Infinity Definition and 988 Threads

Is infinity merely a mental concept, or is it entirely meaningful and common? :confused: Infinity does not exist in the context of a number system. Example: what would infinity minus 1 be? It's not infinite since no finite number plus one equals infinity. We see that the rules of arithmetic...

Homework Statement I am required to express in \varepsilon - \delta way what I'm suppose to prove in case lim_\below{(x \rightarrow \infty)} f(x) = \infty Homework Equations None. The Attempt at a Solution So first, intuitively I thought that what this means is that f(x) is bigger...

how this thing works ? integration of e to the power of (-x) from 0 to infinity sorry , not good in using the symbols ..^.^ ~

Homework Statement Consider the power series. sigma (n=1 to infinity) x^n / [n(n+1)] if f(x) = sigma x^n / [n(n+1)], then compute a closed-form expression for f(x). It says: "Hint: let g(x) = x * f(x) and compute g''(x). Integrate this twice to get back to g(x) and hence derive...

Homework Statement Using the fact that the integral from -Infinity to Infinity of e^-x^2 is equal to Sqrt(Pi), find the integral from -Infinity to Infinity of x^2 * e^-x^2 Homework Equations The Attempt at a Solution I really don't know how to find this using the fact that...

Infinity has always been a problem for me, apart from the concept I do not believe it exists. numbers go on to infinity and even negative infinity but they don't really exist so they don't count (hehe). some people say the universe is infinite in size. well apart from infinite in the same way as...

1. Using Fourier Transforms to solve Definite Integrals with Limits 0 to Infinity I'm trying to understand how to use Fourier Transforms to solve Definite Integrals with limits from 0 to Infinity. I understand how to use Fourier Transforms to solve indefinite integrals, but I believe there...

Homework Statement as x approaches negative infinity, what value does this function approach ? limit square root (X^2+X) + X Homework Equations The Attempt at a Solution First, i manipulated the given function to take out absolute (x) from the square root so...

Can anyone help me ? I am completely lost on this one

There are an infinite amount of zero's that can go into 1, therefore we can say 1 / 0 = infinity, but it is useless to say that because infinity isn't a number. That is why we say the answer is undefined. It is also useless to say it "equals" infinity because you cannot get to infinity. We...

"Infinity" machines... where to buy? To start out with - they don't exist so let's not discuses that. What does exist are these small machines that can run with extremely little friction which I would love to have here on my desktop - my only problem is that I CANNOT find them and I have...

Homework Statement The electric field on the dashed line in the figure vanishes at infinity, but also at two different points a finite distance from the charges. Identify the regions in which you can find E = 0 at a finite distance from the charges. Check all that apply: A)to the...

Homework Statement Lim [2 + 3x + sin(x)] / [x + 2cos(x)] (x->infinity) Homework Equations The Attempt at a Solution My roommate asked me to help him solve this homework question, at first glance I noted the derivative to be: [3 + cos(x)] / [1 - 2sin(x)]...

Where is infinity?? Hello , This is an extract from my book about my problem. http://img98.imageshack.us/i/infinityc.jpg/ I was rold before on this forum that this article is wrong so can u define more what's wrong with it and explain it in a better manner?? Thanks in advance

What will happen if we multiply infinity with zero? how to describe this situation?

Homework Statement Find the lim as x approaches infinity of \frac{sin x}{x-\pi} The Attempt at a Solution This was in the section for L'Hopital's Rule, but if you substitute infinity in the functions you don't get an indeterminate form. I don't know what to do next.

Homework Statement f(x) = lim _{n->\infty}(x{n})/(1+x{n}) Homework Equations Suppose that x=1 The Attempt at a Solution Wouldnt f(x) = 1/2? Because 1^n = 1, so the denominator is 2. The solution says that f(x)=1. Why is that?

I read that "if f : R -> R is an increasing function, then limit as x tend to infinity of f(x) is either infinity, minus infinity or a real number". f an increasing function means { x < y } => { f(x) < or = f(y) }. How do I prove this (if it is true)? Can I apply this to a function g : R ->...

I believe in infinity. I believe the universe is infinite in size and possibilities... I was watching a tv program about this and I fundamentally disagreed with their conclusions. I believe infinity must mean that there can be no repetition and infinite does not mean "impossible". The tv...

Homework Statement Find the limit of the given sequence as n -> inf. ((n!)^2)/(2n)! Homework Equations We have been told that the squeeze theorem may be helpful. The Attempt at a Solution Using the squeeze theorem, I get stuck. I tried factoring some things out, and seem...

Hi there, I have a question regarding infinity and statistics. (I hope there aren't too many questions with infinity on these forums) I was wondering if you had some simple procedure, like say rolling a six sided die, and said you did this an infinite amount of times, would it be valid to...

I was working on the following problem from a textbook. The textbook has no answer. I have included my solution - I am not sure whether it is correct Any ideas and or solutions? (guidance) Question: Suppose that f is any function with domain (-infinity, +infinity) a) Does the function g...

Hi, I'm in Engineering Foundation. I'm stuck in one limit question. Find the limit :_ **********________ Lim (3x + V 9x^2 - x ) x-> -infinity by substitution it gives ( inf - inf ) I tried to solve it and get -inf Can anyone help me please ?

Hi all If I have an integral from -∞ to ∞, then is it always true that we can write it as a limit? I.e. if we have a continuous function f, then is it always true that \int_{ - \infty }^\infty {f(x)dx = \mathop {\lim }\limits_{N \to \infty } \int_{ - N}^N {f(x)dx} } ?

Homework Statement I am trying to take the following limit lim as x goes to infinity of ( e^-x )*sin(x) Homework Equations The Attempt at a Solution Can I say that it ges to '0' just because the 1/e^x goes to '0'. Or there is a better way to solve it?

Euclid's proof: 1) Assume there is a finite number of primes. 2) Let Pn be the largest prime. 3) Let X be the P1 * P2 ... * Pn + 1 At this point the statement is that "X cannot be divided by P1 through Pn", but why is that? This is not self-obvious to me. How can I know this? k

ok so i got (5+cos x)/ex and i compared that with 1/ex (they're both going from 0 to infinity). Turns out that the integral of 1/ex from 0 to infinity converges to 1. But i don't know how to prove that our original function converges as well (which is the answer). Anyone care to help?

which grows faster as x--> infinity? ln(x^2+4) or x-5? so using L'H rule i got lim as x-->infinity of [ln(x2+4)]/(x-5) = [2x/(x2+4)]/1 = 2x/(x2+4) then using L'H rule again i got 2/2x, then again i 0/2 = 0. So, does that mean that x-5 grows faster? And why?

i have such a function z^3 \sin \frac{1}{3} i need to calculate its residium at z=infinity if i substitue infinity instead of a"" into the formal formula res(f(x),a)=\lim_{x->a}(f(x)(x-a)) i get infinity am i correct?

How are you, if you are, responding to the critique about the use of infinity in mathematics from the constructivists?

Hello, This is my first time posting something related to physics. I have never studied physics but I have a question that has been with me since my childhood. When I was about 10 years old, I was sitting alone in my backyard. I had a twig in my hand. I broke the twig in half and was left...

Hi, Can anyone please suggest a solution to the problem: lim 10n/(n!) n->(infinite)

New to the forum, I'll say "Hi," first :) Homework Statement Have a physics assignment to hand in. Very simple experiment - increase the voltage in a circuit and measure the current/voltage across the diode in forward and reverse. The problem comes with dealing with infinity in some of the...

This has been bugging for a while and I haven't found an answer. Say you have a function with a vertical asymptote. This asymptote approaches infinity from both sides. The limit approaching from either side would be infinity. So would you say the limit is infinity or does not exist?

Homework Statement prove that lim(n\rightarrow\infty)(r1/n) = 1 for r> 0 The Attempt at a Solution let \epsilon > 0 be given we need to find n0 \in N such that \left|r1/n - 1 \left| < \epsilon but not really sure where to go from here?

I've been reading Griffths QM recently, and in the book he mentioned a couple of times that though these pathological functions exist, they're not physically realizable. But what's wrong with these functions? What prevents them to be physically realizable ? EDIT：Griffths' statement is wave...

Homework Statement I am trying to understand how to get the voltages Va and Vc in the following circuit. It is assumed the circuit has been like this for a very long time. Homework Equations Kirchoff's voltage law The Attempt at a Solution So I know that the capacitor acts...

An example of a function that attains the value "infinity" on R? I'm reading a couple of books on introductory measure theory (Royden, Stein-Shakarchi), and both of them talk about functions that can possibly attain the value \infty. But they don't define exactly what this means, or give...

Homework Statement what is the summation of a function where n=1 to n=infinity? For example, given a function sin[(pi)nt]. Homework Equations The Attempt at a Solution I asking how I get that I do not know what should I do

x^s/s integrated on the semicircular contour with radius R and center c>0, where x>1, s is the complex variable, and R is meant to go to infinity. please help.

I want to say that f(x) = |1/x| is in L-infinity(E) when m(E)<infinity becuase the function has and esssup on any measurable set, E. Even if E = (-1, 1) f(0) is not a problem since it is only one point... But wait... what *is* the esssup for this function on (-1, 1)? I think it might not have...

I'm learning the proof that L_{\infty} is complete. I do not understand one of the steps. Let f_n be a cauchy sequence in L_{\infty}(E) then there exists a subset A in E such that f_n is "uniformly cauchy" on E\A. For m,n choose A so that |f_n-f_m| \leq ||f_m - f_n||_{\infty} for all x in...

Homework Statement Why is it? lim{x-> infinity} f(x)/x = infinity => lim{x-> infinity} f(x) = infinity What is evidence? Thank you very much.

Another viewpoint: "Zero and infinity are both symmetry states. Every change (that is arithmetical operation) leaves them essentially unchanged. 50 times zero is zero. Likewise 50 times infinity is still infinity." So if ((like I assume)) mathematics is essential for modeling physical world -...

Zero and infinity are both symmetry states. Every change (that is arithmetical operation) leaves them essentially unchanged. 50 times zero is zero. Likewise 50 times infinity is still infinity. Zero represents nothing. Infinity represents everything. Hence - judged on their deep mathematical...

Homework Statement Find and classify the singularities in C* of f(z) = \frac{{\pi z - \pi {z^3}}}{{\sin (\pi z)}}, and give information about Res(f, 0) and Res(f, infinity) The Attempt at a Solution I found that the singularities in C are z = n, with n \in Z, n\neq 0, n\neq 1. These...

Ok, I'm trying to solve this physics problem and I've come to the following integral (d is taken to be some constant): 1. \int^{+\infty}_{-\infty}{\frac{1}{(x^2 + d^2)^\frac{3}{2}}}dx Now, integrating this I am supposed to get 2. {\frac{x}{d^2\sqrt{x^2 + d^2}}}, evaluated at \pm\infty (Sorry...

Homework Statement How can I prove that: \lim_{n \rightarrow \infty} n^{\frac{1}{n}}=1 Isn't \infty^{0} indeterminate? Thanks! Homework Equations The Attempt at a Solution

Homework Statement \stackrel{\infty}{0}\int2e^{ky}dy=3/2Homework Equations The Attempt at a Solution I got up to: \stackrel{lim}{x\rightarrow\infty}\[[e^{ky}]^{x}_{0}=3k/4 \stackrel{lim}{x\rightarrow\infty}\[[e^{kx}]=\frac{3k+4}{4} I have no idea how to work that out. Any help will be much...

hi there What is a Poincare' disc and why is the edges of disc represent infinity? thanks