Infinity Definition and 988 Threads

in the dispersion relation of the surface plasmon the wavelength is proportional to square root of n. according to equation 5 in this paper: https://Newton.ex.ac.uk/research/emag/pubs/pdf/Barnes_JOA_2006.pdf if n goes to infinity, then what will be the value of wavelength. Thank you

I watched a video where apparently the sum of all natural numbers = -1/12. The video starts by saying S = 1-1+1-1+1-1+1-1... to infinity. He then says this sum does not have an answer, it's constantly between 1 and 0 depending on where you stop it. So he just takes the average and says 1/2. How...

Is this true? (∞ - 1) < ∞

Reading Geroch's "What is a Singularity in General Relativity?", it seems that polynomial scalar invariants constructed from the Riemann tensor can diverge if we are at infinite distance, and not in a true singularity. Can someone give an example of space-time whose scalar invariant diverges...

This idea has been bothering me for a while, it started when I thought that if there was an infinite amount of space inside of an inch. ( or even any measurement in the physical world ) Then I thought that maybe that's not a fair argument on the basis that quantum theory says planks length "h"...

So, according to physicsoftheuniverse.com, "In the centre of a black hole is a gravitational singularity, a one-dimensional point which contains infinite mass in an infinitely small space, where gravity become (sic) infinite and space-time curves infinitely, and where the laws of physics as we...

I read about a theory according to which the sum of everything the universe is made of is likely to be zero. For example, forces cancel each other, positive and negative energy cancel each other, and so on. Is there some support for this theory, or is it generally dismissed?

If zero is the additive identity and one is the multiplicative identity, is there an operation for which infinity is the identity?

Hi PF! I'm a long time lurker - only posted a few times in the past. I love this place, and I think there's a lot of like-minded people on here who might (hopefully) find this interesting. I don't mean to be brigading or anything - just wondering if anyone is as excited as I am about this! Some...

if $\lim_{{n}\to{\infty}} {y}_{m+1}={x}^{*}$, Can we say that $\lim_{{n}\to{\infty}} {y}_{n-1}={x}^{*}$...Please pay attention, I say m and n...

I listened to the audiobook version of The Beginning of Infinity by David Deutsch on a recent vacation. I'll always associate the drive from Seattle to Gold Beach, Oregon with Physics! I've read some of Stephen Hawking's and Brian Greene's books, but the way David Deutsch worded some of his...

Homework Statement So I have a problem with the integral ∫ sin(x)/x^0.1dx from pi to infinity My teacher said this wouldn't require any maths beyond calc 3, but for some reason I cannot come up with a solution. Homework EquationsThe Attempt at a Solution I have attempted a maclaurin series...

okay so I have this integral: 2∫cos(kx)dk The bounds are from zero to infinity, this doesn't converge but is there any other way to describe this?

Homework Statement Find \lim_{x\to \infty} \sqrt{x^2+1}-x Homework EquationsThe Attempt at a Solution This is mostly for a refresher. I know it's zero because when we multiply the top and bottom by the conjugate to obtain \frac{1}{\sqrt{x^2+1}+x} and the denominator increases without bound...

I understand that ψ goes to zero as x goes to infinity. Is it also true that dψ/dx must go to zero as x goes to infinity?

The observable universe is a sphere, centered on us, where the radius is the horizon distance, which is the distance light could have traveled since the Big Bang. The observable universe is finite, but is only a subset of the entire universe. Is the entire universe finite or infinite? If the...

Infinity is not a real number right? Then where do infinity stand (complex no?) . Why infinity is not a real number , I thought of it as a very very big real number! Ignore my poor communication skills.

Assuming that this next statement is correct, that there are an infinite amount of numbers between the numbers "1 and 2", and another, different set of infinite numbers between "2 and 3". All I'm trying to take out of this is that infinity doesn't necessarily mean every number, but at the...

micromass submitted a new PF Insights post Questions About Infinity Continue reading the Original PF Insights Post.

Given a system of two charges (+7q and -q) some of the field lines will terminate at -q while others go on towards infinity. I've read that the portion of the field lines that terminate is given by (1/7), but I have no idea why that is. I am supposed to find the maxium angle of a field line...

Is infinity divided by infinity equal to 1? 6 divided by 6 is equal to 1 however as infinity resembles 0 in the sense that 0 dived by 0 is equal to 0, I am uncertain whether infinity divided by infinity would equal 1 or instead, infinity.

I was some youtube videos and i got sucked into this channel called "numberphile". They were talking about infinite sets. In particular the set that is the sum of all natural numbers. Through some creative algebra they demonstrate the proof. Somehow the set that is equal to the sum of all...

How do you prove 1/x = 0 if x= infinite and 1/x = infinite if x=0 No need to use formal language, please just explain what the variables are for the quantifiers, or what you mean by for all and there exists if you are gracious enough.

While reading a paper, i came across the following Expectations: Given that the ##E\left\{e^2_{n-i-1}e^2_{n-j-1}\right\}=E\left\{e^2_{n-i-1}\right\}E\left\{e^2_{n-j-1}\right\}## for ##i\neq j##.\\ Then as ##n\rightarrow\infty## ##E\left\{\left(\sum\limits_{i=0}^{n-2}\alpha^i...

According to relativity, from a photon's frame of reference time is instantaneous, correct? So in an instant a photon would, to its frame of reference, experience being absorbed immediately after its creation, as well as hundreds of years of travel through space in the same instant. Say...

Potential for infinity? According to Inflation theory, (Big Bang type models) The observable Universe can be measured. We put a specific size on space/time of 13.8 billion years based on expansion from some Singularity. My question. When we speak of 'infinity' are we speaking about infinity...

I've recently accepted (reluctantly) that 1+2+3+4+...=-1/12, but wouldn't that mean the limit as x→∞ of f(x)=x not be ∞ but some maybe negative number because if it were ∞ then 1+2+3+4+... should also be ∞. Also, do numbers get so positive they become negative lol.

[Mentor's Note: Thread moved to Astrophysics since it concerns black hole singularities] Dear PF Forum, I am just wondering about this. See if anyone can help me. Is \frac{2}{0} is twice as much as \frac{1}{0}? Is the above question wrong? Is the number of points in 2 cm lines twice as much...

For this function: $$\lim_{{x}\to{-\infty}}\frac {x} {\sqrt{x^2}} = -1$$ Why is this correct? If x is equal to -1, for example, -1 square is 1. And the square root of 1 is 1. So should the answer be 1?

http://tutorial.math.lamar.edu/Classes/CalcI/LimitsAtInfinityI.aspx According to the author, if ##c## is a real number and ##r## is a positive rational number then: $$\lim_{x →\infty} \frac{c}{x^r} = 0$$ If ##x^r## is defined for ##x < 0## then: $$\lim_{x →- \infty} \frac{c}{x^r} = 0$$ I...

Homework Statement $$\lim_{x\to\infty} \dfrac{(-1)^n\sqrt{n+1}}{n}$$ Homework Equations 3. The Attempt at a Solution [/B] This is what I managed to do but I just wanted to verify that this is the correct way of solving it, I'm mainly concerned about the fact that I took the absolute value...

Hello, I was just wondering how to solve this limit: Limit of (3/4)^(n+1) as n approaches infinity My attempt: (3/4)^(n+1) = (3^ (n+1) ) / (4 ^ (n+1)) Top goes to infinity and bottom goes to infinity to use l'hopital rule. lim = ( ln(3) * 1 * 3^(n+1) ) / ( ln(4) * 1 * 4^(n+1) ) But the...

Hello, I was just wondering how to solve this limit: Limit of (3/4)^(n+1) as n approaches infinity My attempt: (3/4)^(n+1) = (3^ (n+1) ) / (4 ^ (n+1)) Top goes to infinity and bottom goes to infinity to use l'hopital rule. lim = ( ln(3) * 1 * 3^(n+1) ) / ( ln(4) * 1 * 4^(n+1) ) But the...

Hello, I am looking for a good textbook covering cardinal and ordinal arithmetic suitable for self study. I'm a recently graduated undergrad (in mathematics) so I could probably handle up to intro graduate level material. I know most good set theory books might have a few chapters about these...

Homework Statement lim x->∞ (2^x-5^x) / (3^x+5^x) Choices : a. -1 b. -2/3 c. 1 d. 6 e. 25 2. The attempt at a solution Hmmm.. I really have no idea about this.. This is an unusual problem.. Please tell me...

Homework Statement Find the potential at a distance from a very long line of charge with linear charge density (charge per unit length) λ. I actually have this solved with the help of my book, but I need an explanation of the results. V = (λ/2πε)ln(rb/ra) Where the electric potential at rb...

Homework Statement A terrestrial creature with mass m = 100kg to is standing on a planet the same size as our moon 1.) what is the gravitational acceleration on the surface of this planet ? Ag = GM/R^2 = 1.63 m/s 2.) work required to take creature off of planets surface and into space ...

Homework Statement Two point charges are located on the x-axis, q1 = -e at x=0 and q2 = +e at x=a. Find the work that must be done by an external force to bring a third point charge q3 = +e from infinity to x = 2a. Homework Equations W = -ΔU The Attempt at a Solution W = -(Ufinal - Uinitial)...

So transfinite is larger than infinity right? So if there was an infinitely large object, would a transfinite object be larger than the infinitely large object?

Homework Statement It is the last part, part (c) that I'm having trouble with, but I'll post the entire question for clarity. Three charges (q) form the vertices of an equilateral triangle. A fourth charge Q ( Q = -q ) is placed at the center of the triangle. (a) will the charges at the...

I try to figure it out but I can't get the answer that I need and when I look upon the solution from the book I don't understand it at all. The answer is " no limit" and there is no explanation why. The question is Determine the limit of lim (x2+y2)- -> infinity (xye-(x+y)2 in this case I use...

Thanks!

I'm trying to solve the following equation (even if I'm not sure if it's well posed) \partial_{x} \, y(x) + a(x)\, y(x) = \delta(x) with ##\quad \lim_{x \rightarrow \pm \infty}y(x) = 0## It would be a classical first order ODE If it were not for the boundary conditions and the Dirac...

Homework Statement Integral of ∫1/x^2 (or ∫x^-2) between 1 and 0.The Attempt at a Solution I can integrate it no problem to give me -1/x or x^-1, but when I put it between the limits of 1 and 0 I get ∞-1 which is just ∞. Is this right or do I need to use L'Hopital's rule. If so, how? I'm...

Homework Statement determine series convergence of divergence summation (n=1 to infinity) n/n^2 +1 Homework EquationsThe Attempt at a Solution I take the limit comparison limit (1/n)/ (n/(n^2 +1) =1 for 1/n if i use p series the series diverge if i use the method to take limit of sequence...

Homework Statement I want to find the following limit, ## \lim_{x \rightarrow \infty } x( \sqrt{ x^{2} +9} -x) ##, without using the Laurent series Homework Equations None. The Attempt at a Solution I used the Laurent Series to expand the square root, giving ## x((x+\frac{9}{2x})-x)##, then...

What is 1 / infinity? Is it even possible to divide by infinity?

Homework Statement Homework Equations https://www.physicsforums.com/attachments/upload_2015-1-15_18-57-56-png.77691/ Density matrix for a 2 state system is: https://www.physicsforums.com/attachments/upload_2015-1-15_19-1-30-png.77694/ The Attempt at a Solution For a 2 finite state...

I am having trouble grasping the idea of countable and uncountable infinity. How can one infinity be larger than another? Also, are there any other types of infinity that exist?

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