Infinity Definition and 988 Threads

I am self-studying Boas and this is a problem from Ch. 1.2. I have developed what I believe is an answer, but I'm not sure it's adequate. The general approach is to show that for all values of n > 1, n^n grows faster than n!, and therefore that (n^n)/n! approaches infinity as n approaches...

Considering the growing consensus that the universe is infinite, being everything everywhere, how is it possible for infinity to expand? In all my research I find confusion among cosmologists about the important distinction between the part of the universe we cqn see and the whole infinite universe.

I want to ask why the answer is not zero. If n approaches infinity, it means each term will approach zero so why the answer is not zero? Thanks

If there are an infinite number of whole numbers, and an infinite number of decimals between any two whole numbers, and an infinite number of decimals in between any two decimals, does that mean that there are infinite infinities? And an infinite number of those infinities? And an infinite...

If the universe is infinite and if it started out of a finite singularity, how did it make this step ? From finite to infinite ? This looks a hard thing to do ?

Is there a Big Crunch in an infinity, Newtonian, symmetrical universe, e.g. an infinity grid, with stars in its nodes, due to the gravitational attraction? One can argue that every net force is 0, so there isn't one. But I think there is an another argument, that leads to a Big Crunch, that...

We have come to accept that Infinity times two is infinity. In the sense of 'size' we use to think about everyday numbers, the rules of arithmetic with infinities seem like nonsense. For example, consider the computable number $$0.100100100100100....$$ In the decimal expansion, there are...

On the one hand, Cantor showed that not all real numbers can be enumerated, while on the other hand he showed that rational numbers can. Cantor demonstrated this with a grid. In the picture below, a natural number (yellow) is assigned to each rational number in order, but since the natural...

I’m male, my nature has always been to question everything explore possibilities, over my latter years convinced that for the short period of time we existed we gained very little, if we did stay around a little longer we may learn a little more, what we cannot prove to be correct is where we...

I understand the mathematics that 1 divided by infinity is virtually zero and so equals zero. I look on the internet and that is the answer that I get. Is this a simplification for early mathematics learning and, if I continue, will I find a more complex answer? The reason that I ask is that I...

Hello, I'm new here and I'm looking to talk about p-adic numbers. It's not a specific school problem . I'm trying to expand p-adic numbers into something that I call "Infinity Numbers". Is it possible here to discuss topics like that? Kind regards

Section 5 (pg. 29) of the Michel Janssen's paper EINSTEIN’S QUEST FOR GENERAL RELATIVITY, 1907–1920(*) says: 1. From the above I understand that the application of general relativity to an infinite universe was considered problematic. 2. On the other hand, I understand that it is currently...

In another question I posted on here, I asked about a hypothetical roulette wheel with an infinite amount of spaces. Each number has a one-in-infinity chance of being selected, yet each time the wheel is spun, one number wins those odds. My initial question was how this was possible, and I had...

Imagine a roulette wheel with an infinite amount of numbers. Every number on the wheel has a one-in-infinity chance of being selected. Every time the wheel is spun, one number wins those one-in-infinity odds. How is this possible? Isn't one-in-infinity basically zero? It's infinitely far from...

I have to write taylor expansion of f(x)=arctan(x) around at x=+∞. My first idea was to set z=1/x and in this case z→0 Thus I can expand f(z)= arctan(1/z) near 0 so I obtain 1/z-1/3(z^3) Then I try to reverse the substitution but this is incorrect .I discovered after that...

I have probably a basic question from Space, Time and Matter area. My 11 years old daughter asked me once why we exist physically in a stable form if everything is infinite. We had a conversation about it but then it got me thinking about this and it seems I can't find the answer. There is...

Why not use these number systems, in place of the real number system, when these allow us to divide by infinity exactly? According to these, division by infinity equals exactly zero! No need for calculus limits, which only can say it approaches zero when tending towards infinity...

Find the limit $$\lim_{x\to \infty} x\left[\frac{1}{e} - \left(\frac{x}{x+1}\right)^x\right]$$

I'm talking about the x^(-4/3) how does it equal 0 when x approch infinite?? so I can use L'Hopital's Rule

Dear everyone, I am having trouble with this problem. I have convinced myself that the ##a^t-a\leq 0## is true. Now, I am trying to applying this inequality for the finite series and I don't know where to start. After that, proving that the p-norm is less or equal to the q-norm. Thanks...

Hi, mathematically in the F = GMm/r^2 equation r can be very close to infinity (or the size of the universe), but gravitational force always will be some number. But how is that in the real world? Let's say we have a perfectly empty universe but only with two sun-like stars. If they are away...

TL;DR Summary: Is infinity the answer of all question that we can not answer? If I ask a scientist how big our universe is? He will say infinite. If i ask how small anything can be? Will scientist say infinitely small ? As our visual limitation or device limitation we might not be able to see...

I imagine ##f(x)## has horizontal asymptote at ##x=k##. Since the graph of ##f(x)## will be close to horizontal as ##x \rightarrow \infty##, the slope of the graph will be close to zero so ##\lim_{x \rightarrow \infty} f'(x) = \lim_{x \rightarrow \infty} f^{"} (x) = 0## But how to put it in...

A Trip to Infinity https://www.netflix.com/title/81273453 (Sept 26, 2022 on Netflix) trailer: https://www.imdb.com/title/tt21929356/ lists the cast as: Anthony Aguirre Stephon Alexander Eugenia Cheng Moon Duchin Kenny Easwaran Delilah Gates Rebecca Goldstein Brian Greene Janna Levin...

If all possibilities happen somewhere, can there be a universe where there are more explanations and content (articles, blogs, videos etc.) in that universe explaining about the multiverse, omniverse, dimensions etc.? And speaking of multiverse, why there is not enough information about...

I am looking for the details of when a famous mathematician in history (Gauss? Euler?) tried to find an infinite sum (integrate?) in two different ways, and got two different answers, one of them one-half and the other one infinity (where maybe a negative was attached to one of them). When he...

I need a help in the following problem. I feel that the question is stupid. Take a function ##f\in C(\mathbb{R}^3)\cap L^1(\mathbb{R}^3)## and a number ##\alpha\in(0,3)##. Prove that $$\lim_{|x|\to\infty}\int_{\mathbb{R}^3}\frac{f(y)dy}{|x-y|^\alpha}=0.$$ I can prove this fact by the Uniform...

I hope I can make this question clear enough. When we have a function such as f(x) = 1/x and calculate the side limits at x = 0, the right side goes to positive infinity. The left side goes to negative infinity. In calculus we are pluggin in values closer and closer to zero and seeing what the...

As we know those relations are true: if a/b = c, then a = b*c and b = a/c Therefore if 1/ ∞ = 0, ∞ * 0 should be equal to 1 and 1/0 = ∞

As n tends to inf, the fraction goes to zero so would the lim just be X?

Apparently there are problems with him snapping his fingers while wearing a glove https://www.sciencenews.org/article/finger-snap-physics-new-high-speed-video-thanos

I'm studying nuclear physics in a text, but at one point that is said: "Both the Coulomb potential that binds the atom and the resulting electronic charge distribution extends to infinity" , I don't understand what is that "resulting electronic charge distribution extends to infinity" what they...

I am familiar with Cantor's work on the concept of infinity and his use of the set theory to explain various types of infinities. Having said that my intuition never seems truly grasp/accept it. Is there a way to train my mind to see this seemingly contradictory situation as a fact? This is...

So I was trying to get a bit better handle on the definition of the difference between an event horizon and a Killing horizon. Locally they are indistinguishable, and the key difference (to my understanding) is that the event horizon is the last Killing horizon that escapes to future null...

Calculate $2\sqrt{2\sqrt[5]{2\sqrt[8]{2\sqrt[11]{2 \cdots}}}}$. I know only that $...=2^{1+{1\over2}+{1\over10}+{1\over80}+{1\over880}+\ldots}$

I'd like to make a large scale infinity dodecahedron, or icosahedron, or something similar. I'm just curious if anyone around here has an idea for a different/more complicated geometry that would work well?

Hi, I have a quick question about whether or not the infinite series of 1/n converges or diverges. My textbook tells me that it diverges, but my textbook also says that by the nth term test if we take the limit from n to infinity of a series, if the limit value is not equal to zero the series...

How would I determine the following limit without substitution of large values of x to see what value is approached by the complex function? ## \lim_{x \rightarrow +\infty} {\dfrac {2^{x}} {x^{2} } } ## where ## x\in \mathbb{R}##

∫tan^2 x ( -infinity to +infinity)

determine the behavior of y as t →∞. If this behavior depends on the initial value of y at t = 0,describe the dependency \begin{array}{lll} \textit{rewrite} &y'-2y=-3\\ \\ u(t) &=\exp\int -2 \, dx=e^{-2t}\\ \\ \textit{product} &(e^{-2t}y)'=-3e^{-2t}\\ \\ \textit{integrate}...

How to lose surface integral in derivation of ampere law from biot-savart law if current goes to infinity? How does current that goes to infinity obey Helmholtz theorem for vector fields?

I am reading several books on infinity as first developed by Georg Cantor. Some physicists claim that the multiverse might be infinite. But they don’t seem to mention two of the kinds of infinity which might (exist?). It makes an infinite difference to make a bad pun. The integers define...

Hello there, I had another similar post, where asking for proof for Hilbert’s Hotel. After rethinking this topic, I want to show you a new example. It tries to show why that the sentence, every guest moves into the next room, hides the fact, that we don’t understand what will happen in this...

Express the condition of 𝜎 where the celestial body B collides against the celestial body ASo this is the original figure of the problem. This is my attempt at a solution Since I need to find σ, I have assumed sigma to be an multiple of the radius ## R ##. So, let ## \sigma = \lambda R ##...

Hilberts Hotel has infinity numbers of rooms and in every room is exactly one guest. On Wikipedia Hilberts Hotel gets described as well: Suppose a new guest arrives and wishes to be accommodated in the hotel. We can (simultaneously) move the guest currently in room 1 to room 2, the guest...

I was thinking, what would be the consequence if we wouldn't adopt the ro in the infinite, and i conclude that it would just irritate the accounts, with one constant more, am i right? Once what matter is the diference between the U, and no the U infact.

I tried to write it as n^2/2^n (1+1/2n)^n But I am stuck there and don't know what to try next.Thanks for any help in advance!

If there is no ##(-1)^2## factor, I can find the limit. But, now I have no idea how to find limit for the ##(-1)^\infty##. I thought ##(-1)^\infty## is an indeterminate form. So, how to modify this? Thanks!

First I assume that $$(1+n^2)^\frac{1}{\ln n}=\exp {\ln (1+n^2)^\frac{1}{\ln n}} $$But, $${\ln (1+n^2)^\frac{1}{\ln n}}={\frac{\ln (1+n^2)}{\ln n}}$$ By L'Hopital Rule, I got $$\lim_{n\to\infty} {\frac{\ln (1+n^2)}{\ln n}}=\frac{\lim_{n\to\infty} (\frac{2n}{1+n^2})}{\lim_{n\to\infty} 1/n}$$...

Hello,This is actually a piece of a little bigger problem (convergence of a series) - you can see the ratio test ak+1 / ak That's why the (n) and (n+1) terms I have lim n->∞ of (n√n) / (n+1)√(n+1) ∞/∞ I have tried L'Hopitals rule (requiring multiple times) and I am not seeing an end...