Infinity Definition and 970 Threads

Hi, Here is the question: Prove that if the sequence {s} has no convergent subsequence then {|s|} diverges to infinity. To me, this seems so easy, but I'm having a really hard time putting it down in a rigorous manner. My thoughts are: every convergent sequence has a convergent...

Hello there, please tell me whether e^{iS} = 0 when S = +\infty S is the action of a particle = \int L dt e.g. when the particle goes to infinity and comes back, kinetic energy blows up, then S blows up.

I can sort of deal with it conceptually, and even work with it mathematically - but are there any examples of it as a property of something in the physical universe? (I'm probably missing something obvious..)

I gave roughly an hour's thought to infinity, and came up with these statements and questions; If infinity exists, where would it go? The only infinity that would make sense is the size of the universe, because you couldn't have an infinite amount of any matter without it taking up literally...

Is it correct that \[ \Re ^\infty = \left\{ {\xi \in \Re ^N \left| {\exists n \in N:\forall k > n\,\xi _k = 0} \right.} \right\} \] , N denoting the natural numbers? If not, is there another symbol for the left hand side of the equation? Is this also used with any other set containing a...

With the real number line. 0 is before -1 and 1. Both zero, and infinity are undefined. How does 0 touch infinity. Both are the same value, and start at 0, so for there to be infinity either infinity starts from infinity, or infinity starts from 0. In fact infinity has both values. It...

Is infinity - 1 still infinity. Also if 1\3 = .333... then wouldent 3\3not only = 1 but .999... as well?

Zero x infinity = -1 ?! when two lines meet perpendicularly, we hv the formula v m1 x m2 = -1 if a horinzontal line meet v a vertical line,by using same formula ,we hv m1 x m2 = -1 zero x infinity = -1 so..does it make sense??! :eek:

can i ask how do we define infinity? Is it a number that cannot be represented mathematically(like something divided by 0) or is it a number too large that our human mind can't think of? what do statements like 'The universe is infinite' mean? Is it too large to be represented or there are...

hello all another simple question would it be true to say \int_{a_{L}}^{b} f = lim_{k \rightarrow \infty }L(f,P_k) thanxs

This question popped up in my head. What is sin x when x tends to infinity? Since sine is a preiodic functions which repeats itself, is the answer 1, -1 or 0 or something else altogether?

Is \infty - \infty = 0?

Another question from someone who doesn't know much about physics. If black holes don't let light out, then it has to stop somewhere, right? There has to be a point where the light is not moving at c. It's been proven that gravity can "bend" light waves, so why could it not stop them? Also, if...

For those who were on the last thread concerning this, I have started a new one over since the last one is dead. I have thought on the rules for a while, and now have made a few new rules and changed the otherones. For those who have not read the last thread, what I am trying to do is create...

Hey, I'm new here. I wanted to ask a question about infinity - I've been playing with something in my mind. If you define infinity as a number that is greater than all numbers except itself, and negative infinity as a number that is less than all numbers except itself... Couldn't both...

if f(c) = infinity and c is in [a,b] is it equivalent to saying f is not cont. at c ? because infinity is undefined? Thanks k.cv

First, i would have put this in the theory development, but i can't. And since this is pure mathmatical, but i do not know what type, I have put it here. Second, you need to keep an open mind and do not call me crazy. Third, the person who came up with imaginary numbers was probally...

I had a dream this morning about a Stargate type device, and i remembered that a singularity is infinity. And i got to thinking that a black hole is supposed to be a singularity. So is a black hole a physics representation of infinity? and what does that mean?

This is the theory I made, saying that every moment is infidential. Lets just say 1 second can be dividied into 100milliseconds, and 100milliseconds can be divided into the next smallest unit and so, this process is infidential... Same with digits. Lets take an interger 1. We can divide it...

Hello! Here is the problem I am attempting: Sum to infinity: \frac{x}{1*2} + \frac{x^2}{2*3} + \frac{x^3}{3*4} + ... Here is what I get: S = \frac{x^n}{(n)(n+1)} \lim_{n \to \infty} \frac{x^n}{(n)(n+1)}} Now what? Should I do partial fractions to split the equation?

Hey can someone tell me the value of the integral of X^2 exp (-aX^2) dx from zero to infinity. I have the general solution from a table of integrals but since the upper limit is infinity, I can't really plug these numbers in. Can't find it in a table of integrals anywhere? If anyone has the...

I'm having a tough time trying to do integration by parts with one of my limits being infinity. My Integral looks like: \int_0^\infty x^z e^{-x} dx with z = \frac{-1}{\pi} Now if I let u = e^{-x} and dv = x^z dx, I will have: du = -e^{-x} dx and v = \frac{1}{z + 1} x^{z + 1} and...

Human brain is an observer , and the problem of this idea is observing himself the brain will observe an observer observe an observer observe an observer ... to infinity. the real problem appears to people who work in computional simulation of brain ( infinite loop ) can this cycle have any...

Is infinity even or odd? If it's even (or both), then it would mean there's a finitely largest prime. By coarsely applying limit concepts, and lim(x->inf)x/2 does not yield a remainder.

I am a Civil Engineer so I have some college education in mathematics and Calculus. But I am also an old fart so it has been quite a few years since my head had to use this stuff seriously (my work never required it). I tell you this so that you know I am a partial dummy and not a total dummy...

Since the function f(x)=xsin[(pi)x] oscillates, shouldn't the limit as x -> infinity not exist? i was told that it is positive infinity.

x + x = 2x infinity + infinity = 2 infinity (or) infinity x-x=0 infinity * infinity = square of infinity (or) infinity :-p :devil: :blushing: :approve:

Hi I was having a debate with some guys, and anyhow they were saying 0 divided by infinity is 0, and I said that it was undefined. Whose correct? Also, they said infinity divided by a number, say 2, is not infinity, that that is undefined, and I said the number is still infinity. I don;t know...

I've had a discussion with two friends about infinity. I am of the opinion that infinities come in different sizes and some infinities can be bigger than others. My argument goes somewhat like this: Between the numbers 1 and 2 there are infinite real numbers. Between 1 and infinity there are...

I have a few questions regarding infinity. Its pretty long so I thought of putting it up on my site instead of here, sorry about that. The URL is: http://deydas.com/blog/archives/4-What-is-infinity.html . Can anybody answer my question please?! Thank you.

well, yesterday i was talking to my friend, and during the conversation he used the term "almost infinity". though he intended to refer to something very large, but he got me thinking. what is "almost infinity"? or let me rephrase it in a beter way. is it correct to use the term "almost...

Would you please proove that (lim n -> infinity) (1 + 1/n)^n = e ?

We are all a part of reality. Reality is the state which results from events which we percieve as being real. To be real implies that events can be defined. Events that have the characteristic of being real can be replicated. If we are able to define something, then we can recreate it...

What is the limit of 1/x as x approaches 0. Is it infinity?

My book tolds me that: \lim_{n\rightarrow\infty} \frac{n(n+1)}{2n^2}= \frac{1}{2}. I don't get it. Maybe this with infinity, I dunno... Please, help!

Hi, could you help me a bit with this limit? \lim_{n \rightarrow \infty} \sqrt[n]{n!} Sure it should be more than \lim_{n \rightarrow \infty} \sqrt[n]{n} But, when I write it as \lim_{n \rightarrow \infty} \sqrt[n]{n!} = \lim_{n \rightarrow \infty} \sqrt[n]{n} ...

does it make sense if i define that the shape of a circle is infinity, which i write its equation as: x^2+y^2 = ∞ i know that infinity means very very big until we cannot define how big is it. in this case, is the equation above still valid? can i still say that the shape of this...

Yep, so infinity is a number or not? Does is exist in reality or not? If it exist can we reach it or not? I have someopinions about this issue, which i cannot promotew it to be "unarguable facts". I want to hear others views on this issue... Cheerz,

By definition, an infinite set is a set whose subset is proportional to the set which contains it. The sequence of numbers whether it be expressed as (n+1) or not, is infinite. Then (I am veturing into grounds I know little of here...) I am guessing it is safe to say that the numbers (n+1< or...

I need to know about how mathematics works with infinity. I am currently reading up on this but it could take me a few weeks to finish this book. Ex: You are created, standing in space. You are flipping a coin over and over for infinity. You thus flip the coin an infinite amount of times...

Here is the question that was plaguing me: If there was an infinitely small chance of something happening, but an infinitely large test area, and and infinitely small amount of time for it to happen in, how many times would it happen? Now, i am not sure how infinity can be used in...

I know i posted this to all the general physics area, but I want an answer by pure mathematicians also so please don't throw this out mentors, i love yall though, just trying to do your job... OK, basically I would like a mathematican or just a smart mathematical person ot explain infinity to...

What are the implications of Infinity in Physics, such as QP, GR, SR. Like i know infinity leads us to black holes and other things. Do they do not pose a serious problem to physics. If anyone can give me some insights of dealing with infinity please do because to me the implications...

Hello, There is a question in Calculus By James Stewart (5e) that says: Find the horizontal and vertical asympotes of y = \frac{x^2 + 4}{x^2 - 1}} I put it in limit as \lim_{\substack{x\rightarrow \infty}} \frac{x^2 + 4}{x^2 - 1}} and divided the numeratir abd denominator byx^2...

Hi all ! I came across an article (link: http://www.math.toronto.edu/mathnet/answers/infinity.html#2) The article states that in the context of a number system, infinity does not exist. Now, being the dimwit that I am, I just wanted to ask/confirm this: I THINK the article is saying...

Please give me some hints: Sum of (i^2)/(4^i) where i is from 0 to infinity.

Here's an old one: starting with 0 (or 1) list all the natural numbers using nothing but 4 4s. I'll go first. 0 = (4 - 4)/(4*4) 1 = (4*4)/(4*4) 2 = (4*4)/(4*sqrt(4)) ... etc

I had an elightening conversation with my calculus teach this past friday we were arguing whether X/0= infinity. we ran out of time, but i wasn't satisfied that when i came up this: Assuming that ALL lines are in fact circles (Bye Bye Euclid) and Infinity is an equal distance from all...

Why does a parabola close at infinity? A science teacher made this statement and I didn't quite get it. :confused: Thanks!

Anyone know how to solve the following problems? Thanks! 1.) An object is placed 12 cm to the left of a diverging lens of focal length -6cm. A converging lens of focal length 12 cm is placed a distance of d to the right of the diverging lens. Find the distance d that places the final image...