Infinity Definition and 970 Threads

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...

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...

Hello everyone I'm confused...i was just doing RL and RC circuits without a driven source, they made sense after doing them a few 100 times. Now I'm at Driven RL circuits. My professor said: iL(infinity) = 2mA iL(0+) = 0. From my understanding, i thought at infinity, the switch has been...

We defined the definition of a closed set to be: "F\subset\mathbb{R} is closed if the limit of any convergent sequence in F is an element of F." Now we have also defined that a sequence may "converge to infinity". Is infinity considered a point in N?

I was wondering if it would be possible to find the average value of a function with the only condition that x is element of R. For example, could we say that f(x)=4 has an average value of 4 since no matter what values we give for a or b in the integral from a to b of f(x)/(b-a) (b is not equal...

Working on pervect's "messy unsolved" problem has led me to an interesting result. Let \left( x , t \right) be a global inertial coordinate system for Minkowski spacetime. Consider the worldline given by t \left( \tau \right) = \frac{\tau^3}{3} - \frac{1}{4 \tau} x \left( \tau \right) =...

may i know (cos n pi ) with n to infinity is converges or diverges?? may i know (cos n pi ) with n to infinity is converges or diverges??

may i know is it lim x to 0 (1/sinx - 1/x ) is equals to infinity??

Hello I was watching lectures on Quantum Computing another day and I came up with a problem. I talked to my school teachers about it but everyone seemed to dodge my question except for one, my math team teacher who told me that without assuming anything it cannot be solved. Or we can take the...

Hi, What is the limit of ln(\frac{1+1/ \sqrt(1+1/R)}{1-1/ \sqrt(1+1/R}) as R reaches infinity. (latex did not show it very well. But the numerator is same as denominator except there is a + sign instead of a - sign. As R reaches infinity the argument of the ln reaches...

I have an interest in physics, I have not studied it at any high levels (as u will soon find out :smile: ), i just like to read and think about it, but I have a question, please don't blind me with maths! If a singularity at a black hole has infinity density, I'm guessing this means it has...

let,s suppose that we have the limit with n tending to infinity: \frac{f(n)}{g(n)}=1 then i suppose that for n tending to infinity we should get: f(n)\rightarrow{g(n)} or what is the same the function f(n) diverges as g(n) as an special case: \pi(n)\rightarrow{n/ln(n)} where Pi is the...

of doing this \lim_{x\rightarrow +\infty }\cos^{x}\frac{\pi}{x} than using \cos x \simeq 1- \frac{x^{2}}{2} \mbox {when "x" goes to zero} ? Daniel.

Hello Everyone, I'm doing some practice problems and I am stuck on the following limits. 1) Limit as x approaches infinity of (sin^2(x))/x^2 Now for this one I thought that the answer would just be 1 seeing as the limit of sinx/x is 1, however the answer is apparently 0 and I can't see the...

I heard about this debate and wanted to share with you what information I have gathered so far...maybe you'all can find more out about it. I'll try and keep you posted, and thought maybe this would be a great subject to keep posted on!? For now though, I just wanted to let you know about it...

Hey, I recenty took an exam and the professor asked us to turn in a corrected version of the exam based on the comments he made to us (I guess people didn't do as well as he expected). On one of the problems it asks: How much work does it take for you to move a charge Q from infinity to the...

are the input impedances for both inverting and non-inverting amplifiers infinity?