Infinity Definition and 970 Threads

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...

Summary:: Would nothing & infinity be considered polar opposites? Neither can be observed and are hypothetical at 2 extremes. "Nothing" is one of the questions much like "infinity", I find myself questioning these supposedly two "real" expressions. Logically they both make sense.

From integration by parts, and using y(10) = 0, I get the equation ##2e^{3t-30} = \frac{|y-2|}{|y+1|}.## Let ##f(t) = 2e^{3t-30}##. Since it's for t>10, f(10) = 2, and we have ##2=\frac{|y-2|}{|y+1|}##. Depending on the sign I choose to use, I get either that y=-4 or y =0. Since ##t: 10...

I don't know what do do from here other than i can make the 3/e^x a 0 due to the fact its divided by such a large number. What do i do with the e^-3x? Thanks for the help

I tried by ##S=1+(1/1!)(1/4)+(1.3/2!)(1/4)^2+...## ##S/4=1/4+(1/1!)(1/4)^2+(1.3/2!)(1/4)^3..## And then subtracting the two equations but i arrived at nothing What shall i do further?

My question is Why is the sum to infinity used as opposed to Sum to n? and How can I deduce that the sum to infinity must be used from the question?Total Distance = h + 2*Sum of Geometric progression (to infinity) h + 2*h/3 / 1-1/3 h + 2h/3 *3/2 = h + h = 2h At first I did sum to infinity...

Summary: Trouble with infinity and complex numbers, just curious. I'm not too familiar with set theory ... but <-∞, ∞> contains just real numbers? Does something similar to <-∞, ∞> exist in Complex numbers? My question, is it "wrong"?

There are meaningful ways to assign values to things like 1 - 1 + 1 + ... or 1 - 2 + 3 - 4 + ... In a similar spirit, is it possible to assign a value to the integral of a function like this: ##f(x)=x*sin(x)## or this one: ##g(x)=Re(x^{1+5i})## (Integrals from some value, say zero, up...

lim 2x + 3 = ∞. x→∞ Pretty intuitive when considering the graph of the function. But how would I show this using the epsilon-delta definition?Thanks!

1) Can I say that humans in history named, recognized countable set of numbers (1,2..Pi,sqrt(2) ... etc) the count of this set is named aleph-0 ? 2) Do mathematicians investigate the "other" continuum set of numbers which is infinity bigger ? Do we suspect, knows anything about that set like...

I wrote cos(pi(n^2+n)^(1/2)) as cot(pi(n^2+n)^(1/2))/cosec(pi(n^2+n)^(1/2)) and as we know cot(npi)=infinity and cosec(npi)=infinity , so i applied L'Hospital.After i differentiated i again got the same form but this time cosec/cot which is again infinity/infinity.But if i differentiate it i...

16.1 Show that $e^{2x}$, sin(2x) are linearly independent on $(-\infty,+\infty)$ https://www.physicsforums.com/attachments/9064 that was the example but... \begin{align*} w(e^x,\cos x)&=\left|\begin{array}{rr}e^x&\cos{x} \\ e^x&-\cos{x} \\ \end{array}\right|\\ &=??\\ &=?? \end{align*}

I was always wondering if you can lift anything (no matter how heavy it is) if you just use a really long pipe. Or does torque increases in a way like ##e^x## , ##a^x## and after some point it barely increases? Also if this can be explained mathematically, I would love to see it.

If actual infinity represents a completed set of infinite data points, wouldn't that be a contradiction of terms?

In Mathematical Methods in the Physical Sciences by Mary Boas, the author defines the Laplace transform as... $${L(f)=}\int_0^\infty{f(t)}e^{-pt}{dt=F(p)}$$ The author then states that "...since we integrate from 0 to ##\infty##, ##{L(f)}## is the same no matter how ##{f(t)}## is defined for...

Einstein mentioned that our universe if a finite spherical universe inside an infinite space. If this said infinite space is, as said, infinite, then infinity is possible? How do you explain the science of infinity?

Good morning. Not sure if I am doing this right, but I just wanted to ask a question.

First off, this is just an assumption. My knowledge of the field is extremely limited and I beg you to come and correct my mistakes, so I can learn. So, I guess we all know how that space-time fabric is bended by gravity. When a star dies, all of the atoms are brought extremely close...

I've been taught that $$1^\infty$$ is undetermined case. Why is it so? Isn't $$1*1*1...=1$$ whatever times you would multiply it? So if you take a limit, say $$\lim_{n\to\infty} 1^n$$, doesn't it converge to 1? So why would the limit not exist?

I have come across a paper where it is stated that if the infinity assumption in the FT is removed, the uncertainty doesn't hold. Is this a sensible argument? Thank you.

I need to collimate an extended source (for example a cell phone) to infinity or as far as possible. I show an illustration below The collimator lens is about 2cm from the eye and the extended source is about 60cm from the eye. My understanding is that a collimator lens with a focal length...

Hi, I wanted to clarify a point about the magnetic fields of a solenoid and wire. Do the fields extend to infinity? In my opinion, they don't but they can assuming the current also goes to infinity. They don't extend to infinity for a limited amount of current because they need to follow a...

When have a function and I know by investigation of that it getting "bigger and bigger" or getting "smaller and smaller", how could I know that in infinity it continue by that way always?

$$\lim_{{T}\to{\infty}}N \bar{h}\omega \left( \frac{1}{2} + \frac{1}{e^{\frac{ \bar{h}\omega}{k_BT}}-1} \right)$$ In term $$\lim_{{T}\to{\infty}}N \bar{h}\omega \left( \frac{1}{e^{\frac{ \bar{h}\omega}{k_BT}}-1} \right)=N \bar{h}\omega \lim_{{T}\to{\infty}}\left( \frac{1}{e^{\frac{...

Homework Statement Hi everyone, I'm currently making my way through Spivak's calculus and got stuck in question 41 of chapter 5. It's important to note that at this point, the book has only reached the subject of limits (haven't reached continuous functions, derivatives, integrals, series...

All those joke bars to walk into. Ever consider the people already inside? Let's hang out at Infinity Bar. Yes, located between the Adiabatic AC Repair shop and Moe's Many Manifolds ("Put an edge to your Universe!"). Slide into Infinity Bar and join the fun: ----------------> linguist: "...

Homework Statement Evaluate the limit as K goes to infinity of s_1,2 (K) Homework EquationsThe Attempt at a Solution Apparently my value for plus the square root is incorrect, apparently the correct answer is 1. Apparently my value for minus the square root is correct, it's negative...

Hi. Is infinity multiplied by zero defined and is it zero ? And is infinity multiplied by any positive number , infinity ?

How do we integrate this function? It is possible if the range is from 0 to infinity, but from xg to infinity? This equation comes from page 512 of the 1961 paper by William Shockley and Hans J. Queisser.

Homework Statement prove (5-n^2)/(3n+1) diverges to negative infinity as n approaches infinity Homework Equations For all M>0 there exists an N in the natural numbers such that for all n >= N, x_n <= -M The Attempt at a Solution Let M be an element of the field of the real numbers. Let N in...

Supposedly, infininity has been purged from mathematics. Both the infinitely small and the infinitely large have been replaced by the idea of a "limit." For example, a series x0+x1+x3+... is not considered to be a literal infinite sum with infinite terms but only the limiting value of an...

what the differences between actual infinity to potentially infinity?

I had a conversation with someone once upon a time (it was quite a while back actually), and we came to the question of whether or not Turing machines could ever understand infinity. We agreed that we as humans are intimate with the extant and divisible infinities mainly through our...

Homework Statement Let ##\sum_{n=1}^{\infty}a_n## be a series with nonnegative terms which diverges, and let ##(s_n)## be the sequence of partial sums. Prove that ##\lim_{n\to\infty} s_n = \infty##. Homework EquationsThe Attempt at a Solution This isn't a difficult problem, but I want to make...

Hello everyone, I am stuck on this homework problem. I got up to (ln (b / (b+1) - ln 1 / (1+1) ) but I'm not sure how to go to the red boxed step where they have (1 - 1 / (b+1) ) if anyone can figure it out Id really appreciate it. thank you very much.

We have a Universe that can be seen by Hubble maximum and we can imagine millions time more than that but if there is no boundary, there may be another millions of universe. Suppose we gather this all millions of universe and say this is a giant universe of universes and thus matter do not stop...

Homework Statement Solve the ##\lim_{n \rightarrow +\infty} \sqrt [n] \frac {n²+1} {n⁷-2} ## 3. The attempt of a solution: First I thought about using L'Hopital's rule, but the nth root makes it useless. Then I thought about to eliminate the root multiplying it by something that is one, but...

While using L' Hospital's rule in evaluating limits, one comes across limits of the following type: $$\lim_{x \to 0} x \ln x$$ Such limits are generally evaluated by taking ##x## to the denominator and make it ##x^{-1}##. In such a case, an indeterminate form ##\frac{\infty}{\infty}## comes...

In Hilbert infinity hotel, all the rooms were occupied. Then how did the occupant were able to shift to their adjoining room?? Here I understand, by full mean, ALL the infinite room has a corresponding occupant. I also understand some infinity number are greater because it can be proove when...

Art Hobson said that quanta propagate in space to infinity. (sorry can not give a link)

I know this has been discussed ad infinitum (pun intended) however I have recently been informed by Max Tegmark's book Our Mathematical Universe, that apparently the multiverse concept is becoming mainstream. In fact he mentioned at a recent quantum conference that a show of hands revealed no...

First off please keep this thread SPOILER FREE, at least for the time being seeing the film has just released, spoilers go in spoiler tags. Carrying on. Just saw it. Absolutely loved it. Highly recommend dropping whatever you are doing now and to immediately go see it in IMAX asap. Also, and...

Homework Statement Homework Equations F = k(q1q1/r^2) K = (mv^2)/2 The Attempt at a Solution I got number 18 easy enough, number 19 seems simple but I'm not getting the right answer. I'm calculating Force exerted by each charge on the new charge using F = k(q1q1/r^2) for the three charges...

Pretty self explanatory really. If a photon has a mass (1.67 * 10^-27 kg), and it travels at the speed of light, why does it's mass not increase to infinity?

I have two isolated plates A and B, kept parallel to each other. Now I give charge +Q to the plate A, it will redistribute itself as +Q/2 on the outer plate A and + Q/2 on the inner plate A. Right? Now this will induce charge -Q/2 on the inner plate B and +Q/2 charge on the outer plate B...

Dear Members, I tried to prove this indeterminate form of infinity / infinity as 1. I could come up a reasonable approach with Gamma and Product functions. I posted my proof as video in Youtube. Here is the URL for the video. I would like to receive feedback and challenges on where my...

Is infinity truly infinite if it has something else in it? Put differently, say there's an infinite volume of water that has some rocks in it, is the volume of water truly infinite? Though there's a place where there's no water?

I'm writing some notes on set theory, Aleph Null, etc., and was wondering if there's a Notation or Symbol that abbreviates this (inaccessible/strong/uncountable etc. cardinals). I'm not sure if I've seen notation before but it seems like symbols resembling Theta and phi have been used.

Homework Statement : Find [/B] limx->∞(xα(sin2x!)/(x+1) α∈(0,1) Options are: a)0 b)1 c)inifinity d)does not existHomework Equations : -[/B]The Attempt at a Solution : limx->∞(xαsin2x!)/(x+1)[/B] Dividing the numerator and denominator by xα, we have:limx->∞sin2x!)/(x1-α+x-α) clearly x−αis tending...

Homework Statement Finding the value of the limit: $$\lim_{t\to +\infty} t+\frac{1-\sqrt{1+a^2t^2}}{a}$$ ##a## is just a costant The Attempt at a Solution At first sight I had thought that the limit was ##\infty## but then I realized that there is an indeterminate form ##\infty - \infty##. I...