What is Infinite: Definition and 1000 Discussions

Infinite (stylised as infinite) is the twentieth studio album by English rock band Deep Purple, released on 7 April 2017.

View More On Wikipedia.org
  1. P

    I Question on an infinite summation series

    Is the infinite series ##\sum_{n=1,3,5,...}^\infty \frac {1} {n^6}## somewhat related to the Riemann zeta function?The attached image suggest the value to be inverse of the co-efficient of the series.Is there any integral representation of the series from where the series can be evaluated?
  2. F

    Find the distance a particle travels

    My answer is d = (e+3)/e x(t) = ∫01 3t2 dt (0 ≤ t ≤1) = t3 |01 = 13 - 03 = 1m x(t) = ∫1∞ 3e-t dt (t > 1) = -3e-t |1∞ = lim(t->∞)[-3e-t] - [-3e-1] = 0 + 3e-1 = 3/e m Therefore total distance = 1m + 3/e m = (e+3)/e m However, the textbook answer gives...
  3. keyzan

    Probability of finding a particle in the right half of a rectangular potential well

    Hi guys it's me again. I need help with this exercise which reads: a particle of mass m, placed in an infinite rectangular one-dimensional potential well that confines it in the segment between ##x = -\frac{a}{2} and x=\frac{a}{2}##, is at instant ##t=0## in the state: ##|\psi \rangle =...
  4. Weightlifting

    Finding the direction of infinite limits

    Since ##\left|3x+2\right|=0\rightarrow\ x=-\frac{2}{3}##, we know the vertical asymptote is at ##x=-\frac{2}{3}##. Looking at the limit at that point, and also looking at the left- and right-sided limit, I cannot simplify it any further...
  5. A

    I Why Is a Flat Universe Infinite?

    I cannot find an answer online. Help please.
  6. A

    A Extending reals with logarithm of zero

    What do you guys have to say about this Mathoverflow post? Do you have any interesting ideas about this? https://mathoverflow.net/questions/432396/extending-reals-with-logarithm-of-zero-properties-and-reference-request
  7. Feynstein100

    B Proof that pattern recognition is unending?

    So I've thought of an admittedly crude proof that the process of pattern recognition i.e. finding patterns, be they linguistic, mathematical, artistic, whatever, is a process that can never end. It goes like this: Imagine we find all patterns, and I mean ALL of them, and we list them on a...
  8. S

    I Optics: infinite light source illusion question - can you help?

    Hi. I’m trying to solve an optics problem and really struggling. The problem is best described as follows… Imagine you have a section of a wall that you want to look like a window on a spaceship. So you want to look at this “window” and see through it some “stars” (i.e. pinpoints of light) that...
  9. milkism

    Method of Images, combination of an infinite plane and a hemisphere

    Problem: I have done part a) in spherical polar coordinates. For part b) I thought it would be just: $$\sigma = -\epsilon_0 \frac{\partial V}{\partial r}$$ But I got confused by "You may want to use different coordinate systems .." So I assume partial derivative w.r.t to r is the spherical...
  10. T

    I Infinite product representation of Bessel's function of the 2nd kind

    An infinite product representation of Bessel's function of the first kind is: $$J_\alpha(z) =\frac{(z/2)^\alpha}{\Gamma(\alpha+1)}\prod_{n=1}^\infty(1-\frac{z^2}{j_{n,\alpha}^2})$$ Here, the ##j_{n,\alpha}## are the various roots of the Bessel functions of the first kind. I found this...
  11. N

    A Double integral with infinite limits

    I have the following problem and am almost sure of the answer but can't quite prove it: ##f(y)## is nonnegative, and I know that ##\int_0^{\infty } f(y) \, dy## is finite. I now need to calculate (or simplify) the double integral: $$\int_0^{\infty } \left(\int_x^{\infty } f(y) \, dy\right) \...
  12. Feynstein100

    B Arithmetic mean of an infinite number of points?

    So I was thinking about arithmetic, geometric and harmonic means when I had a thought. Let's say we have a curve y = x^2. We want to find the AM of the points on the curve between x=1 and x=2 i.e. y = 1 and y = 4. To make thing easier, we'll start with just the endpoints and keep adding...
  13. D

    I Momentum eigenfunctions in an infinite well

    Hi For an infinite well , solving the Schrodinger equation gives wavefunctions of the form sin(nπx/L). These are not eigenfunctions of the momentum operator which means there are no eigenvalues of the momentum operator. Does this mean momentum cannot be measured ? Inside the infinite well the...
  14. Q

    A particle in an infinite square well

    What I am lost about is b, rather the rest of B. I am not sure what it means by probability density and a stationary state.
  15. Euge

    POTW Steenrod Squares over an Infinite Projective Space

    Let ##u## be a generator of ##H^1(\mathbb{R} P^\infty; \mathbb{F}_2)##. Prove the relations $$\text{Sq}^i(u^n) =\binom{n}{i} u^{n+i}$$
  16. C

    Infinite number of pairs of Force and distance R from AoR

    For part (b), The solution is However, is there really an infinite number of pairs physically speaking? It would be very hard, say, vary the force applied by ##0.0000001N## for example. Many thanks!
  17. J

    I Is there a "smallest" infinite subset of the naturals?

    The natural numbers are the smallest infinite set, aleph_0. By taking out an infinite subset to the natural numbers (the odd naturals), we get an infinite subset, the even numbers, which has the same size, aleph_0 (e.g. the map n->2n). We can take an even "sparser" subset of the natural...
  18. C

    Infinite discontinuity question

    For 6(b), The solution is, However, for ##a = 1## they could have also said that f is not continuous since f(1) is not defined (vertical asymptote) correct? Many thanks!
  19. M

    Unimaginable Numbers: What is 1.36 x 10^495 times 20 Million?

    Kurzesagt in a Nutshell said that the number of possible protein combinations the human body can have is 6.8 x 10^495. I asked GPT to multiple it by 20 million (which is the hypothetical number of possible alien civilizations in the Milky Way galaxy give or take). The chatbot gave me 1.36 x...
  20. M

    A Infinite series of this type converges?

    ##\sum_{n=1}^\infty n^{-a}## converge s for ##a\gt 1## - otherwise diverges. Is there any theory for ##a_n##? For example ##a_n\gt 1## and ##\lim_{n\to \infty} a_n =1##. How about non-convergent with ##\liminf a_n=1##?
  21. loversphisics

    I Proving Behavior of Particle in Infinite Potential: Wave Function?

    Hello, guys! I have a question. How can I prove the behavior of a particle subjected to an infinite potential? Will the wave function exist?
  22. F

    Synchronous generator on an infinite bus

    I'm reviewing some subjects that I long forgot and now I'm studying synchronous machines. So, when you change the field current (of the rotor) of s synchronous generator, the result is a change in the magnetic flux, which change the internal voltage (Ea). That will result in a change in the...
  23. Chunkythunk

    B Is the Universe really infinite?

    I believe the universe could not possibly be infinite. I am not denying it is of extremely large scale but it still must be finite. No true infinity is found in nature but only in mathematics. why should it differ here ?
  24. Kyuubi

    Current on Infinite Periodic LC Circuit

    I wrote down the equation of motion for In(t) and I'm trying to match it with infinite spring mass system equation solution. In the spring mass system, we consider A to be the equilibrium length of the springs, and we can thus write Xn(t) = X(nA,t) and put it back into the equation of motion...
  25. D

    I Are there an infinite number of infinities?

    How many whole numbers are there? infinity. How many tenths of whole numbers are there? ten times infinity. How many hundredths of whole numbers are there? 100 times infinity. How many millionths of whole numbers are there? 1,000,000 times infinity How many decimal numbers are there? infinity...
  26. tworitdash

    A How to sum an infinite convergent series that has a term from the end

    From my physical problem, I ended up having a sum that looks like the following. S_N(\omega) = \sum_{q = 1}^{N-1} \left(1 - \frac{q}{N}\right) \exp{\left(-\frac{q^2\sigma^2}{2}\right)} \cos{\left(\left(\mu - \omega\right)q\right)} I want to know what is the sum when N \to \infty. Here...
  27. H

    Stationary states infinite cubic well

    For a state to be stationary it must be time independent. Naively, I tried to find the values of c where I don't have any time dependency. ##e^{c \cdot L_z} \psi (r,t) = e^{c L_z} \sqrt{\frac{8}{l^3}} sin(\frac{2 \pi x}{l}) sin(\frac{2 \pi u}{l}) sin(\frac{2 \pi z}{l}) e^{-iEt/\hbar}##...
  28. Lotto

    What is the length of an infinite potential well for an electron?

    I have a nanoparticle of cadmium selenide with a diameter d. When it emits a photon with a wavelenght lambda, it happens because an electron jumps from the conduction band to the occupied band across a forbidden band. I can suppose that jump as a jump from a higher energy level (the conduction...
  29. Ssnow

    B Notation for infinite iteration

    Hi Physics Forum, I want to ask if there is an "appropriate" notation for the infinite self-iteraction of an analytic function ##f(x)##, that is ##f(f(f(...)))##. For example I know ##f^{(+\infty)}(x)## can be a way, but there is an operator notation as for the infinite sum...
  30. Euge

    POTW Infinite Sequences of Sines

    Prove the existence of a strictly increasing sequence ##m_1 < m_2 < m_3 < \cdots## of integers satisfying the property that for all positive integers ##\ell##, the sequence ##\sin(\ell m_1), \sin(\ell m_2), \sin (\ell m_3),\ldots## converges.
  31. H

    Learning to use the Cauchy criterion for infinite series

    ##s_1=2## ##s_2=4## ##s_3=5.333## ##s_4=5.9999## ##(s_n)## is increasing, but unable to guess a bound. Let's see if Cauchy criterion can do something. For n>2, $$ s_{n+k} - s_n = \frac{2^{n+1} }{(n+1)!} + \frac{ 2^{n+2} }{(n+2)!} + \cdots \frac{2^{n+k} }{(n+k)!} $$ $$ s_{n+k} - s_n <...
  32. A

    I Thinking about equality of infinite sets

    I am reading an abstract algebra textbook and enjoying it. I am working through preliminaries some more to refine my knowledge on proofs with sets before really digging in. I understand that if $$X \subseteq Y$$ and $$ Y \subseteq X$$ Then $$ X = Y$$ This makes sense to me. However, the...
  33. Y

    I Exploring the Possibility of Infinite Energy with Magnets

    This is not homework, just a question of curiosity. Something that came to my mind last night. Say I have a magnet and a piece of iron. Say I use it to do weight training exercise. I stick the magnet on the wall and stick the iron on the magnet. Say it takes 100lbs of force to pull the piece of...
  34. Buzz Bloom

    I Question re flat infinite universe with a preferred direction

    The implication seems to be that from the beginning of the post expansion era, there was everywhere an average velocity of a large volume of matter which was (very near) zero everywhere with respect to a common fixed coordinate system (with a spacially uniform time expansion of distances)...
  35. Graham87

    Quantum mechanics - infinite square well problem

    I have solved c), but don’t know how to solve the integral in d. It looks like an integral to get c_n (photo below), but I still can’t figure out what to make of c) in the integral of d). I also thought maybe you can rewrite c) into an initial wave function (photo below) with A,x,a but don’t...
  36. S

    I Would infinite entropy break all symmetries?

    If the Universe could somehow reach a state of infinite entropy (or at least a state of extremely high entropy), would all fundamental symmetries of the physical laws (gauge symmetries, Lorentz symmetry, CPT symmetry, symmetries linked to conservation principles...etc) fail to hold or be...
  37. Orodruin

    Insights Symmetry Arguments and the Infinite Wire with a Current

    [url="https://www.physicsforums.com/insights/symmetry-arguments-and-the-infinite-wire-with-a-current/"]Continue reading...
  38. J

    A POVMs for Infinite Dimensional Hilbert Spaces

    After reading up on some of the discussion in the Quantum Interpretations forums, I became interested in learning more about POVMs. However, most of the examples are from the finite dimensional setting. If I wanted to model a POVM that approximately measures position and momentum...
  39. M

    Quantum Tunneling to an infinite wall

    I have the equations for all three regions but usually for region 3, which is Ce^ikx+De-ikx, the C term would be zero since there is no reflection, but with the infinite wall would it reflect? Would the whole wavefunction go to zero like when working with the infinite square wall? I'm stuck on...
  40. A

    Sphere and electric field of infinite plate

    The solution says that the tension in the string in the negative x direction is balanced by the force of the plate on the ball (red). Why is the repulsive force of the ball on the plate (in blue) not included in this calculation?
  41. A

    Find the electric field everywhere resulting from two infinite planes

    What I don't understand is how come the electric field of the negative plane isn't pointing towards the positive plane (in blue) and cancelling out the electric field of the positive plane (in red). See image
  42. D

    Why does a free particle in an infinite well have uncertainty bigger than h/2 ?

    So I think I use the right approach and I get uncertainty like this: And it's interval irrelevant(ofc), So what kind of wave function gives us \h_bar / 2 ? I guess a normal curve? if so, why is normal curve could be? if not then what's kind of wave function can reach the lower bound
  43. J

    The infinite limits of the probability transition matrix for Markov chain

    Consider a Markov chain with state space {1, 2, 3, 4} and transition matrix P given below: Now, I have already figured out the solutions for parts a,b and c. However, I don't know how to go about solving part d? I mean the question says we can't use higher powers of matrices to justify our...
  44. docnet

    Sum of Infinite Series: Finding the Value of S

    Using the given rule for the ##x_n##, write $$ \sum_l y_l = x_1 + \frac{1}{2} x_2 + \frac{1}{6} x_2 + \frac{1}{3} x_3 + \frac{1}{12} x_2 + \frac{1}{12} x_3 + \frac{1}{20} x_2 + \cdots + \frac{1}{n} x_n $$ $$ = x_1 + \sum_{n=2}^\infty \frac{1}{n(n-1)} x_2 + \sum_{n=3}^\infty \frac{2}{n(n-1)} x_3...
  45. B

    MHB Sampling Distribution of the Sample Means from an Infinite Population

    1. Individual students’ scores on a national test have a normal distribution with a mean of 18.5 and a standard deviation of 7.8. At a Trade School, 84 students took the test. If the scores at this school have the same distribution as national scores, what is the mean, standard deviation and...
  46. J

    What is the electric field inside an infinite cylinder?

    3 cm is inside the cylinder. We can use a gaussian cylinder to enclose the inside of the cylinder up to 3 cm. Because the outer cylinder is infinite there is no flux out of the end caps with the inner cylinder. There is also no charge enclosed in the cylinder. So the electric field 3cm away from...
  47. J

    Calculating the Electric field inside an infinite planar slab using Gauss' Law

    Draw a Gaussian pill box that starts from 0 (half way between the slab) and extends towards 2 cm.$$A \times \int_{0}^{0.02} \rho dz$$ I'm not sure if I should multiply the integral by A (area) or V (volume) And if area would I multiply by 0.02^2? I'm confused here. Thanks for your help.
  48. L

    I Is anything in the physical world infinite?

    Is anything in the physical universe unlimited or infinite or does Infinity only exist to make some math work? Is Infinity a real thing outside of math?
  49. guyvsdcsniper

    Boundary Conditions for an infinite rectangular pipe

    Does setting up the problem symmetrically on this axis and the boundary conditions applied make sense? I don't believe I will have a problem solving for the potential inside, but i just want to make sure I have my B.C and axis correct before proceeding. EDIT: Or should this be a 2-D lapace...