Continuous Definition and 1000 Threads

Hello, it's been a while since I've done any proper electrostatics, but I have a problem where I have a bunch of discrete point charges within some volume V bounded by a surface S. I am wondering if it is possible to replace the discrete charge density in my volume V by some continuous surface...

Hello, I understand that continuous sinusoids can have any arbitrary frequency ##f## and are always periodic with period ##T=1/f##. A continuous sinusoid looks like this: $$x(t)= sin(2\pi f t+\theta_0)$$ On the other hand, discrete-time sinusoids are not always periodic. They are periodic only...

I've read these two pages that discuss going from qubit to continuous variable - https://arxiv.org/abs/quant-ph/0008040 and https://arxiv.org/abs/1907.09832 . I'm curious if anyone knows some papers that discuss going the other way around? I.e. qubitizing a continuous variable model? Any insight...

Now that currents don't flow past the interior of capacitors at any time (charging/discharging etc), currents should be functions of a spatial coordinate, i(x), in that i(x) is non zero in wires and 0 in capacitors. But in circuits usually currents are assumed constant in the same branch. What...

Weierstrass function is the classic example of a continuous function which is nowhere differentiable. What happens when a function is monotone? My guess that it cannot be nowhere differentiable. It seems to me the reverse is true - it is differentiable almost everywhere. Any light on the...

Suppose ##\alpha=0##. Then ##\alpha f=0##, the zero map. Hence, the distance between the images of any two ##x_1,x_2 \in D## through ##f##, that is to say, the absolute difference of ##(\alpha f)(x_1)=0## and ##(\alpha f)(x_2)=0##, is less than any ##\epsilon>0## regardless of the choice of...

Poll Question:Discrete space lacks the smoothness needed to justify connectivity between two spatial values. Continuous space has no points of reference to mark phase difference or relative displacement. Upon measurement, we somehow correlate two separate events as a unified whole.Space is:A...

I maintain that a continuous connectivity exists between an observer and every observation he ever makes in spacetime. At any particular time and position an observer retains at least probabilistic interaction with all his past, present and future observed events. Observations effected in the...

How would you work this?If S is a set with the discrete topology and f:S->T is any transformation of S into a topologized set T, show f is continuous.------------------------------"Mushrooms always grow in damp places, thus they look like umbrellas."

Please tell me how express the fact thatP1.P2= P(1 and 2) by independent discrete parameters for independent CONTINUOS parameters. I know that for continous parameters existprobality density. So density times density = density? ThanksNothing is all

Hi, this question has been bothering me for a while now.lim f(x) as x approaches infinity is infinity. The domain is [0, infinity] and f(x) is continuous. Prove that f(x) has an absolute minimum.since f(x) is conitnuous than the deriative would have to be positive. That means the only place...

I learned that there is a small oscillator circuit inside of the cheap, disposable cameras that produces 400vAC from a single 1.5vDC battery. I was just curious if anyone would know of a way to build a similar oscillator, which looks like it consists of a npn transistor, a transformer, and a...

First of...Is space "discrete" or "continuous"? In other words, can a particle be in only "set" positions or is there an infinite number of positions that it can be in. (At a very small scale, a particle could be in an infinite number of positions, or... it can only be in a discrete number of...

Let's say a perfect blackbody has a temperature like that of our sun, and emits a planck curve in the visible range of the spectrum.If one refacts this light in a small prism a continuum spectra will emerge. Now, hypothetically, if one could build an infinitely large prism, would the continuum...

I havent persued the life of physics since I got my A-level over 2 years ago - but somthing I have always wondered....In my parents room they have walk-in wardrobes on both sides of the room, each with double sliding mirror doors. Each wardrobe reflecting the other.I assume the reflection is...

How could to universe not intersect ever if they keep on growing then how could they not.

Is time and moverment continueous ?i.e take an atom, now when it moves it must make its moverment in steps so at the very smallest measurment it will go from X to Y instantly ( kind of teleport itself ) rarther than progress from X to Y.If not than we must have infinity the smaller you progress.

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 3: Continuous Functions on Intervals and am currently focused on Section 3.1 Limits and Continuity ... ... I need some help in understanding the proof of Proposition 3.12...

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 3: Continuous Functions on Intervals and am currently focused on Section 3.1 Limits and Continuity ... ... I need some help in understanding the proof of Proposition 3.12...

The first thing I thought about doing was to prove that f is continuous using the Heine–Cantor theorem proof. But I do not know at all whether it is possible to prove with the data that I have continuous. I would love to get help. Thanks

Can someone please help me to prove that the function f(x) = Arcsin x is continuous on the interval [-1, 1] ... Peter

I was reading introduction to quantum mechanics by DJ Griffiths and while discussing the formalism of quantum mechanics, he says that if for a hermitian operator, the eigenvalues are continuous, the eigenfunctions are non-normalizable whereas if the eigenvalues are discrete, then they can be...

Given the probability density function f(x) = b[1-(4x/10-6/10)^2] for 1.5 < x <4. and f(x) = 0 elsewhere. 1. What is the value of b such that f(x) becomes a valid density function 2. What is the cumulative distribution function F(x) of f(x) 3. What is the Expectation of X, E[X] 4. What is...

Hi, I was watching this Youtube video (please remove the parentheses) : https://youtu.(be/mtH1fmUVkfE?t=215) While watching it, a question came to my mind. In the picture, you can easily calculate the total number of customers. It's 1000. For my question, I'm going to use the same picture...

I am reading Tom M Apostol's book "Mathematical Analysis" (Second Edition) ... I am focused on Chapter 4: Limits and Continuity ... ... I need help in order to fully understand the proof of Theorem 4.25 ... ... Theorem 4.25 (including its proof) reads as follows: In the above proof by...

In another forum, some people argue that time and space are discrete, due to Planck time and Planck length. However, I disagree with this idea. I think, the Planck time and Planck length are just some scales that we can measure, but they do not forbid continuous time and space shorter than...

Hello, I am currently stumped over a question that has to do with the continuous uniform distribution. The question was taken from a stats exam, and while I understand the solution given in the mark scheme, I don't understand why my way of thinking doesn't work. The problem is: The sides of a...

My understanding of this is based upon the assumption that energy level transition is the only mechanism responsible for blackbody photons.

Summary: In which scenario a current may exhibit alternated and continuous character together? Hi All, I would like to know in which scenario an electric current may exhibit alternated and continuous character? Something like $$ I(t) = I_0 \sin (\omega t) + I_1 $$.

An electric dipole is a system of two opposite point charges when their separation goes to zero and their charge goes to infinity in a way that the product of the charge and the separation remains finite. Now how can we have a continuous electric dipole volume distribution from such a...

I'm working through Griffiths EM 3rd ed. in section 2.4.2 (point charge distribution) and 2.4.3 (continuous charge distribution). I understand from the section on point charge distributions that when we add up all the work (excluding the work necessary in creating the charge itself), one clever...

If we would, for sake of argument, adopt the MWI interpretation, then are there wavefunctions (like for instance position) that have a continuous probability spectrum, and will MWI then propose that there are an infinite number of actual universes that each represent a position in that...

For 1) I found two ways but I get difference results. The first way is I use P(A|B) = P(A and B)/P(B). I get P(X<1|Y<1)=(∫_0^1▒∫_0^1▒〖3/4 (2-x-y)dydx〗)/(∫_0^1▒∫_0^1▒〖3/4 (2-x-y)dydx〗+∫_1^2▒∫_0^(2-x)▒〖3/4 (2-x-y)dydx〗)=6/7 The 2nd method is I use is f(x│y)=f(x,y)/(f_X (x)...

According to QFT or Quantum Gravitation Theory space and time are discrete or continuous?

Hey, I've got this problem that I've been trying to crack for a while. I can't find any info for multi-variable expected values in my textbook, and I couldn't find a lot of stuff that made sense to me online. Here's the problem. Find $E(C)$ Find $Var(C)$ I tried to get the limits from the...

Hi all, I have learned the very basics of entanglement (discrete, 2 particle systems) and was hoping that someone can recommend introductory (undergrad-level) material for continuous-variable, 2 particle entanglement. Stuff I have found online so far (like this...

The Hubble deep field image was constructed by collecting photons from a specific region of space over a continuous duration of time; in this case ten days. As the number of collected photons increase, higher the resolution of the image. If this duration increases, how much more resolution do...

I do not know to start. Here is the problem.Determine if the given function is piecewise continuous, piecewise smooth, or neither. Here $x\neq0$ is in the interval $[-1,1]$ and $f(0)=0$ in all cases. 1. $f(x)=sin(\frac{1}{x})$ 2. $f(x)=xsin(\frac{1}{x})$ 3. $f(x)={x}^{2}sin(\frac{1}{x})$ 4...

Homework Statement A clock runs irregularly but after 24 hours it has neither gained nor lost overall. Find a way the clock can run irregularly such that there is no continuous 576 minutes during which the clock shows that 576 minutes have passed. Homework Equations 24 hours = 1440 minutes and...

Homework Statement Let ##R## be the ring of all continuous real-valued functions ##f : [0,1] \to \mathbb{R}## with pointwise addition and pointwise multiplication of functions as its two operations. Let ##c \in [0,1]## and denote ##M_c = \{f\in R : f(c) = 0\}##. a) Show that any ##f\in R##...

i could use a bit of tutelage with Matlab. I have a rather simple equation I would like to plot. I want to create a rational series of primes divided by their corresponding W value from the equation I have. P are primes 2,3,5,7,11,13... I am still working on this. Thanks

Homework Statement Let ##f## be defined on ##[0,1]## by the formula $$ f(x) = \left\{ \begin{array}{ll} x & \text{if } x \text{ is rational} \\ 0 & \text{if } x \text{ is irrational} \\ \end{array} \right. $$ Prove that ##f## is continuous only at ##0##. Homework EquationsThe Attempt...

Definition: A function f mapping from the topological space X to the topological space Y is continuous if the inverse image of every open set in Y is an open set in X. The book I'm reading (Charles Nash: Topology and Geometry for Physicists) emphasizes that inversing this definition would not...

In analysis, the pasting or gluing lemma, is an important result which says that two continuous functions can be "glued together" to create another continuous function. The lemma is implicit in the use of piecewise functions. Can we have a similar situation for uniform continuous functions?

So if you have a rocket let's say that discards all the structural and engine mass continuously at zero velocity that is relative to the rocket until only the payload is traveling at the final velocity - then what will the equation of motion will look like? we can neglect the drag and...

Take for ex f(x,y) = x/y. Domain is all (x,y) except for y = 0. It's continuous everywhere except for y = 0. Is this always the case? The function is continuous everywhere in its domain?

Ok, I'm a bit confused with the spectrum of the Sun. Is the spectrum of the Sun continuous or absorption? Better yet, is it both? Or am I totally confusing myself? I understand that the source itself is continuous but it is partially absorbed (wrong phrasing?) as it passes through the outer...

Homework Statement f(x) = (3/4)(-x^2 + 6x - 8) for 2 < x < 4 (0 elsewhere) A) Find F(x) integral 2 to 4 ((3/4)(-x^2 + 6x - 8))dx B) Use F(x) to find P(3 < X < 3.5) integral 3 to 3.5 ((3/4)(-x^2 + 6x - 8))dx 11/32 C) Use F(x) to find P(X > 3.5) 1-( P(3 < X < 3.5)) = 21/31 D) Find E(X)...

Hello, I have attached the question and the steps worked out. I am not sure if my steps are correctly. Need advise on that. Next, I am not sure how to show f''(0) exist or not. Thanks in advance!

It doesn't make sense to me that absorption spectra are (mostly) continuous. Here are my beliefs. Please tell me which piece/pieces is a/are misconception(s). 1) When light is absorbed, the energy is used to excite an electron to some discrete energy level. 2) To get to this discrete energy...