What is Infinite: Definition and 1000 Discussions

A person asked this question of me recently and it generated some discussion amongst the people in the room (many of whom had a limited background in physics). The original question went something like this: suppose that a ball is initially at rest in a wagon and the wagon is given a horizontal...

A theorem on equivalence relation states that for any set S, the set of equivalence classes of S under an equivalence relation R constitutes a partition of a set. Moreover, given any partition of a set, one can define an equivalence relation on the set. What allows you to "create" a partition...

I was listening to Brian Cox on Intelligence Squared and he somewhat casually mentioned the general acceptance among physicists of a possibly "infinitely long" period of cold inflation predating the big bang and of the "sudden" stop to this inflation as the source of energy for the big bang...

Homework Statement For the following series ∑∞an determine if they are convergent or divergent. If convergent find the sum. (ii) ∑∞n=0 cos(θ)2n+sin(θ)2n[/B]Homework Equations geometric series, [/B]The Attempt at a Solution First I have to show that the equation is convergent. Both cos(θ)...

Statistical probabilities of a objects qualities as is emerging out of infinite variable states. Can an equal emergence occur again, and as a unavoidable fact of infinites result in endless occurrences, given infinite chance in an eternal cosmos? I say no. If the (falsely inferred as)...

What happens if you flip a coin with infinite heads and infinite tails? I am not sure if this is the right place to post this question, or if my question even makes sense! just thought about it after reading about the simulation argument

I have got to know that the voltage and frequency of the supply in the power grids is kept as infinity.>! But what is the reason behind it..?? Well for the voltage to be infinity , I have studied that losses are inversely proportional to square of supply voltage ..so higher is the voltage ...

One of the most common questions on this forum over the years is, “What is the universe expanding into?” The common answer in one form or another is always ‘nothing.’ My question is, why does current thinking preclude an eternal and infinite space… a void populated by the physical stuff we know...

Homework Statement Consider \frac{\partial u}{\partial t} = k\left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} \right) \\ 0<x<L\\ y>0 subject to the initial condition IC: u(x,y,0) = f(x,y) And solve with the following boundary conditions: BC1: \quad u(0,y,t) = 0...

hi, i know unitary transformation - but could not get where do we need finite and infinite unitary transformation ? please help me in this regard. thanks

hello I solve neutron diff eq for plane source in the vicinity of slab of water but if i substitute source term with 1 the flux in some places is greater than one! how it possible?! i am sure about my calculation so someone say me how it possible?

Not all DEs have a closed form solution. Some DEs have an implicit solution only - you cannot algebraically solve one variable of interest for another. I have seen on this forum people solving DEs in terms of infinite series. How does one arrive at such a solution, and can an implicit...

O.k. I am seriously confused... Not being to good at math but nevertheless interested in set theory, infinity, etc. I started reading Mary Tiles, The Philosophy of Set Theory (Dover edition). I particularly wanted to know more about the relation between infinite ordinals and cardinality, but...

Homework Statement So it says solve this wave equation : [y][/tt] - 4 [y][/xx] = 0 on the domain -infinity<x<infinity with initial conditions y(x,0) = e^(-x^2), yt(x,0) = x*(e^(-x^2)) Homework Equations I used the D Alembert's solution which is 1/2(f(x+ct)+f(x-ct)) + 1/2c ∫ g(z) dz The...

Homework Statement Find the ground and first excited state eigenfunctions of for the 1D infinite square well with boundaries -L/2 and +L/2 Homework Equations $$\frac{-\hbar^2}{2m}\frac{\partial^2}{\partial x^2}\psi(x) = E\psi(x)$$ The Attempt at a Solution Okay so I know how to solve it and...

Could somebody explain what does mean "infinite wavelength antenna" and what advantages does it have? What is resonant antenna and advantages? http://webcache.googleusercontent.com/search?q=cache:fHdO6P-aoIIJ:dspace.nitrkl.ac.in:8080/dspace/bitstream/2080/1320/1/MMET.pdf+&cd=4&hl=en&ct=clnk&gl=ca

For a particle in a box that is described with a wave function, why can there only be a standing wave when there is an infinite potential well? From my understanding, the infinite potential well makes it impossible for the particle to tunnel through the barrier and so the wave function cannot...

Sum= ...- 1 + 1 -1 +1-1+1... until infinite It is just an infinite sum of -1 plus 1. Can anyone tell me the sum of this infinite series and a demonstration of that result? THanks!

I am reading Paul E. Bland's book, "Rings and Their Modules". I am trying to understand Section 1.4 which introduces modules. I need help with one of the definitions included in the statement of Proposition 1.4.4. Proposition 1.4.4 reads as follows: In (2) in the above Proposition Bland...

Homework Statement An electron is confined to a narrow evacuated tube. The tube, which has length of 2m functions as a one dimensional infinite potential well. A: What is the energy difference between the electrons ground state and the first excitied state. B: What quantum number n would the...

Hi guys, I'm a mathematician from Miami Florida working in paraquaternionic and symplectic differential geometry, but I come from a very extensive physics background, pretty much well-versed in all modern physics. But my favorite of all is probably the philosophy of mathematics and science as...

Homework Statement A particle in two-dimensional infinite potential well $$ H=\frac{p^2}{2m}+\left\{\begin{matrix} 0, & |x|<\frac{a}{2}\text{ and }|y|<\frac{a}{2}\\ \infty , & \text{otherwise} \end{matrix}\right.$$ a) Find eigenfunctions and their energies. Also describe the degeneration of...

[Note from mentor: this thread originated in a non-homework forum, therefore it doesn't use the standard homework template] ------------------------------------------ This exercise pops up in the Cavendish Quantum Mechanics Primer (M. Warner and A. Cheung) but I can't seem to figure it out. So...

Homework Statement An infinite cylindrical wire of radius ##R## carries a current per unit area ##\vec{J}## which varies with the distance from the axis as ##J(s)=ks^2\hat{z}## for ##0<s<R## and zero otherwise where k is a constant. Find the magnetic field ##\vec{B(s)}## in all space. Homework...

My textbook reads : The graph of a_n=\frac{n}{n+1} are approaching 1 as n becomes large . In fact the difference 1-\frac{n}{n+1}=\frac{1}{n+1} can be made as small as we like by taking n sufficently large. We indicate this by writing \lim_{n \to \infty} \frac{n}{n+1}=1 I don't understand where...

Evaluate $\displaystyle \lim_{{n}\to{\infty}} \prod_{k=3}^{n}\left(1-\tan^4\dfrac{\pi}{2^k}\right)$.

Homework Statement Evaluate the limit 1 1 1 lim ∫ ∫ ... ∫ cos^2((pi/2n)(x1 + x2 +... xn))dx1 dx2 ... dxn 0 0 0 n→∞Homework Equations Well, I know that we can change this using a double angle rule, so that the integrals become 1/2 + 1/2 cos (2*pi/2n)(x1 +...

Heard that line on one of those science channel shows. Forget who they were interviewing. But my question is what is the mathematics behind discovering this fact? How could we possibly know that our galaxy is one of the biggest in the Universe unless we counted all or most of them, how could we...

Hi, let's take the sum: $\displaystyle \sum_{n=1}^{\infty}\frac{1}{9n^2 + 3n - 2}$ $\implies 9n^2 + 3n - 2 = 9n^2 + 6n - 3n - 2 = 3n(3n + 2) - (3n + 2) = (3n - 1)(3n - 2)$ The simplest way would be to use partial fractions, and then convert this into a telescoping series. Which makes the sum...

Hello, I have began my journey on infinite sums, which are very interesting. Here is the issue: I am trying to understand this: $\displaystyle \sum_{n=1}^{\infty} e^{-n}$ using integrals, what I have though: $= \displaystyle \lim_{m\to\infty} \sum_{n=1}^{m} e^{-n}$ $= \displaystyle...

Hello, I am well aware of the ratio method, and the sum = 1/(1-r) but I want to try this method. I am trying to understand this: \displaystyle \sum_{n=1}^{\infty} e^{-n} using integrals, what I have though: = \displaystyle \lim_{m\to\infty} \sum_{n=1}^{m} e^{-n} = \displaystyle...

Homework Statement An explosive is to be stored in large slabs of thickness 2L clad on both sides with a protective sheath. The rate at which heat is generated within the explosive is temperature-dependent and can be approximated by the linear relation ##\dot Q_{gen} = a + b(T - T_{\infty})##...

EM field strength dies quickly with distance, what's so special about going up and down that allows EM waves to maintain their energy over infinite distance?

NB. first time using Latex so apologies if something came out wrong, I've done my best to double check it. Consider the curve y = \frac{1}{x} from x=1 to x=\infty. Rotate this curve around the x-axis to create a funnel-like surface of revolution. By slicing up the funnel into disks with...

a) Derive the expression for the potential difference due to two uniform infinite sheet charges at y=5 and y=-5 in free space. b) If V=4V at (0,2,10) find V at (-4,3,1) . The surface charge density on the two sheet charges are ?s=?0 col/m2 What you guys be able to help me with this ?

I'm trying to figure out what it says in my book. Here is the link of the picture. http://i941.photobucket.com/albums/...oads/7D0D3CE4-A11E-4F0F-A2A5-836D03945AE5.jpg Could someone explain the part where it says "Otherwise, there would be a net tension force acting on the sections, and they...

Hi there I am trying to find bound state energies assuming infinite potential. I have been told it can be done by analytically solving Right Hand Side and Left Hand Side of an equation such as: E^1/2 tan(2ma^2E/4hbar)^1/2 = (V0-E)^1/2 If solved properly, it should give one curve (RHS), crossed...

Hey! :o Show that an infinite $\sigma-$algebra is uncountable. Could you give me some hints what I could do?? Do I have to start by supposing that an infinite $\sigma-$algebra is countable?? But how could I get a contradiction?? (Wondering)

Homework Statement There is an infinite conducting cylinder positioned at the axis with radius R. An infinite line charge (+λ) is placed distance d from the axis and d>R. I was supposed to 1. Find the potential and then 2. find the surface charge on the cylinder. Homework Equations V = -∫...

Homework Statement The wording of the question is throwing me off. It is a standard inf. pot. well problem and we are given the initial position of the particle to be in the left fourth of the box, \Psi(x,0)=\sqrt{\frac{4}{a}} We are asked to a) write the expansion of the wave function in...

"The extent of solubility ranges widely, from infinitely soluble (without limit) (fully miscible[1]) such as ethanol in water, to poorly soluble, such as silver chloride in water." from wiki page of solubility So does it mean that you can solve ethanol in water as much as you want? Even if...

I read somewhere that at 90% the speed of light the mass doubles. So does mass only nearly double at the speed of light and does mass not become infinite at the speed of light? I thought nothing with mass can travel at the speed of light because mass would become infinite at light speed. Also...

It would seem to me that we exist in an infinitely large space. That a big bang could not encompass all matter because all space extends infinitely. That with infinite space there is infinite possibilities for things to happen, such as for matter to exist. That space can exist and is infinite...

This question seems to come up often, but I cannot find a satisfying explanation. There is a point charge +Q some distance above an infinite conducting plane. Supposedly, the electric field below the plane must be zero. I have trouble understanding why this is true. The total charge on the...

Homework Statement Let V consist of all infinite sequences {xn} of real numbers for which the series summation xn2 converges. If x = {xn} and y = {yn} are two elements of V, define (x,y) = summation (n=1 to infinity) xnyn. Prove that this series converges absolutely. Homework Equations The...

The problem I have is about a simple remark made in the book 'Berkeley Physics Course Volume 2, Electricity and Magnetism', chap. 3 figure 3.4 b. It says that if we have an infinite sheet of charge but with 'other charges' present elsewhere in the system, the only thing we can predict is that...

I am reading An Introduction to Rings and Modules With K-Theory in View by A.J. Berrick and M.E. Keating (B&K). In Chapter2: Direct Sums and Short Exact Sequences in Sections 2.1.11 and 2.1.12 B&K deal with infinite direct products and infinite direct sums (external and internal). In Section...

Homework Statement The potential for a particle mass m moving in one dimension is: V(x) = infinity for x < 0 = 0 for 0< x <L = V for L< x <2L = infinity for x > 2L Assume the energy of the particle is in the range 0 < E < V Find the energy eigenfunctions and the equation...

Homework Statement http://puu.sh/bTtVx/ba89b717b8.png Homework Equations I've tried using the integral method of Schrodinger's eq, getting: (X/L - (1/4pi)sin(4xpi/L) from x1 to x2. The Attempt at a Solution I've tried plugging in the values of x given in the problem to the above equation...

Homework Statement A particle of mass ##m## is constrained to move between two concentric hard spheres of radii ##r = a## and ##r = b##. There is no potential between the spheres. Find the ground state energy and wave function. Homework Equations $$\frac{-\hbar^2}{2m} \frac{d^2 u}{dr^2} +...