Infinity Definition and 988 Threads

Let f be a differentiable complex valued function on R. If f is square integrable, then it is not the case that f(x) must approach zero at infinity. counterexample: f(x)=x^2 exp(-x^8 sin^2(20x)). If I also require that the derivative of f be square integrable, is that enough to guarantee that...

I'd really appreciate it if someone could help me with the point below! It relates to a real philosophical problem but I'm baffled by the maths. Assuming no other variables apply, if there is infinite space in which a substance *could* exist, let's call it x, and there are not limits to how...

I wasn't sure where to post this, so I'll post it here. Depending on your answers, I may have a few more questions. What's greater: \infty^2 or 2^\infty? Why?

G'day! In the paper "Black holes and entropy" (JD Bekenstein, Phys Rev D 7 2333, 1973), in the section on Geroch's perpetual motion* machine, I'm trying to understand why they can state "its energy as measured from infinity vanishes"? What they mean is that the work extracted by lowering...

Infinity : Beyond the Beyond the Beyond by Lillian Lieber, and Hugh Lieber I am not sure how many of you on this forum are familiar with this book but I have a copy of it and it seems very interesting but very strange. I want to know if its worth a read. I enjoy the talk of SAM and I want...

I've wanted to ask this for a while since it has been confusing me for too long now... if our universe is infinite and nothing can possibly exist outside of it (other than a putative God although no one has an idea how that could be, since Kant proved quite a while ago that existence itself is...

What is the induction at infinity ? I told teacher it to be 0 but she disagreed. Using the formula for calculating induction and substituting big distances into the formula gives me also 0. Is my teacher stupid ?

In what regard might positive infinity be equivalent to negative infinity?

Hello, Please excuse me if I may sound an ignorant compared to all of you, but I was always stupid and never paid attention to any of my physics classes and now I feel so stupid for missing on the most important subject of our lives and our universe. I was discussing a notion with a friend of...

hey in advanced maths , does +infinity and -infinity join at some point ? a bit like if the axis was a cilinder

I had a sort of odd question on my homework, Sin(x)^3 dx, integrated over all reals (from negative infinity to infinity). The problem also gives this morsel of ambiguity: "Hint: think before integrating. this is easy" Now my initial guess because of the antisymmetry of the...

Homework Statement This question asks you to evaluate the limit of the following function lim sqrt(9x^2-3x) -3x x-> infinity I did it using 2 methods: 1) lim sqrt(9x^2-3x) -3x x-> infinity = lim x(sqrt(9-3/x)) -3x...

Does subtracting infinity from infinity leave you with zero? Or could you subtract infinity from infinity and still have infinity?

*edit* nm sorry didn't see this has been covered before.

Hey, Just a tiny question, what is the space called: Reals union infinity?

Alright, so if I want to find the distance of the ∞-norm between two vectors in lR^3, then would I take the max of the vectors first and then subtract, or should I subtract the vectors and then take the max? I think that the vectors are subtracted, and then the norm is taken, but I just want to...

help! limit find the limit as p goes to infinity a_p = sqrt(p^2+p)-p really don't know how to solve this... i know the limit is 1/2, but i need to prove that 1/2 is really the limit!1

I was thinking about how math was taught to me as a kid and how it was taught in symbols, not shapes. I am visual thinker, not a symbolic thinker, I see pictures and reflections of the world in my mind as a "movie" or virtual world I guess you could say. I can create very complex shapes...

Dear Friends, My longtime pending doubt here...! When we focus a mirror on the wall we get bright spot of the light. Ok. Now say, there is cube 6" x 6" x 6" whose inner walls are of mirror surfaces and opaque surfaces are the outer surfaces of the cube. In the center of the cube, in...

Dear Friends, My longtime pending doubt here...! When we focus a mirror on the wall we get bright spot of the light. Ok. Now say, there is cube 6" x 6" x 6" whose inner walls are of mirror surfaces and opaque surfaces are the outer surfaces of the cube. In the center of the cube, in...

Homework Statement limit as x-> -oo of x+(x^2+3)^(1/2) (square root) Homework Equations n/a The Attempt at a Solution i first multiplied the top and bottom (which is just 1) by the conjugate to get: -3 -------------- [x - (x^2+3)^(1/2)] then i divided by x on top and...

Find the limit as x-> -infinity for (x+(x^2+12x)^1/2) so first of all..i multiply and divide by the conjugent then i get... -12x/(x-(x^2+12x)^1/2) i divide by x in both the nummerator and denominator to get ... -12/1-(1+12/x)^1/2 so the 12/x goes to 0 and the squroot of 1 is 1 so it...

i've to show (as part of a bigger assignment) that a^n/p(n), where p is any polynomial and a>1, tends to infinity as n does. I've proved that: a^n/n^k does so, but I'm not sure how to extend this to a complete polynomial such as (c1)n+(c2)n^2+(c3)n^3... thanks for any help NB: edited

I'm calculating the order of a pole of some function and I'm wondering: is it possible that a pole has order infinity?

Taking the Limit As N --> Infinity \mathop {\lim }\limits_{n \to \infty } \frac{{n^n x}}{{(n + 1)^n }} Does this limit exist? Somehow it's supposed to come down to x/e

I don't remember any rules on how to calculate limits approaching infinity. for example, can someone please explain the following limit to me (-1/2) lim (t->infinity) 1/(t^2 + 2) + 1/4 = 0 + 1/4 = 1/4 Thanks!

This issue of infinity (undefined?) keeps coming up in the following problems. For example, the following question: Computer the image of the sector 0 \leq r \leq 1, 0 \leq \theta \leq \pi, under the map ln(z). ------------- So I first graphed this thing in the x,y (z-plane) and obviously...

\frac{1}{\sqrt{2 \pi \sigma^2}} \int_{-\infty}^{\infty} x^2 e^{\frac{-x^2}{2 \sigma^2}} dx I think just slving this would be fine too \int_{-\infty}^{\infty} x^2 e^{-x^2} dx what is the trick to solving this?/ Cnat integrate by parts because that would yeild Erf function which i have no...

I've been staring at this stupid problem for a while, and finally gave up and came here. The question is to evaluate the sum of 3k/k! from 0 to infinity. Basically, I'm looking for a starting spot, since I have none. The closest thing to a strategy I've come up with is plugging it into the...

Is it just me or do all high probabilities dwindle to nothing as time approaches infinity and all small probabilities increase to 1 as time approaches infinity?

Using the definition of a limit, show that \lim_{n \rightarrow \infty} \frac{2^n}{n!}=0 If someone could get me started that would be great. thanks josh

Given infinite time, can one do infinite tasks an infinite amount of times? How many times can one do infinite tasks in infinite time? One would think the ansewr to that question could not be >1, for that would mean that the tasks must have an end and all of them can eventually be...

According to photon's standpoint, since light travels any distance in 0 time, then doesn't it mean that it can travel infinity in 0 time, but for my mind, that doesn't really made sense b/c I thought nothing could reach infinity, but apparently, light can.

Does infinity have direction? Dimensions? As we all know it does, then doesn't it mean that infinity is actually limited? Just like values b/w 1 and 2 x values are infinity but have a total sum.

I have this problem, with three functions: f(x)=5x(x-2)(1/(x-2)) g(x)=5x(x-2)(1/(x-2)^2) h(x) 5x(x-2)^2(1/(x-2) The problem says that as x approaches 2, the functions take the form 0 times infinity, and asks you to "show" this. I tried plugging in 2 for x, but I got 0 times 1/0 (either...

I understand that the limit of sec^2(x) as x approaches pi/2 is infinity (increasing without bound), and I understand the meaning of this in terms of the epsilon-delta definition of an infinite limit. I also understand why the limit of sec(x) as x approaches pi/2 doesn't exist. What I'm a...

So we talked about this in class but there's nothing in the textbook. Basically I want to make sure I get this: Reals are uncountable, while natural numbers, integers, and rationals are countable. So really the cardinality: |Z| = |R| = |Q| < |R| then there are only 2 sizes of infinity...

Where might I learn more about the behaviour of algorithms given an infinite amount of time, if such a question makes sense?

Lets say you have a function that is constant except at interval [-2,2] where it drains down to infinity. The whole function is reflected symetrically at x=0. Is the limit of this function, as x approaches 0, negative infinity?

Please follow the following arguments. 5/3=1.66 5/2=2.5 5/1=5 5/0.5=10 ... ... 5/0=infinity and then 5/(-1)= -5 What you see? As the denominator is...

Hi there everyone! Have a quick question for you. The question is: The sum to infinity of a geometric series is 9/2 The second term of the series is -2 Find the value of r, the common ratio of the series. I understand that we have to use the sum to infinity of a geometric series...

I am a high school student, and I am doing extension mathematics, and me and the rest of the class always get into big arguments about number planes. I say that on a basic 2d numberline with a parabola or hyperbola, when x = infinity, y = 1/infinity, which I think is zero, but they think...

What is the derivative of cos\frac{1}{x}? Also, would cos\frac{1}{x} equal 0 or infinity?

I'm trying to learn some elementary complex variables, and I was reading this book on it when I came upon this Consider the function f(x)=\left\{\begin{array}{cc}0\Leftrightarrow Im(x)\neq 0\\e^x\Leftrightarrow Im(x)=0\end{array}\right. Wouldn't it make more sense if we had a concept of...

Infinity has been something that has been talked about a lot. A lot of Questions are being posted on this forum and elsewhere about the paradoxes involving infinity. I want to know if anybody knows some alternate treatment of infinity.

0 * infinity What is up? I read that it this expression is called an "indeterminate form." Why isn't zero multiplied by infinity equal to zero? Even if infinity is really big, if there are zero amounts of infinity, that would make zero. How about 1infinity? 1? Guess not. infinity / infinity...

Ampere's law states that, the closed integral of B over the loop enclosed it equals uI, where u = permeability of the material and I = current "passing" through the loop. I feel confused, because, should the current be extended to infinity? I mean, when we have an infinite wire of current...

Hi, could someone explain what it means for a function to be holomorphic on \mathbb{C}\cup \{\infty\}? More precisely, what does it mean for it to be holomorphic at \infty. Thx.

Why does my calculator tell me -1/(0^2) = -infinity. How is this different from 1/0?

I have tried to understand Cantors ideas of infinity, but they still don't make sense to me. If you use the mathematical concept of sets to investigate something like this - a 'value' that can't be written because it has no end - then surely the size of the set is what you are evaluating ? How...