Infinity Definition and 988 Threads

Question 1: Find the Laurent series of \cos{\frac{1}{z}} at the singularity z = 0. The answer is often given as, \cos\frac{1}{z} = 1 - \frac{1}{2z^2} + \frac{1}{24z^4} - ... Which is the MacLaurin series for \cos{u} with u = \frac{1}{z}. The MacLaurin series is the Taylor series when u_0 = 0...

Hi! For the probability interpretation of wave functions to work, the latter have to be square integrable and therefore, they vanish at infinity. I'm reading Gasiorowicz's Quantum Physics and, as you can see in the attached image of the page, he works his way to find the momentum operator. My...

Hey guys! I have heard of this concept in various places and sort of understands what it attempts to do. Can anybody please explain it to me in more detail like how it works, how to notate it, and how to expand it to infinities and infinitesimals. Thanks in advance! Aakash Lakshmanan xphysx.com...

Homework Statement \lim_{n\rightarrow ∞}\frac{n^n}{n!} Homework Equations n! = (1)⋅(2)⋅(3)⋅...⋅(n-1)⋅n The Attempt at a Solution \lim_{n\rightarrow ∞}\frac{n^n}{n!} \lim_{n\rightarrow ∞}\frac{n^n}{(1)⋅(2)⋅...⋅(n-1)⋅n} I then factor n out of the denominator n times, or rather, nn, leaving...

Hello. First of all, I must say that I'm new to this forum, so I apologize if I'm posting in the wrong section. I'm a 17 year old with not that much knowledge about physics, so if what I'm talking about makes no sense or is completely stupid, just let me know. A couple of days ago I asked...

Homework Statement Find the limit $$\lim_{x\to-\infty} \frac{\sqrt{9x^6 - x}}{x^3 + 9}$$ Homework Equations N/A The Attempt at a Solution To solve this, I start off by dividing everything by ##x^3##: Numerator becomes ##\frac{\sqrt{9x^6 - x}}{x^3} = \sqrt{\frac{9x^6 - x}{x^6}} = \sqrt{9 -...

Homework Statement Limx--> ∞ Ln(x^2-1) -Ln(2x^2+3) Homework EquationsThe Attempt at a Solution Ln(x^2-1)/(2x^2+3) Then I divided the top and bottom by x^2 so in the end I got (1/2). Is this right?

Homework Statement lim as x tends to -∞ (x)^3/5 - (x)^1/5 Homework EquationsThe Attempt at a Solution The first thing I did was convert it into a radical so it becomes fifthroot√x^3 - fifthroot√x. Then I rationalized to get ( x^3-x)/(fifthrt√x^3+fifthroot√x) . I then divided the top by x^3...

Hi. An electric dipole field (two opposite point charges separated by some distance) has fields lines from the positive to the negative charge, but also field lines reaching to and coming from infinity. Starting from the positive charge, is there a way to compute the opening angle of the cone...

The (most popular) flat model of Universe is space-infinite. How the infinity is measured? Can you give me references to the papers about the actual infinity of space?

I am trying to prove how this set is countably infinite: q∈Q:q=a/b where a is even and b is odd a needs to be even and b needs to be odd, so I thought this would prove that it would be countably infinite: q = a/b + x/x, where x is any even number. a always needs to be even and b always...

I had a question after watching a Discovery Channel show on the universe. They talked about how some speculate the infinitude of the universe as opposed to a finite sized universe and I have also heard the same on this forum...and it got me to thinking... Isn't an infinite universe...

When the observable universe was the size of a baseball, did its gravity (field?) extend to (as opposed to towards) infinity?

If you divided the circumference of an infinitely large circle by its diameter, would the result be pi?

I have $$5^n - 3^n \le 2^n$$ (as n approaches infinity) but I'm not sure how to prove this to myself.

When we talk about a particular problem in Physics. For instance, let's say that light is coming from somewhere to hit the earth. We often say that the light is coming from "infinity." Let's say that we're tackling a black hole and we have a person somewhere as an example and we say that let's...

Since the success of the Penrose Hawking singularity theorems many people have claimed that the universe must have a beginning . In recent years though people have explored models of the universe that resolve the singularity and imply the universe may have existed before the big bang. In such...

Is ## "\frac{0}{\infty}"=0 ## ?

The universe- from our understanding, is expanding, thus the regions (for lack of a better word) particles have not yet reached do not exist. How far our universe can/ will expand is unknown, it may be infinite, but we can conclude at this time, as it is still expanding, that it is finite. True...

$\large{8.8.16} $ $\tiny\text{LCC 206 Integral at infinity}$ $$I=\int_{0}^{\infty}\frac{x}{\sqrt[5] {x^2 +1}} \,dx= \infty \\$$ $\text{presume just taking the limit makes the } \\ x\implies\infty \\ \text{thus the integral goes to } \infty$ $\tiny\text{ Surf the Nations math study group}$...

From the perspective of a 4D observer would 3D infinity appear to exist? Why/why not?

$\Large{§8.8.15} \\ \tiny\text {Leeward 206 Integration to Infinity}$ $$\displaystyle \int_{e^{2}}^{\infty} \frac{dx}{x\ln^p\left({x}\right)}\,dx \,, p>1$$ $\text{not sure how to deal with this} $ $\text{since there are two variables x and p} $ $\text{answer by maxima is:'} $...

$$\Large{§8.8. 14} \\ \tiny\text {Leeward 206 Integration to Infinity}\\ \displaystyle I=\int_{2 }^{\infty} \frac{1}{x\ln\left({x}\right)}\,dx \\ \begin{align}\displaystyle u& = \ln\left({x}\right) & du&=\frac{1}{x} \ d{x} \end{align} \\ \displaystyle I=\int_{2}^{\infty}\frac{1}{u}...

$\tiny\text{Leeward 206 {8.13} Integral at infinity}$ $$I=\int_{0} ^{\infty} e^{-ax} \,dx \ a>0 = \\ \begin{align}\displaystyle u& = -ax & du&=-a \ d{x} \end{align} \\ \text{then} \\ I=-\frac{1}{a}\int_{0} ^{\infty} e^{x} \,dx =-\dfrac{\mathrm{e}^{-ax}}{a}+C \\ \text{hopefully, wasn't...

Hello everyone. I need help trying to calculate/ trying to realize what the limit function of (sin nx)/(sin x) as n goes to infinity is. from another topic here on MBH ("Show δn = (sin nx) / (pi x) is a delta distribution") and after research with Wolfram Alpha I know that the limit function...

Homework Statement (Not for homework/assignment. Just doing problems for practice) This is from Griffiths Introduction to Electrodynamics, 4th edition, p.112 Problem 2.60 " A point charge q is at the centre of an uncharged spherical conducting shell of inner radius a and outer radius b...

Hey! 1. Homework Statement One must simply calculate the magnetic field at a distance s to the wire, which carries a steady current I Homework Equations Should I write the point vector as: \mathbf{r} = s\hat{s} + \phi \hat{\phi} + z \hat{z} or \mathbf{r} = s\hat{s} + z \hat{z} ? The Attempt...

Am using Spivak and he defines limit of a function f 1. As it approaches a point a. 2.As it approaches infinity. He also defines limit f(x)=∞ x->a But though in solving exercises, we can see that all the three definitions are consistent with each other, I am not...

I know this thread, about why the Universe can't expand inward, is fairly old; but I stumbled across it today and there was something mentioned here that sparked a question I feel like people here would be qualified to answer. What was mentioned, was that a singularity is a point at which our...

To what extent is the term infinity used in the physical world. When talking in terms of mathematics we can have a set of all natural numbers called an infinity, then we can have a value that comes after this set of infinity (lets call it 'a'). After 'a' comes 'a+1' then after this set of...

With basic fractions, the limits of 1/x as x approaches infinity or zero is easily determine: For example, \begin{equation} \lim_{x\to\infty} \frac{1}{x} = 0 \end{equation} \begin{equation} \lim_{x\to 0} \frac{1}{x} = \infty \end{equation} But, we with a operation like ##\frac{f(x)}{g(x)}##...

Hello! I've read on several pages that plane mirrors have an infinite amount of focal points. I don't understand? I thought plane mirrors have no focal points because the rays are parallel and don't focus in the first place. Why does a plane mirror have infinity focal points and what does it mean?

Homework Statement find the limit of arccoshx - ln x as x -> infinity Homework Equations ##arccosh x = \ln (x +\sqrt[]{x^2-1} )## The Attempt at a Solution ## \lim_{x \to \infty }(\ln (x + \sqrt{x^2-1} ) - \ln (x)) = \lim_{x \to \infty} \ln (\frac{x+\sqrt{x^2-1}}{x}) \ln (1 + \lim_{x \to...

Let's say for example, there was a dye in which any number with any amount of digits could be scored. You also had an equal chance of scoring every number. Which means that you have the same chance of rolling a 1 as you do 5 billion. If you rolled that dye, how many digits would that number...

A movie on the life of Srinivasa Ramanujan staring Dev Patel and Jeremy Irons: https://en.wikipedia.org/wiki/The_Man_Who_Knew_Infinity_(film) with a planned April 29, 2016 release date. The trailer looks pretty good. The producers are Manjul Bhargava and Ken Ono, two well-known and...

To show that the Lagrangian ##L## is invariant under a rotation of ##\theta##, it is common practice to show that it is invariant under a rotation of ##\delta\theta##, an infinitesimal angle, and then use the fact that a rotation of ##\theta## is a composite of many rotations of...

Hi everyone, So we were writting our math test today and I am not completely sure about one concept. For the sake of simplicity let's say that f(x)=x2 and let's say we were asked to find, lim f(x) as x--->infinity = ? is the correct answer here undefined or infinity. Thanks for the help

Homework Statement A proton is moving at speed v from infinity toward a second stationary proton, as shown below. Determine the minimal distance between them. http://s27.postimg.org/lmw3d21j7/Untitled.png Homework Equations W = \frac{kq_1q_2}{r} E_k = \frac{mv^2}{2} The Attempt at a...

Homework Statement Charges 2q and -q are located on the x-axis at x=0 and x=a respectively. (a) Find the point on the x-axis where the electric field is zero, and make a rough sketch of some field lines. (b) You should find that some of the field lines that start on the 2q charge end up on...

Homework Statement I am trying to solve a problem from a popular quantum mechanics text. I am learning on my own. I am trying to calculate the variance, which is <x^2>-<x>^2 = variance in x. I posted a photo of the problem as a picture that is linked below as well as the solution, I simply...

Hi everybody, I have this function to study ##\frac{(x+1)}{arctan(x+1)}## I need the limit to infinity,it's oblique and I have to find q,from y=mx+q. so q=lim(x->inf) ##\frac{(x+1)}{arctan(x+1)} -2x/\pi## I don't know how to solve it.the limit gives infinity to me.but calculators online give...

hey I was browsing the web a while ago and I found an equation for infinity to equal 1.5 when subjected to a equation. however I can no longer find this. I was wondering if anyone knew what it was and if they could explain how it works. many thanks Ewen

dextercioby submitted a new PF Insights post The Need of Infinity in Physics Continue reading the Original PF Insights Post.

Hello everyone, I have a problem with finding a residue of a function: f(z)={\frac{z^3*exp(1/z)}{(1+z)}} in infinity. I tried to present it in Laurent series: \frac{z^3}{1+z} sum_{n=0}^\infty\frac{1}{n!z^n} I know that residue will be equal to coefficient a_{-1}, but i don't know how to find it.

Homework Statement Homework EquationsThe Attempt at a Solution I tried using the rule of multiplying with the "conjugate", for example what's above multiplied by (√n^3+3n)+(√n^3+2n^2+3)/(√n^3+3n)+(√n^3+2n^2+3). But I'm left with a huge mess :( I also tried dividing the top and the bottom by...

How do you show that $\displaystyle \lim_{x \to \infty} \frac{50x^{10}+100}{x^{11}+x^6+1}=0$ What I tried: $\displaystyle \lim_{x \to \infty} \frac{50x^{10}+100}{x^{11}+x^6+1} =\lim_{x \to \infty} \frac{50+100/x^{11}}{1+1/x^{5}+1/x^{11}} = \frac{50+0}{1+0+0} = 50.$ But this is wrong. (Angry)

I'm trying to find $\displaystyle \lim_{x \to 20^{+}}\frac{5x^3+1}{20x^3-8000x}$ $\displaystyle \lim_{x \to 20^{+}}\frac{5x^3+1}{20x^3-8000x} =\lim_{x \to 20^{+}}\frac{5+1/x^3}{20-8000/x^2} = \frac{5+\lim_{x \to 20^{+}}1/x^3}{20-\lim_{x \to 20^{+}}8000/x^2} =...

So I derived the E-field of a hollow sphere with a surface charge σ at z and I got: E(r)=\hat{z}\frac{\sigma R^2}{2\varepsilon _{0}z^2}\left ( \frac{R+z}{\left | R+z \right |}-\frac{R-z}{\left | R-z \right |} \right ) at z>R, the equation becomes: E(r)=\hat{z}\frac{\sigma R^2}{\varepsilon...

This seems a very simple case to me, yet I have heard it said that the answer is some undefined real number. Yet zero times anything means no iterations of whatever the object is; whether that be a real number , an imaginary number or an undefined number. Whatever it is I don't see how one can...

I am reading Micheal Searcoid's book: Elements of Abstract Analysis ( Springer Undergraduate Mathematics Series) ... I am currently focussed on Searcoid's treatment of ZFC in Chapter 1: Sets ... I am struggling to attain a full understanding of the Axiom of Infinity which reads as shown...