What is Infinite: Definition and 1000 Discussions

To anyone that can help me with this - You have to pick the FIRST correct reason. Work below (exception of 4 because I cannot figure it out), but in order to get the question right you must have all correct and I cannot figure it out. Any help is appreciated. [Moderator's note: Moved from a...

Hello i am currently struggling with a problem, F denotes either the set of all Real or Complex numbers. The aim is to prove that ##F^\infty## is infinite dimensional. First of i am not sure i understand the books definition of this collection. It says it consists of all sequences of elements...

Say that these pictures are accurate. Personally, I think I can solve this problem, but the issue is, that I had a debate on it with my Physics teacher. This is how my teacher would solve it; my teacher says that each Fk on each side is constructed from half of F and Fx. So, F = 2 * Fk * sin...

Let X=C[O,1] and Y=span($X_{0},X_{1},···$), where $X_{j}={t}^{i}$, so that Y is the set of all polynomials. Y is not closed in X.

So I figured to get e-field at point (4,4,0), I need to find the resultant e-field from the negatively charged particle and the plate ##E_{resultant}=E_{particle}+E_{plate}## ##E_{particle}=\frac{kq}{d^2}=\frac{(9*10^9)(-2*10^-6)}{4^2}=-1125N/C## Now for the plate is where I'm confused. If this...

Gödel numbers are used to encode wffs of formal systems that are strong enough in order to deal with Arithmetic. In my question, Gödel numbers are used to encode wffs as follows: Syntactically (by formalism without semantics) there is set A (the set which is postulated to be infinite), such...

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Evaluate ##\lim_{n \rightarrow +\infty} \frac {1} {n} [(\frac {1}{n})^{1.5} + (\frac {2}{n})^{1.5} +(\frac {3}{n})^{1.5}+ (\frac {4}{n})^{1.5}+...+(\frac {n}{n})^{1.5}]## Hello. So I'm solving this question at the moment. I know I'm supposed to find out the summation of this before being able...

Consider two opposing mirrors. If they are exactly parallel planes I think there is only a single image in each but if they are slightly angled there appears an "infinite" number of reflections. Similarly, suppose we have grounded conducting planes instead of mirrors with a charge in between...

Hello, I am trying to find the solution of Schrödinger equation on matlab. However, when I apply boundary conditions, MATLAB only gives me the solution with both coefficients 0. I want to find the solution : Asin(n*pi*x/L) You can see my code below. Could you please tell me where is my mistake...

Okay so I begin first by mentioning the length of the well to be L, with upper bound, L/2 and lower bound, -L/2 and the conjugate u* = Aexp{-iz} First I begin by writing out the expectation formula: ## \langle p \rangle = \int_{\frac{L}{2}}^{ \frac{L}{2} } Aexp(-iu) -i \hbar \frac{ \partial }{...

The problem is: Solve the time independent Schrodinger Equation for infinite square well centered at origin. Show that the energy is same as in the original case(well between x=0 and x=L). Also show that the solution to the this case can be obtained by setting x to x-L/2 in ##\psi## in the...

I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help In order to formulate a rigorous proof to the proposition stated in Exercise 2.3.10 (1) ... ... Exercise 2.3.10 (1) reads as...

I'm troubled by what I think the 'community' considers them to be, but I'm not sure if I'm correct. It appears as though finite is thought to have both an end and a beginning, but is it true that infinite (infinity) is thought to only have no end? Is this accurate? If so, then it would seem like...

I tried finding the cone's Flux and from there i have no idea ,can anybody pls help me ? Thanks in Advance Regards Harish R

First I worked out the dispersion relations, which is pretty easy: ##M \ddot x_j = K x_{j-1} + K x_{j+1} - 2K x_j -mg \frac {x_j} {l} ## (All t-derivatives) We know ##x_j## will be in the form ##Ae^{ijka}e^{-i\omega t}## so the above becomes: ## -\omega^2M = K (e^{-ika}+e^{ika}-2)-\frac {g}...

Summary: Starting on basics of computational learnability, I am missing the key intuition that allows results about finite processes to reference results from the infinite domain. Snowball: (a) Hazard brought my attention to a popular article...

For example integral of f(x)=sqrt(1-x^2) from 0 to 1 is a problem, since the derivative of the function is -x/sqrt(1-x^2) so putting in 1 in the place of x ruins the whole thing.

Summary: Potential at origin of an infinite set of point charges with charge (4^n)q and distance (3^n)a along x-axis where n starts at 1. From V=q/r, we find Vtotal=sum from 1 to infinity of (4/3)^n(q/a), which diverges. There cannot be infinite potential because there is a finite electric...

I've been thinking about this problem for some time now and think that I need to find E to solve for σ, but I have no idea how to go about that. How do I approach this problem?

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...

Hello, Let's imagine we have an infinite plane (or large enough compared to the region of interest and measurements) pierced in normal direction by magnetic field B which is uniformly distributed but time varying. For the sake of simplicity we'll presume the magnetic induction is linearly (and...

Hello! I'm trying to understand the concept of escape velocity, and I know you equate the initial mechanical energy to the final mechanical energy, where the final mechanical energy is at a distance of infinity. I know that the gravitational potential energy approaches 0 as the distance r gets...

Let ##(x_1,y_1)## and ##(x_2,y_2)## be the point where the rods intersect the ##x,y## plane. I know that on any given point there will be the superpositions of ##E_1=\frac{2\lambda}{4\pi \epsilon_0}\frac{1}{(x-x_1)^2+(y-y_1)^2}\hat{r}_1## and ##E_2=\frac{2\lambda}{4\pi...

I am currently stuck trying to work this out. I have an infinite potential with walls at x=0 and x=a, with the initial state: $$ \psi(x,0) = A_2(exp(i\pi(x-a)/a)-1) $$ I am trying to find psi(x,t). I know that $$ A_2(exp(i\pi(x-a)/a)-1) = A_2(-exp(i\pi/a)-1) $$ And this enables me to find...

Homework Statement Construct the four lowest-energy configurations for particles of spin-##\frac{1}{2}## in the infinite square well, and specify their energies and their degeneracies. Suggestion: use the notation ##\psi_{n_1,n_2}(x_1, x_2) |s,m>##. The notation is defined in the textbook...

Homework Statement Hi. in my problem there is an infinite half cylinder uniformly charged with ρ. What is the force is the cylinder is making on a test charge on a charge located on the position that is shown on the following picture: Homework Equations ∫qdQ/(r2) The Attempt at a Solution Well...

I have a calculus 2 midterm coming up and given the exam review questions, this seems like this question can potentially be on it. I've tried to look it up, but I always find the famous painters example, which I don't find satisfying.

Homework Statement I'm having trouble understanding the existence of valence shells. I understood that valence shell is the last energy level for the electrons to populate around an atom. But, according to Bohr model , an atom can have infinite energy levels , so I don't understand: How can...

##1+x+x^2 = \dfrac{1-x^3}{1-x} = (1-x^3)\cdot \dfrac{1}{1-x} = (1-x^3)\sum_{k=0}^\infty x^k##. Isn't this a contradiction since the LHS has degree ##2## while the RHS has infinite degree?

Homework Statement Homework Equations V=k∑q/r E=-dV/dsThe Attempt at a Solution I found part A plenty fine, 2kq/a From here, I thought that the derivative of -V would give me the electric field, giving -2kq/a^2, but that's not the answer according to what my professor sent. I'm wondering...

<Moderator's note: Moved from a technical forum and thus no template.> $$\lim_{x\rightarrow 0} (x-tanx)/x^3$$ I solve it like this, $$\lim_{x\rightarrow 0}1/x^2 - tanx/x^3=\lim_{x\rightarrow 0}1/x^2 - tanx/x*1/x^2$$ Now using the property $$\lim_{x\rightarrow 0}tanx/x=1$$,we have ...

I've been taught that $$1^\infty$$ is undetermined case. Why is it so? Isn't $$1*1*1...=1$$ whatever times you would multiply it? So if you take a limit, say $$\lim_{n\to\infty} 1^n$$, doesn't it converge to 1? So why would the limit not exist?

Homework Statement Homework EquationsThe Attempt at a Solution How do you know the left plate (or the right plane) produces a field (1/2ε) σ to the left and right? How do you apply Gauss Law? For one infinite plane, we can use Gauss law because of symmetry, so we can assume the electric flux...

Homework Statement Homework Equations dE= k dq/r2 The Attempt at a Solution [/B] I started off taking a derivative of q(x). dq = -qo/l ⋅ e-x/ldx Then, I decided that r was the distance x along the rod + .02m. r=(.02+x) Following that, I plugged everything into the formula: dE = k⋅qo/l...

Hey, I'm tutor for theoretical physics for first year students and I found a question that I couldn't answer so far. It's about the rocket equation. I tried to derive the acceleration without using infinite small variables, but somehow there is one term left that shouldn't be there. In the...

I have recently been curious about heat diffusion. If there is space in one dimension with any kind of temperature dispersed throughout, then the heat equation states that the derivative of the temperature with respect to time at any point equals some constant (k) multiplied by the second...

Homework Statement My doubts are on c) Homework Equations $$< H > = \int \Psi^* \hat H \Psi dx = \frac{2}{a} \int_{0}^{a} sin (x\frac{\pi}{a}) \hat H sin (x\frac{\pi}{a}) dx$$ The Attempt at a Solution I understand that mathematically the following equation yields (which is the right...

Hi. I know that eixe-ix = 1 but if I write the product of the 2 exponentials as infinite series I get ΣnΣm xn/(n!) (-x)m/(m!) without knowing the result is 1 using exponentials how would I get the result of this product of 2 infinite sums ? Thanks

I was wondering if I placed an infinite number of light polarizers in an array, each rotating an infinitesimal amount from the next, would I be able to get 100% of the photons shun thru them on the other side?

For this problem at t=0 Ψ(x,0)=Ψ1-Ψ3 Where Ψ1 and Ψ3are the normalised eigenstates corresponding to energy level 1 and 3 of the infinite square well potential. Now for it's time evolution it will be Ψ1exp(-iE1t/ħ)- Ψ3exp(-iE3t/ħ) And taking the time given in the question the time part of the...

Homework Statement Homework Equations For this question my ans. is coming option (3) since the time part of the wave comes out to be same for both the energy states which is (-1)^(-1/8) and (-1)^(-9/8) respectively (using exp(-iEt/ħ)). But the correct option is given option (4). Am I right...

Homework Statement Show that it is not necessarily true that the infinite union of closed sets is closed Homework EquationsThe Attempt at a Solution From intuition, I came up with the following counter-example: ##\displaystyle \bigcup_{n=2}^{\infty} \left[ \frac{1}{n}, \frac{n}{n+1} \right] =...

I have wondered if there is a symmetric current configuration that gives the magnetic field of a half-infinite solenoid. With some thought I think I came up with such a configuration of current loops that produces the same magnetic field as a half-infinite solenoid Suppose we have a large but...

Hi. If a function f is normalizable ,ie f→0 as | x | → infinity or r→ infinity then I presume the following surface integral f dS over infinite space is zero ? But I thought about this again and it seems like a case of zero x infinity. The function is zero at the infinite surface but the area...

Lusin's Theorem: Let $f$ be a real-valued measurable function on $E$. Then for each $\epsilon > 0$, there is a continuous function $g$ on $R$ and a closed set $F$ contained in $E$ for which $f=g$ on $F$ and $m(E - F)<\epsilon$. I'm going through exercises in the book... almost finals time. The...

Homework Statement Find the sum of the series Homework EquationsThe Attempt at a Solution Not sure exactly where to start. If I move 3 outside the sum I'm left with 3*sigma(1/n*4^n), which I can rewrite to 3*sigma((1/n)*(1/4)^n), which party looks like a geometric series..Any tips?

Much as the title of this thread asks: does quantum mechanics use n-dimensional or infinite dimensional integrals? I'm merely curious as I studied the n-dimensional case as a hobby and wondered if I'd ever get to use it for anything cool like QM. If so, please maybe post one such integral so I...

Homework Statement Think that we have only conservative force in this question and no nonconservative force like friction exists. Also## U ##means potential energy (eg Gravitational Potential Energy),##K## means Kinetic Energy (##1/2 mv^2##) and ##E = K + U = constant## We have a arbitrary...

There are infinite number of charges each with charge q along a straight line at a distance of 1,2,4,8,16,… … … unit from a point. What is the electric field at this point? No idea about it.Please help me out.