Infinite Definition and 1000 Threads

Question 1) Write ⊆ or ⊄: {x/(x+1) : x∈N} ________ QNOTE: ⊆ means SUBSET ⊄ means NOT A SUBSET ∈ means ELEMENT N means Natural Numbers Q means Rational Numbers Question 2) Which of the following sets are infinite and uncountable? R - Q {n∈N: gcd(n,15) = 3} (-2,2) N*N {1,2,9,16,...} i.e...

On the bottom of page 24 & top of page 25 of this pdf an integral is beautifully computed by breaking it up into an infinite series. Is there any reference where I could get practice in working integrals like these?

After all, numbers are part of the universe. :biggrin:

What is the sum of an infinite Dirac series and why? 1 or infinity? \sum_{n=-\infty}^{\infty}\delta (n) I can see it being 1 because it's like a series version of the integral: \int_{-\infty}^{\infty}\delta (t)dt = 1 But for the series where n=0, \delta (0) = \infty :confused:

Hey guys, this is my first post so go easy on me. I was looking over the simple case of a 1D particle restrained inside an infinite square well potential ("particle in a box") and was having some difficulty understanding the relationship between the energy states and the expectation value for...

Let's say I have an unbreakable pole. Let's also say I'm in an infinite vacuum. This pole is 240,000,000 meters in length. You are at the other end of the pole. I move the pole to the right 1 meter over the course of 0.9 seconds. Does the other end of the pole move immediately? If so, does it...

Homework Statement Infinite uniform line charges of 5nc/m lie along the (positive and negative) x and y axes in free space. Find E at :P(0,3,4) Homework Equations E due to line charge along the Z-axis is given by: E=(λ/(2∏*ε*r))*ar where λ=line charge density;ε=...

Homework Statement Particle in well: V(x)=0 for |x|<\frac{L}{2} V(x)=∞ for |x|>\frac{L}{2} initial wave function \Psi(x,0)=\frac{1}{√L}[cos\frac{\pi*x}{L}+ i*sin\frac{2*\pi*x}{L}] a) calc P(p,t) (momentum prob density) Homework Equations Anything from Griffiths QM The Attempt at a...

Homework Statement Determine convergence or divergence using any method covered so far*: Ʃ(1/(n*ln(n)^2 - n)) from n = 1 to infinity*The methods are the following: - Dichotomy for positive series (if the partial sums are bounded above and the series is positive, the series converges) -...

Homework Statement Determine whether the series diverges or converges. (1+2) / (1+3)+ ((1+2+4)/(1+3+9))+ ((1+2+4+8)/(1+3+9+27)) + ...The Attempt at a Solution I have split up the series into two (denominator and numerator): an = (1+2) + (1+2+4) + (1+2+4+8)+... = (1)n + 2n + 4(n-1) + ... bn...

I've never fully understood how anything can actually fall into a black hole without the black hole evaporating first. Since time dilates exponentially as I fall into a black hole, a point will come where a few seconds for me will be millions of years in the outside world...trillions in fact...

-In the first few fractions of a second after the big bang, was the universe finite and closed during early inflation, before it smoothed out and became flat and infinite? I am wondering because I would like to know if the theory implies that the universe initially inflated with a finite...

How can I integrate this expression: \[ \int_0^{\infty} \mathcal{J}_1(kR)e^{-kz}dk = \frac{1}{R} \left[1 - \frac{z^2}{\sqrt{R^2 + z^2}} \right] \] where \(\mathcal{J}_1\) is the Bessel function of order 1.

Homework Statement A particle, mass m propagates freely in a box, length L. The energy states are: ϕ_n(x) = (2/L)^(1/2)sin(n∏x/L) and energies E_n = n^2∏^2/(2mL^2) at time t=0 the system is in state ϕ_1 and the perturbation V=kx is applied (k constant) and turned off at t=T...

Homework Statement Given a volume charge density function defined as follows: \rho=\frac{dQ}{d\tau}= \begin{cases}z-z^{2} & 0<z<1\\ z+z^{2} & -1<z<0\\ 0 & \text{everywhere else} \end{cases} and is independent of x...

Work done= force.displacement In space, with no external forces, air drag, gravity etc if you apply a force to object if will move forever in the direction of force unless any resultant force act on it to change its momentum. In this case let's take force as 2N so we get w.d=2N.s s will...

Homework Statement An electron in a one-dimensional infinite square well potential of length L is in a quantum superposition given by ψ = aψ1+bψ2, where ψ1 corresponds to the n = 1 state, ψ2 corresponds to the n = 2 state, and a and b are constants. (a) If a = 1/3, use the normalization...

I was watching a video about how if the universe is infinite, that there is a possibility there is another galaxy exactly like ours and doing the same thing. Every possibility that I can imagine of do exist if the universe is infinite. Then I imagined me from another universe visiting me...

Is anyone familiar with plotting an infinite domain PDE where the solution is an integral. Take the solution \[ T(x,t) = \frac{100}{\pi}\int_0^{\infty}\int_{-\infty}^{\infty} \frac{\sinh(u(10-y)}{\sinh(10u)} \cos(u(\xi-x))d\xi du \] How could I plot this in Matlab, Mathematica, or Python? As a...

Homework Statement Let S be the surface z = 1/(x^{2} + y^{2})^{1/2}, 1 ≤ z < ∞. Show that the area of S is infinite. Homework Equations the surface S is given by z=f(x,y) with f(x,y)=1/(x^{2}+y^{2})^{1/2} and for x,y in the disk D which is the circle seen when the surface is viewed from the...

From a distant frame of reference a falling object never reaches the event horizon due to time dilation. If I drop a meter stick into a black hole lengthwise I should see both ends of the stick getting asymptotically closer and closer but never reaching the horizon, thus the stick should appear...

Hello everyone and thanks for reading my post. I have a problem with an electron, which actually is confined into a region 0 ≤ x≤ L with infinite potential around it, and its energy in the ground state is 0.38eV. Then on the x > L region the potential is 5eV and the energy of the lowest...

Suppose that x\in H, where H is a Hilbert space. Then x has an orthogonal decomposition x = \sum_{i=0}^\infty x_i. I have a linear operator P (more specifically a projection operator), and I want to write: P(x) = \sum_{i=0}^\infty P(x_i). How can I justify taking the operator inside the...

Trying to solve this infinite series?? Hey folks! I've spent hours trying to solve this and have exhausted all available resources.. I just need to be pointed in the right direction! Homework Statement Compute the sum of the infinite series (I believe this is an arithmetico geometric...

As we know, the 1d infinite potential well has a stationary state. The function that depends on x onky is a sin function. However, I don't understand the concept in this question. I have the answer of this question and this is not a homework. I am not asking for the answer so please don't put...

Suppose you have an electron in the infinite square well. The system is completely isolated from the rest of the world and has been its entire lifetime. Do we then know that the wave function describing the electron is an eigenstate of the Hamiltonian? The question arose because I was given a...

Homework Statement A particle of mass m is trapped in a one-dimensional infinite square well running from x= -L/2 to L/2. The particle is in a linear combination of its ground state and first excited state such that its expectation value of momentum takes on its largest possible value at...

A particle of mass m is trapped in a one-dimensional infinite square well running from x= -L/2 to L/2. The particle is in a linear combination of its ground state and first excited state such that its expectation value of momentum takes on its largest possible value at t=0.I know the process of...

Suppose that some infinite set S spans V. Then this means every vector in V is expressible as some linear combination of the vectors in S. Does this combination have to be finite? It couldn't be infinite, because that necessarily invokes notions of convergence and norm which do not...

Homework Statement \rho_{wire}=a, surface charge density \rho_S What is potential difference of a point a distance of b measured from the centre of the infinitely long wire, and the surface of the wire? Since all of the charge is dispersed on the surface of the conductor, there will exist no...

Hello people, I am doing some work where I need to look at a simplified situation regarding a conductor for which the conductivity distribution does not change along the z-direction of an infinite cylinder. The distribution itself is not symmetric in any way. Presume 2 infinitely long...

So, I've read conference proceedings and they appear to talk about counter-intuitive it was to create an infinite-energy state for the harmonic oscillator with a normalizable wave function (i.e. a linear combination of eigenstates). How exactly could those even exist in the first place?

1. Homework Statement . Let ##(X,d)## be a complete metric space. Prove that if ##P \subset X## is perfect, then P is not countably infinite. 3. The Attempt at a Solution . Well, I couldn't think of a direct proof, I thought that in this case it may be easier to assume is countably infinite...

Lets say i have a infinitely long wire with charge per length, λ and a point, p of a position with its closest distance to the wire is y. The wire extend infinitely parallel to X-Axis. How to determine the voltage at the position p? Can i first regard the voltage contributed by a very small...

I'd just like to preface by saying that I'm not in any way an expert on high-level physics, but I would like to think that after reading a few books and taking a healthy interest in things like cosmology that I have a decent understanding of some concepts, so if you could please bear with me...

in physics II, i learned about how the electric potential goes to zero as r goes to infinity. Okay, well, this was when we were dealing with two positive charges. ie a repulsive force. now I'm learning about gravitational potential now and i see this in my notes: \Phi\rightarrow0, r\rightarrow∞...

Consider the following solution to the steady state heat diffusion problem on an infinite y domain. \[ T(x, y) = \sum_{n = 1}^{\infty}c_n\exp\left(-\frac{\pi n}{\ell} y\right) \sin\left(\frac{\pi...

Homework Statement We are to assume an infinite transmission line with the following parameters: capacitance: 296 ρF/ft Zc=52Ω inductance: 8.0 × 10-7 H/ft We are told that a 100MHz signal is attenuated 31 dB per 100 feet and asked based on the information, assuming no leakage through...

So I've been wondering.. from my previous post: https://www.physicsforums.com/showthread.php?p=4500082#post4500082 if we have a plane of infinite charge, then electric field does not depend on distance however, for a infinite line of charge: If we use a cylinder with radius 'r' as our...

What is the electric field at a point P, a distance h = 29.9 cm above an infinite sheet of charge, with a charge distribution of 2.29 C/m^2 and a hole of radius r = 4.49 cm with P directly above the center of the hole, as shown in the figure? Equations used: Edisk= (-σ/2ε)[1-(z/sqrt(z^2 +...

Homework Statement Blah Blah irrelevant context.. positively charged plate occupying the x - y plane with charge density ##σ=5.2{\frac{nC}{m^2}}##.This maybe modeled as an infinite charged plane. There is a Charged wire running parallel to the y-axis through the point ##(-2.0cm, 0, 1.0cm)##...

Homework Statement http://imgur.com/sg8czUR An infinite sheet of charge has a charge density of σ= -2.1 uc/m2. (uc is micro-coulombs). The inner edge of the infinite conductor slab is 2.6 cm away. The outer edge is 4.2 cm away. The conductor slab has a charge density of σ= 74 uc/m2. What is...

In gravitational field its a constant exchange of photons right? Then in ideal circumstances, if one object orbits the other one forever, then it means we get the exchange of photons forever right?which means infinite energy, I get that it can't be observed but that's possible for infinite...

Homework Statement Find h so that: -8x + -7y = 7 16x + hy = 14 has infinitely many solutions (solve this exercise with matrices). Homework Equations - The Attempt at a Solution I converted the system to matrix form, but when I try to convert it to echelon form, I get the...

Homework Statement Give S = {(x,|x|,2|x|) | x \in R} \bigcup {(0,2,4),(-1,3,6)}, find span(S) Homework Equations I know that span of a finite set of vectors is given by <a(0,2,4) + b(-1,3,6)+c(x,|x|,2|x|)>, where a,b,c are any real numbers. Can i use that same way to find the span of this...

I saw the below statement which is intuitively correct: If a set has cardinality m then none of its subsets has cardinality greater than m. Is it necessarily true for a infinite set case?

Homework Statement Preliminary test: If the terms of an infinite series do not tend to zero, the series diverges. In other words if ##\lim_{ n \to \infty}a_n \neq 0## then the series diverges. But if the limit is 0 we have to test further. Suppose a series a series satisfy this condition...

Homework Statement lim (3/n)^(2n) n→ ∞Homework Equations L'hopital's rule: lim F(a)/G(a) is indeterminate form, then the limit can be written as lim F'(a)/G'(a) x → a x→ a The...

Homework Statement I want to show that $$ \tan^{-1}(x)=\sum\limits_{n=0}^{\infty}\frac{(-1)^{n}}{2n+1}x^{2n+1}. $$ Homework Equations I start with $$ \int\frac{1}{1+x^{2}}dx. $$ The Attempt at a Solution I want to be able to do the following: $$...

Hi, I have a program that is entering a infinite loop in the last if else of this loop. The program is printing 3 endless times. Here is the code that generates it: else { for (j=1;j<n;j++) { if (j<=(n/2)) { a[1][j] = j-1; printf ("%d", a[1][j]); }...