@Slereah This is wrong. You need to cancel the $d$‘s.

I'm confused about something is sets. You know how there's: S = {x | x > 5} for example. I'm confused about this: S = {2x | x > 5}. What is the first form thingy

I'm confused about how the first part of the set works

nvm I think I got it somewhat

it's like "the form" of the set. For example, if it's 2x, the condition afterward will be applied to only 2, 4, 6, 8...

so for example, S = {2x | 0 < x < 6} then S = {2, 4, 6, 8, 10}

@JingleBells You got it. Strictly speaking, that notation should mention the domain of x, whether its integers, or reals, etc, but people often don't bother with that if it's obvious from the context.

@JingleBells It's like a list or set comprehension in Python. Your last example could be written in Python as s = {2*x for x in range(1, 6)}

We should be seeing a lot more presence of SE staff on the network in a couple of weeks:

Nobody with any significant amount of rep has zero downvotes (if you include votes on deleted posts).

@FakeMod I won't be surprised to see physics questions from SE staff. And they may also write some answers. ACM isn't the only person with a physics degree who works in IT. And not all SE staff are IT people.

@FakeMod You can have a serious attitude in your comments, abd I think being stern is ok, but we should try to avoid being snarky.

Snarkiness was more common in the early days, but the powers that be decided it was too unwelcoming. So snark can be flagged as unkind.

@FakeMod Borderline. You can probably get away with "Physics.SE is not a free homework service".

Better: "If you want help with this problem you need to ask a specific conceptual question, as explained here [link to homework policy]."

@FakeMod They'll learn that shortly, when their question gets closed. :evil grin: Or if they read the homework policy link.

@FakeMod There's a lot of discussion about this on the various metas, especially MSO & MSE. Basically, online text is more ambiguous than face to face communication. Especially among an international community. So it can be really hard to tell the emotional impact of what you write. You might intend a little playful snarkiness, other people may think you're being nasty & thoughtless. So SE decided we need to present a nice smiling welcoming face, especially to the newbies.

It's a shame the old XKCD forums disappeared. People were expected to behave in a civilized fashion, but there was room for humour & snarkiness. And mods weren't afraid to retaliate when dealing wirh trolls &/or idiots.

One of the methods I am using for my Master's thesis is working fine, but now I have found a much better way to do it. However, I don't have enough time to implement this new method. I am struggling a bit with how to present this in writing, without sounding like I am not implementing because of laziness.

So the problem is basically presenting my method in a natural way, even though it is not very motivated anymore

@FakeMod The page for user no. 1 isn't a deleted user, it's just empty (moderator can usually see some information on deleted users). Looks like it never was an actual account.

@FakeMod Years ago (ugh!), I used to leave somewhat aggressive comments like "Have you read [our homework policy]?". They used to get some more upvotes than my current canned comment (people love snark), but they didn't get any better results, and in my impression more users responded negatively to them. Think about why you're leaving the comment.

@FakeMod The normal amount of information on a deleted user.

@B.Brekke I think it's perfectly fine to describe why you initially pursued the method you actually implemented and its result, then explaining how you found the better way the (and why you think it's better), then leaving its implementation to a mention in a "Future Work" section.

I think there is value to seeing how ideas and approaches evolve, and we often focus too much on presenting a perfect end result, and not enough on how to get there, leaving many expositions to be a variant of this

@FakeMod I feel your pain. But don't bother wasting time & energy like that. If an edit rollback "war" occurs, an automatic mod flag is raised, and mods can lock the post, if they think it's necessary. They probably wouldn't bother locking a closed (& unanswered) homework post though. The Roomba will delete it, eventually.

@ACuriousMind I would actually feel nice to be a bit honest about my initial thoughts. There are some nice lessons to learn from it. I just have to make sure it is formally written and doesn't end up like a diary

In a simple electric circuit with wires(ideal) a resistor and A battery

At steady state

The field inside the wires is zero

But it isnt Zero inside the resistor, correct?

@PM2Ring you mean the domain of f(x)? The domain of a function is basically the numbers that go into it (the input), so the domain is 2x, meaning only 2, 4, 6, 8... will be inputs

Z/2Z?

No wait that's integers my bad. N/2N.

@Thormund that for me?

Yeah its an easier way to write {2,4,6,....}

oh xD

actually, 2x is easier

sorry I dont' understasnd what you mean

So a group $G$ and a subgroup $N$, we say the quotient group of $G/N$ is removing elements in $N$ from $G$.

I have no idea what you're talking about. The easiest way to write a set of {2, 4, 6, 8...} is $S = \{2x | x \in W\}$

Now I confused myself too woops. Does the quotient group yield 2 seperate classes?

I have not yet learned about quotient groups, this is sets.

@JingleBells The domain of a function y = f(x) is the set of values that x comes from, and the set of corresponding y values is called the codomain (some older books call the codomain the range). See en.wikipedia.org/wiki/Domain_of_a_function

@JingleBells Yeah, don't worry about groups for the moment. Get used to sets first. There's a nice (but old) site that's a good introduction to groups. I think the site was created to help people learn enough group theory to understand & create Rubik's Cube algorithms. dogschool.tripod.com

Here it is: dogschool.tripod.com

@Thormund Yes, what you wrote is the finite group with two elements

The set JingleBells describes is just $2\mathbb{N}$.

Ah yes my bad 😅

I'm learning about the locus in sets, which basically means "all points that" and usually adds up to a continuous shape and I was wondering, how is a line made up of dots? My math source also says that the dots have no size, weird.

I suppose a line would be a set of infinite amounts of dots with infinitely small sizes.

(just a guess tho)

$S = \{x : x \in \R, 5 < x < 10}$ <-- a line?

What is your definition of 'size'?

damn u latex

@ACuriousMind how big the thing is xDD

jk

@ACuriousMind i'm not sure :p

In math you have to be careful not to use concepts that aren't even defined for the objects you're dealing with - a set, without further structure, has no notions of size or how "close" its elements are. For a notion of closeness (the minimum to need to talk about things in at least vaguely geometrical terms), you need topology.

Oh, I'm not talking about sets, I was just wondering what a line is

$S = \{x : x \in \R, 5 < x < 10\}$

oh my gooodddd

I think latex is harder than math

Is topology the calculus of graphs?

I never realized how interesting math can be. I'm hooked.

$\R$

why the \R doesn't work :(

$\mathbb{R}$

yay

I meant "Is topology the calculus of geometry" lol

$\frac{1.52}{0.51}$ <-- That's not a rational number?

Usually you need something more than topology to do what we usually think of as geometry (e.g. you need a distance function, a "metric"), but topology endows a set with a notion of "nearness" e.g. it allows you to express what it means for a point to be infinitely close to a given subset ("limit point")

@JingleBells of course it is

@ACuriousMind But the definition of rational numbers is when you divide two integers, no?

Your number is the same as $\frac{152}{51}$.

lol

Got it

hi guys

hello satan

just tried reading the "hydraulic analogy" for circuits

the analogy for a resistor is bothering me

They describe it as a constricted pipe

and it is claimed that a difference in pressure accours

*occurs

however

@satan29 That's Bernoulli's principle - changes in diameter affect the speed, which in turn affects the pressure.

If you use The bernoulli equation

p + 1/2 (rho)v^2 = constant

at the ends of the constricted pipe, Velocity is the same

so p is the same?

Ah, yes, if they claim the pressure is different in parts of the pipe with the same diameter, that's wrong

v changes only inside the constricted pipe

Keep in mind it's just an analogy, it breaks when you stretch it too far

But then i am slightly confused regarding a potential "drop"

consider normal circuit elements

the velocity of the electrons is the same at the ends of the resistor

so, there is no overall change in KE of electrons as they move from one end to the resistor to the othrer end

since w= delta(ke)

now if we define Voltage as work/unit charge

uhh

work energy theorem

@satan29 An actual wire is a quantum mechanical system where the drift velocity of the electrons (the speed with which they actually move along the electric field on average) is much lower than the speed of electric signals anyway.

Total work done= change in KE

Thinking about little balls moving through the wire is not what happens.

although

hows this for an explanation:

wait @FakeMod

voltage = work done by electric forces/ charge

through the resistor

Electric field does worl

k

on the charges

and elements of the resistor also does work on the charges

total work being zero

on the charge

And, charge does work on the resistor elements: Which appears as heat

is this explanation reasonable

@FakeMod where does the visocity come from - visocity is a property of the fluid, not of a location

I think the best analogy for a resistor is a water wheel.

ah yes, John Rennie said the sam

The current deposits energy at a resistor just like a water flow deposits energy when turning a water wheel

e

@ACuriousMind (not considering the analogy, rather the circuit elements) is my explanation reasonable?

@FakeMod Reputation calculation respects the temporal sequence of events. If you get a downvote while you're at 1 rep and then get an upvote, you end up at 11 rep, not 9.

so the constricted pipe analogy is garbage?

I don't find it particularly useful, yeah

Thank god, i thought i was missing something obvious

circuits arent as intuitive as you'd think , If you try to explain every single nuance

IMO thats electrocstatics in general

btw @fake

@FakeMod Hows exam prep going on

Well, I expected some sort of explanation for everything that isnt QM :P

I just watched a video and when we talk about electric current, the electrons actually move slow, but the pulse wave between them is what it gives the super fast speed. How does that work?

lmao

oh vnm

Do you mean "matter waves"?

nvm I think I got it

The electrons don't mechanically move super quickly, but they push each other in a chain-like reaction which reaches the end very quickly

@JingleBells I don't know what you mean by "pulse wave", but the idea is similar to how sound propagates: When you speak, sound travels pretty fast because the air molecules all move a bit and push on the next one which pushes on the next one etc., but at no point does any volume of air individually travel with the speed of sound.

@ACuriousMind Yes exactly, thanks for the analogy.

By the way, current loses energy as the "push wave" travels more distance, right? Just like sound?

Just like Minecraft Redstone

In ordinary conductors, yes, because ordinary wires have non-zero resistance. This is not analogous to sound, however, because sound loses power mostly because it expands in all directions.

@ACuriousMind Got it, thanks

@JingleBells "how is a line made up of dots?" Mathematicians have been pondering how a line is "made of" points for about 2500 years. For most of that time, people just hand-waved the tricky issues, or talked about the paradoxes that arise in building a line from points.

We started to make real progress in the 1800s, especially after Cantor invented set theory. Other notable names from that time period include Dedekind and Weierstrass. The theory of infinite sets has made a lot of progress since then, but it's still a field of active research.

Cardinals and ordinals

my favourite infinities

Hello

anybody ?

hi?

i am confused about the constants appearing in the lagrangian

I'm not an expert but can you be more specific?

say i would like to derive the Klein gordon equation

or dirac equation

we have hbar the planck's constant in those equations

I do not know QFT sorry, I'm sure someone else here can help you though if they see this

yeah no problem

maybe some other time or I post

Does anyone know what algorithm AI uses to recognize and count for example cars on the road? I know we can use a CNN (Convolutional Neural Network) and train it on a dataset of cars, but how would we go about recognizing and counting a few cars on a road? One crappy way I can think of is to make a scanner (let's say 5x5 pixels) that will go through the big image of the road and spot cars.

And I've seen algorithms such as YOLO which does real-time object detection, and sure, you can train a CNN to recognize and label different objects (by having a huge dataset), but how is the other part done? - Recognizing multiple objects on a single image? And I suppose that the way it's made real-time is by basically taking an image of the live feed every x seconds and doing a recognition scan on it.

I think I found what I was looking for - Region Proposal Network (RPN)

towardsdatascience.com/…

It's almost dawn. I am going to sleep.

Guys I feel like an absolute idiot

I can't seem to get that relation

Any suggestions on method?

just substitute the expression for $p$, then try to pull everything in front of the second $\partial_t$ inside it.

$\rho$ is a function of time right?

Probably? It's your exercise, you should know what $\rho$ is :P

Sorry, it definitely is.

I'm unsure as to how to pull it in that right derivative though

You'll probably have to use the product rule. You can then also take the time derivative of the term you want to show is constant, use the product rule, and start staring really hard at both expressions until you figure out why they're equal

Mhm I tried that

Lemme try again

Must be making some silly mistake

@JakeRose I mean pulling in like $f \partial_t(g) = \partial_t(fg) - \partial_t(f) g$.

Yeah that was what I did

I must have just made a mistake

will try gain

@ACuriousMind I'm still getting stuck

Not seeming to spot the link

I get $\partial_t (\rho R^3)(1+w) - \partial_t (R^3) \rho w = 0$

From the fluid equation

But I can't get constant equation in a form that matches this

FINALLY

I got it in quite a round about way

Not sure if it was the most direct

Took the second and differentiated it wrt $R^3$ to get the $(1+w)$ term

Then used chain rule to swap for a time derivative