls?

Keshav Srinivasan

@ACuriousMind Here's a proof that infintiesimal rotations commute to first order: mathworld.wolfram.com/InfinitesimalRotation.html

Bernard Meurer

Dank souls

Obliv

Okay but I thought it was in a cutscene or something.. i don't know lol

how else do you get a shot like that? (oblivious)

@bernard I think I know that area. that was in DS3* right

Bernard Meurer

@Obliv I just have it for the rare pepe

Obliv

oh ok

gonenc

7:55 PM

should we do anything about this user?

Albert Einstein Adolf Hitler

1

the answer is he provided is clearly a spam

and his username is not the nicest one on earth

Keshav Srinivasan

@ACuriousMind "I don't see what adding angular velocities is supposed to have to do with infinitesimal rotations." The connection is that the infinitesimal rotation that a rigid body undergoes between time t and time t+dt can be written as $\vec{omega}(t)dt$.

Sanya

@gonenc if I could flag usernames, I would

ACuriousMind

@KeshavSrinivasan Aha, now I know what you're talking about. The confusion on my end was that I considered $T^a$ to be an "infinitesimal rotation" while you consider $1+\epsilon T^a$ for infinitesimal $\epsilon$ to be an infinitesimal rotation.

Bernard Meurer

@gonenc That's the best username on this site probably

gonenc

@Sanya well s/he is clearly a troll look at this answer

-3

A: Scalar QCD with yukawa interaction

You cant explain the divergence like this becouse in not boson instance for the sake of electron camp magnetic power after the possibility of the elettric field behiavor dragon power

Keshav Srinivasan

7:57 PM

@ACuriousMind Oh ok

Bernard Meurer

@gonenc What do you mean? I clearly understand his point and agree

gonenc

oh I didn't actually see the dragon power part

now it makes sense!

Sanya

@gonenc well, I custom flagged it, maybe some mod power can do something ...

0celo7

@ACuriousMind ok feral ghouls are fucking scary

Help

ACuriousMind

@gonenc 1. It's not spam by the technical definition of spam here (no link, no service or site or article promoted), but it's clearly not an answer/very low quality. 2. User profiles are the areas with the greatest leeway. I will check if this is above the threshhold where we do something.

Keshav Srinivasan

7:59 PM

@ACuriousMind So do you have any thoughts on my actual question?

Bernard Meurer

@gonenc If you don't factor the dragon power it really doesn't fit!

@ACuriousMind Fascist

gonenc

@ACuriousMind I know that is why I didn't flag it as spam but rather as low quality :)

btw how do I un-accept an edit? or is it even possible?

I'm referring to this answer: physics.stackexchange.com/a/285918/68030

I thought it was the same person, who edited it (since they have the same profile pic) and found weird that it got in the queue

ACuriousMind

@KeshavSrinivasan I'm afraid not

@gonenc Good

@gonenc If you think the edit should be reverted, go to the revision history and click on "rollback" at the version you want to restore. However, I don't see that that edit made anything worse, so why do it?

0celo7

@ACuriousMind can I get a house or something

I've got stuff that I don't want to sell but I can't carry antrhjnf

Anything

ACuriousMind

Not exactly a house, no, but you will get some places to store your stuff I think

gonenc

8:06 PM

@ACuriousMind adding a video to someone else's answer is not too neat (ethically speaking)... I wouldn't want anyone adding some random video to my answer for example.

0celo7

Does the pip boy have a light?

I'm really scared

gonenc

and I wouldn't know what HUP is. Heisenberg UP was kind of like ok but..

ACuriousMind

@gonenc Oh, I didn't see it was a video

Hm

Let me check something

Obliv

@0celo7 did u fight the boss yet

0celo7

What boss

Obliv

8:10 PM

idk i never played the game <|8O)

ACuriousMind

@gonenc Dealt with.

gonenc

@ACuriousMind thanks :)

0celo7

Oh my god I'm so scared

Bernard Meurer

Damn, they just killed Einstein

ACuriousMind

@0celo7 Maybe? Try holding...tab? It's been a while

0celo7

8:16 PM

Hallelujah

<3

Wtf is happening

Jason Bright?

@ACuriousMind ok I'm really scared

What are these demons

ACuriousMind

hehehehe

Bernard Meurer

How do I know if an equation is linear?

Problem 1-1 here fenix.tecnico.ulisboa.pt/downloadFile/282093452026636/…

0celo7

If it equals it's linearizarion

@ACuriousMind what's funny :(((((

ACuriousMind

@BernardMeurer Check whether the sum of two solutions is again a solution.

Bernard Meurer

Hm? Wat?

0celo7

8:22 PM

Ahhhhh going into the basement

Wtf why is this so scary

Bernard Meurer

$$x_1 + 7^{\frac{1}{3}}x_2 -\sqrt{5}x_3=1$$

ACuriousMind

@BernardMeurer A linear equation is one where for two solutions $(x_1,\dots,x_n)$ and $(x_1',\dots,x_2')$ the sum $(x_1+x_1',\dots,x_n+x_n')$ is also a solution.

Bernard Meurer

How the heck do I verify that for linearity

So I gotta find two solutions and then test for a third?

You gotta be shitting me

ACuriousMind

@BernardMeurer No, not like that

Sanya

no, you've got to assume that you have solutions

ACuriousMind

8:24 PM

You assume that you have two solutions and show that their sum also is one from that

Sanya

big difference :D

Bernard Meurer

Don't understand it. Really, not joking here

Don't remember seeing this in class even

0celo7

HOLY SHIT WHAT

WHY

ACuriousMind

@BernardMeurer Okay, I'll do it as an example for $2 x_1+4 x_2 = 5$, okay?

Bernard Meurer

Okay, thank you

ACuriousMind

8:27 PM

Let $(y_1,y_2)$ and $(z_1,z_2)$ be two solutions, i.e. $2y_1 + 4y_2 = 5$ and $2z_1+4z_2 = 5$ hold. Then $2(y_1 + z_1) + 4(y_2+z_2) = (2y_1+4y_2) + (2z_1 + 4z_2) = 5 + 5 \neq 5$, so the equation is not linear.

Obliv

I love @0celo7 just freaking out about fallout while you guys try to converse about linear algebra

dude you should play five nights at freddys or an actual scary game haha

you would not last

ACuriousMind

If we replace $5$ by $0$, it becomes linear, since then $2(y_1+z_1) + 4(y_2+z_2) = 0$ holds.

0celo7

How many of these damn things are there

Bernard Meurer

@ACuriousMind AAAAAAAAH

I see!

Thanks!

So for the case I listed suppose $(a,b,c)$ and $(x,y,x)$ are solutions. We then have $$a + x + 7^{\frac{1}{3}}(b + y) - \sqrt{5}(c+z)=1 +1$$

?

but... 2 is not a solution @ACuriousMind ?

Sir Cumference

I hate how SE has no private messaging

0celo7

8:35 PM

Fuck

Bernard Meurer

@0celo7 Halp?

Sir Cumference

You all are able to read my stupid messages

0celo7

I accidentally knocked over antler :(

ACuriousMind

@BernardMeurer That's a bit weirdly phrased. What's not a solution is $(a+x,b+y,c+z)$, because the r.h.s should be 1 and not 2 for it to be a solution.

Bernard Meurer

r.h.s.?

ACuriousMind

8:36 PM

@SirCumference This is not a social network

@BernardMeurer right hand side, i.e. the 1+1.

Sir Cumference

@ACuriousMind Yes, yes, I know

Bernard Meurer

@ACuriousMind But, the solution says that it is linear

I'm bombing this exam

Sir Cumference

All right, might as well ask here. @ACuriousMind Can you do me a favor? And this is gonna sound bizarre

ACuriousMind

@BernardMeurer oO

Obliv

@bernard can't $a = 1$

then you have 1 on the right side

ACuriousMind

8:38 PM

@SirCumference I don't commit to doing favours before knowing what they are

@BernardMeurer Oh!

Bernard Meurer

$$x_1 + 7^{\frac{1}{3}}x_2 -\sqrt{5}x_3=1$$

Sir Cumference

@ACuriousMind I'm helping fix an SE script and I need a mod to go to physics.stackexchange.com, hover their mouse over the mod diamond button, and tell me what the yellow box that pops up says

ACuriousMind

I'm sorry, my definition of linear equation was slightly too strict

Bernard Meurer

Bloody germans :p

Sir Cumference

@ACuriousMind Can you do that?

Bernard Meurer

8:39 PM

@ACuriousMind It's a scam he'll steal your credit card don't do it

Sir Cumference

._.

ACuriousMind

@SirCumference The "mod diamond button"?

0celo7

@ACuriousMind there's no girl, is there

This is a trap, isn't it

Sir Cumference

@ACuriousMind Yeah, this

On the topbar

ACuriousMind

It says "moderator inbox"

Sir Cumference

8:40 PM

That's what it says when you hover over it?

"Moderator inbox"?

Could you screencap?

Bernard Meurer

@ACuriousMind So, what is the less rigorous definition?

gonenc

@Sanya more like some presidential candidates then...

@BernardMeurer well if you see some $x^n$ terms with $n>0$ then it is probably not a linear equation

for an easy check you can also just try recaling stuff

Bernard Meurer

@gonenc Sure, but then why is $5x + xy − z = 0$ not linear?

gonenc

e.g. if $x$ is a solution so $\lambda x$ should also be a solution

in particular $0$ has to solve the equation

Bernard Meurer

Well zero doesn't solve $x_1 + 7^{\frac{1}{3}}x_2 -\sqrt{5}x_3=1$ does it?

It says here that goddamn thing is linear

Sanya

8:49 PM

@gonenc nah, they pretend, we assume

big difference in that

@BernardMeurer maybe they mean "linear is everything you can write in Matrix form, i.e. vector = Matrix * vector", even though I think then it'd be hard to prove non-linearity

Bernard Meurer

Also, @ACuriousMind, How do I know when to use Gauss or Gauss-Jordan

gonenc

@BernardMeurer I'm not 100% sure whether I'd call that an affine equation

just have to do some googling

general question: my problem stems from the word linear equation, which I'm pretty sure we have defined in LA1 as an equation of the form f(x) = 0 for which f is a linear function

but I don't have my lecture notes with me

but wiki seems to disagree

inst.eecs.berkeley.edu/~ee127a/book/login/l_lineqs_def.html

^berkeley seems to agree

@BernardMeurer I guess I'm confusing you more than I'm helping you :(

Sanya

0

Q: Conduction electron density and atoms per volume, help with equations

I need help understanding these two equations. I cannot figure out their relationship and why they are correct. Starting from the first equation, can I derive the second? Can I derive any them from the "normal" mass density $\rho=m/V$? And also, why is $\rho_m$ missing in the second equation? ...

solid-state-physics atomic-physics semiconductor-physics

Seriously?

Bernard Meurer

@gonenc This is insane dood

gonenc

@BernardMeurer so what is the definition that you are supposedly use?

Bernard Meurer

8:59 PM

@gonenc No clue

gonenc

@BernardMeurer that is not helping :D :D

I mean don't you have lecture notes or anything?

Bernard Meurer

@gonenc No, really, I have no idea, it's nowhere on my notes

My notes begin on row-echelon form discussions

I don't remember ever seeing what a linear equation is

gonenc

@BernardMeurer so let me tell you my definition

a linear equation is an equation, for which the set of answers constitute a linear space aka a vector space

e.g. $5x = 0$

an affine equation is an equation, for which the set of solutions is an affine set

e.g. $5x - 2 = 0$

but apparently some people also say that my affine equation is a linear equation

Obliv

@bernard afaics, your test for 1-1 proves its linear

Bernard Meurer

@gonenc YOU KNOW ACM?!

You both go to heidelberg

mein god

@Obliv how?

gonenc

9:06 PM

@rob thanks for solving the conflict

rob

@goenc No worries

Obliv

actually no I don't see it. According to that definition ACM provided, it looks like the only case where that equation would be linear is if it equals 0

gonenc

@Sanya tomayto, tomahto...

Sanya

@gonenc ???

gonenc

tomayto, tomahto

== English == === Alternative forms === tomato, tomato tomayto tomahto potayto, potahto (from another line in the song) === Etymology === Uses the American English and British English pronunciations of the word tomato. Allusion to George Gershwin's song "Let's Call the Whole Thing Off": "You like tomatoes (/təˈmeɪtoʊz/) and I like tomatoes (/təˈmɑːtoʊz/)". === Pronunciation === IPA(key): /təˈmeɪtoʊ təˈmɑːtəʊ/ === Phrase === tomayto, tomahto (idiomatic) Used to dismiss a correction to one's adherence to an alternative standard (idiomatic) Used to dismissively suggest that something ...

2. meaning to be precise

Sanya

9:11 PM

then we'll need to agree to disagree :)

gonenc

@Obliv this should be the case for the field of reals but I bet a mathematician can cook up something for you that disputes that

since if $x$ is a solution then $x+x=2x$ must also be a solution, so basically scaling with natural numbers should be ok, which is not if it is not equal to zero

@Sanya I actually agree that pretend and assume are different :D

Sanya

@gonenc now I'm completely confused

gonenc

@Sanya just don't listen to what I'm saying atm :D

Obliv

@gonenc isn't a linear equation a plane?

in r^3 anyway

gonenc

@Obliv I'd say that it has to be a plane, which goes through the origin

or a line

or a point for that matter

Obliv

9:17 PM

so how do you prove if something is a plane? If it has a plane of solutions?

Bernard Meurer

@Obliv You start by giving up

gonenc

@Obliv you look at the dimension of the underlying space.

Obliv

What do you recall from class? I haven't ever proved if something was a plane. Just if things lied in it or not, etc.

gonenc

that is how do you describe the set of solutions with 2 parameters then you get a plane

Obliv

@gonenc The space is R^3 almost certainly @bernard right?

gonenc

9:19 PM

@Obliv what do you mean by that?

Obliv

the vector space is probably r^3?

gonenc

@Obliv btw what level of abstraction are we talking about here? :)

Obliv

@gonenc we're only going as far as we need to in order to solve his problem :P

gonenc

I really don't know if you are in university taking the class as "physicists maths" or like a pure maths class

Obliv

problem is fenix.tecnico.ulisboa.pt/downloadFile/282093452026636/… 1-1

showing a) is a linear equation

Bernard Meurer

9:22 PM

The first problem of the first problem set and a room full of physicists can't solve it wtf is going on lol

Obliv

ACM is probably busy, i don't think anyone else here is a physicist (anyone responding anyway)

actually I should really finish this write up .. sorry :D good luck bernard.

Bernard Meurer

well, people who know maths, you get the point :p

@dmckee Halp

gonenc

@Obliv wow I'm not sure if this is an insult or just pointing out that I'm being too abstract

0celo7

@ACuriousMind this game is pretty cool

Obliv

@gonenc I don't think anyone here is a physicist. It says on your profile you're still a student so I just assumed you weren't.

gonenc

9:26 PM

@Obliv acm is also a student he is just doing his masters afaik

or has finished it idk :D

anyhow

@Obliv ok so what you have is $\mathbb R$ vector space is $\mathbb R^3$

and I think your course is for engineering class (what google translate tells me) so I don't think that you'd have to care about some exotic vector spaces

again from what I understand from the sheet you provided is that you call what I called an affine equation a non-homogeneous linear equation

@Obliv you know about matrices right?

Obliv

@gonenc this is @bernard 's class. Currently busy sorry

gonenc

if so an equation or set of equations is linear iff you can write it as $A \vec x = \vec y$

for some matrix

@Obliv ops sorry :D

@BernardMeurer do you know about matrices

Bernard Meurer

@gonenc Yes

I've been touched by matrices in my nightmares

gonenc

jesus you gotta learn to love em

@BernardMeurer ok so an equation is linear when you write it in the form $A \vec x = \vec y$ at least that is what I'd take as a definition in this case

does that help?

dmckee

10:08 PM

@Obliv Several regular users are working full time as physicists or physics instructors at the post-secondary level. A few (generally less active) users are physics professors at R1 universities.

@BernardMeurer If you stick with physics you will eventually be promoted to dreaming about spherical harmonics. Trust me, that's worse.

Sanya

@dmckee what's an R1 university? :o

dmckee

@Sanya A major research university. A place where most professors teach half-time or less because they get a lot of grant money and do a lot of research.

Sanya

ah ok ... thanks, I didn't know that name

ACuriousMind

@BernardMeurer (Sorry, was needed elsewhere) Not less rigorous, less narrow: You can allow that Not the solutions must sum, but that the solution space must be of the form $x+ c$ , where $c$ is a constant vector and $x$ is an element from a subvectorspace of the possible inputs

Sanya

or class(ification)

peterh

10:23 PM

@ACuriousMind There is objective morality also in the real world. Only character sheets aren't.

DanielSank

10:37 PM

@Obliv lolwut?

You don't think anyone here is a physicist?

Bernard Meurer

@ACuriousMind I'll just skip that question

Which didn't help much because It's my second page of trying to solve a simple matrix

and I didn't even have beer today

heather

Okay, let's say I have the expression $\frac{2^{n-2}}{n}$

Is there any way to further reduce that?

I don't think so

But I kind of was wondering if you could somehow turn the $2^{n-2}$ into an exponent like $n^{\text{whatever}}$ if that makes sense.

Bernard Meurer

@ACuriousMind I just failed 6 times in a row to do a simple Gauss :(

I want to cry right now

ffs

vzn

11:00 PM

Gravitational Waves May Permanently Alter Spacetime / pbs

Sanya

@heather there's no further reduction, besides maybe writing $\frac{2^n}{4n}$ - $2^n = n^x$ implies $ ln(2) n = ln(n) x$, so $x = n \frac{ln(2)}{ln(n)}$, which doesn't really make it more appealing, does it?

by the way, congratulations for the 6k mark O_O

gonenc

11:25 PM

@BernardMeurer just write a computer program, which gives you each step. I'll guarantee you you'll learn it better than doing it 100s of times.

@dmckee who is actually a prof at a R1 uni?

who is also somewhat active in the community?

rob

11:45 PM

@vzn Hmmm, interesting.

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