What is Example: Definition and 877 Discussions

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  1. B

    Counter example to a Sequentially Compact question

    Can you provide one to show a separable complete boundd metr. space X is not always seq. compact.
  2. bcrowell

    *simple* example of mechanics problem with no closed-form solution?

    I'm looking for a good example for a freshman mechanics class to demonstrate how one can integrate the equations of motion numerically when there is no closed-form solution. The problem below is the best I've been able to come up with yet, but I'm not totally happy with it, and I'm wondering if...
  3. X

    Conway Functional Analysis text example?

    Hello, I'm reading through John Conway's A Course in Functional Analysis and I'm having trouble understanding example 1.5 on page 168 (2nd edition): Let (X, \Omega, \mu) and M_\phi : L^p(\mu) \to L^p(\mu) be as in Example III.2.2 (i.e., sigma-finite measure space and M_\phi f = \phi f is a...
  4. L

    In an ionic equation, how do you know what pairs with what? For example:?

    molecular: Pb(NO3)2 (aq) + 2 KI (aq) ----->2KNO3 (aq) + Pbl2 (s) Ionic equation Pb2+ (aq) + 2NO3- (aq) + 2 K (aq) + 2 I- (aq)----->2K+ (aq)+ 2NO3- (aq) + PbI2 (s) I know why they break apart in the ionic part, its because ionic things aer broken up, but how would you know that they join...
  5. G

    Mathematica [Mathematica] Simplify can't handle this trivial example

    Hi everyone, I'm wondering why Mathematica (8.0) can't bring this to the obvious form -1, and leaves the expression as is: Simplify[(b^8 + c^4) /a^8, a^8 + b^8 + c^4 == 0] Is there any nice and elegant way how to achieve that? (I know, that I could take e.g. /.c->(-a^8-b^8)^(1/4), but...
  6. Y

    Question on an example in Griffiths' book, Not a homework

    The is example 10.1 in page 417. The example is the find the current density from given condition: V=0,\;\;\hbox{ and } \;\;\vec A=\frac{\mu_0 k}{4c}(ct-|x|)^2 \hat z \;\hbox { for x = +ve and }\;\; \vec A=0 \;\;\hbox { for x = -ve.} c=\frac 1 {\sqrt{\mu_0 \epsilon_0}} From this...
  7. S

    Laser light an example of quantum coherence?

    There seems to be some debate as to whether laser light is an example of quantum coherence (as posted in this thread: link). I think it deserves its own discussion. I'm no expert in this field, so I mainly go by what I read; I found this interesting Wikipedia reference here: Comments?
  8. H

    Example of a Diverging Series & Converging Integral

    Homework Statement Give an example of a continuous, non-negative function f: [1, infinity) --> R such that if an = f(n) for each positive integer n, the series \sum an diverges, while the improper integral from 1 to infinity of f converges. Justify your answer. Homework Equations N/A...
  9. L

    What is the relevance in knowing that the universe for example is expanding?

    Why exactly is it so important to know about the models of the universe(flat/open/closed)? Why is it so important to know that the universe is expanding? What do we benefit from it? what is the relevance of it? Even if we know the "truth", what does it mean to "us"? I don't really mean these...
  10. S

    Why is the denominator of the ratio possible if the forward rate is 2nd order?

    In my textbook there is an example with the following reaction and rate: C6H6 + 3H2 -> C6H12 Rf = kf[C6H6][H2] Then the the example claims that the ratio of the rate constants is: kf / kr = [C6H12] / ( [H2]3 [C6H6] ) How is the denominator of that ratio possible if the forward...
  11. R

    Understanding Little Oh Notation with Example Problem

    Homework Statement So, this isn't a Homework problem, but I think I am having a little trouble understanding little oh notation, so here is a problem: Show that Sum(k^3) (k=1 to n) = (1+o(1))(n^4)/4 Homework Equations No relevant equations. The Attempt at a Solution Let S =...
  12. B

    Need example of real application of differential equation

    I'm teaching Calculus and am looking for an example of a first order differential equation application that is reasonably easy to explain in terms of where the equation comes from, but difficult or impossible to solve. I'm trying to show when you would need to use approximation techniques...
  13. B

    Problem with relativity of simultaneity original example

    In special relativity the relativity of simultaneity is explained with the following example. We have one frame of reference - a train moving from left to right with constant speed v relatively to the embankment, and second frame of reference - the embankment itself. On the embankment there are...
  14. K

    Solving Unintuitive Homework: An Example of C ≠ f^(-1)(f(c))

    Homework Statement Homework Equations The Attempt at a Solution I don't know how to start a proof for this. Intuitively I would think think that C = f^(-1)(f(c)), which would imply that C is a subset of f^(-1)(f(c)), however that is not the case and the problem asks for an...
  15. D

    Providing a proof or counter example.

    Homework Statement Prove or give a counterexample: for all x > 0 we have x2+1< (x+1)2\leq 2(x2+1)Homework Equations The Attempt at a Solution I used my calculator to do the graph of all 3 functions and saw that the statement was always true (at least for x>0). So I couldn't see another proof...
  16. X

    Need example of a continuous function map cauchy sequence to non-cauchy sequence

    Homework Statement I need a example of a continuous function f:(X, d) -> Y(Y, p) does NOT map a Cauchy sequence [xn in X] to a Cauchy sequence of its images [f(xn) in Y] in the complex plane between metric spaces. Homework Equations If a function f is continuous in metric space (X, d), then...
  17. X

    Give example of matrices such that AB=AC but B=/=C

    [b]1. Let M(2,R) be the set of all 2 x 2 matrics over R. Give an example of matrices A,B,C in M(2,R) such that AB=AC, but B is not equal to C. [b]3.
  18. K

    Example of functions satisfying differentiation properties

    Suppose the function f has the following four properties: 1. f is continuous for x >=0; 2. f'(x) exists for x > 0; 3. f(0) = 0; 4. f'is monotonically increasing. I'm just looking for functions that have these 4 properties to better understand what f represents. So far, I came...
  19. D

    Wrong example of Covariant Vector

    I have a question about covariant and contravariant vectors. I tried making concrete examples and in one example I succeed, in another I fail. It is said that displacement vectors transform contravariantly, and gradients of a scalar transform covariantly. I can get the whole story working in...
  20. G

    Find an example for 2 planes with parameters

    I have to find two planes z=f_1(x,y)=a1*x+b1*y+c1 z=f_2(x,y)=a2*x+b2*y+c2 That satisfy: 1. both planes go through (-5,9,8) 2. the intersection line between the planes is located outside of the Cylinder x^2+y^2=4 3. the surface area of x^2+y^2=4 that is bounded between f1 and f2 is...
  21. L

    Is there a 4D compact smooth manifold with specific properties?

    I am looking for an example of a 4 dimensional compact smooth manifold that has the following properties - it is orientable - it can be smoothly embedded in R^8 - its Euler characteristic is odd - its second Stiefel-Whitney class is zero
  22. Drakkith

    Time Dilation Light Clock Example

    I'm missing something here on the light clock example from http://en.wikipedia.org/wiki/Time_dilation. I understand the math on the picture, but I'm missing how that applies to time dilation. Why does the light pulse take on a diagonal path for the moving observer? Is the light pulse still...
  23. B

    Worked Out Example of Consecutive Observations in QM

    I know that in QM, one observation like position will alter the wavefunction so that momentum changes. But how do we see this mathematically when we include time dependence, whether in matrix mechanics or wave mechanics? Is it as simple as writing PQx where x is the state, Q position matrix, P...
  24. P

    Finding Normal Compressive & Tensile Stress: a Example

    Homework Statement [PLAIN]http://img12.imageshack.us/img12/6109/17007711.jpg The attempt at a solution For part (a), I can only find a normal compressive stress. It is as follows: \sigma_{c} = \frac{F}{A} \sigma_{c} = \frac{100*9.81}{\pi(0.013)^{2}} \sigma_{c} = 1847704 Pa...
  25. D

    Lagrange Multipliers: A theoretical question and an example

    Hello physicsforums community. I have recently learned about Lagrange multipliers and have been given three problems to solve. Could you guys please go over my work and see if I have the gist of it? One question, a theoretical one, I have no idea how to begin. Any advice regarding this would be...
  26. B

    Geometric Example of Torsion Cycles and Relative Cycles (in Homology)

    Hi, Everybody: I am trying to understand torsion and relative cycles in a more geometric way; I think I understand some of the machinery behind relative cycles (i.e., the LES, and the induced maps.), and I understand that by ,e .g., Poincare duality, in order to have torsion in...
  27. G

    Contradiction in Taylor-Wheeler's example of spacetime invariance

    In section 1.2 of Taylor and Wheeler's Spacetime Physics, a rocket moves past a laboratory (on Earth). Attached to the rocket is a pin. From that pin a spark is emitted at two locations in the lab, separated by 2 meters. The observer in the rocket measures the elapsed time between the sparks, as...
  28. T

    Disk moment of inertia example.

    A disk, cylinder shaped, of mass m and radius r is initially motionless on an ice rink. It has a massless string wound around it which you pull with a constant force F. After your hand has moved a distance d. How far has the c.m. of the disk moved? If someone could show me how I could do this...
  29. L

    Confused About Fourier Trick: Exploring an Example

    Homework Statement Hey I am confussed about how the Fourier trick works. In my book they have an example ...=integral from 0 to pie Pl(cos@)Pl'(cos@)sin(@) d@ then somehow they get ={0 if l' does not equal l and 2/2l+1 if l'=l Thanks Homework Equations The Attempt at a...
  30. DocZaius

    Feynman Turnscrew Example Question

    Very early on in Feynman's Lectures on Physics, he offers the example of a screwjack with a mass on it to demonstrate the conservation of energy (picture attached). He asks how much force would be needed to lift the one ton sitting on top of the screwjack. He then comes up with 1.6 pounds...
  31. R

    Can someone help me come up with an example? (analysis)

    Homework Statement let X be the set of all infinite dimensional vectors with finite nonzero components consider 2 distance functions on X d=euclidean distance=\sqrt{\sum(Xi-Yi)^{2}r=max distance=max{|X1-Y1|, |X2-Y2|, ...} give an example of a sequence where it converges under r but not...
  32. L

    What happens when an acid or base reacts with a metal, for example, Mg.

    The acid: Hydrochloric What happens step by step? I am unfamiliar with acids and bases, so I just want to know what's happening to help figure out. Thanks.
  33. B

    Example of Codimension-1 Manifolds that are not Isotopic.?

    Hi, Everyone: A question on knots, please; comments,references appreciated. The main points of confusion are noted with a ***: 1)I am trying to understand how to describe the knot group Pi_1(S^3-K) as a handlebody ( this is not the Wirtinger presentation; this is from some...
  34. M

    Example of a linear subset of Hilbert space that is not closed

    Homework Statement Prove that for a linear set M a subset of Hilbert space, that the set perpendicular to the set perpendicular to M is equal to M iff M is closed. The Attempt at a Solution I already have my proof -- but what is an example of a linear subset of H that is not closed? I think...
  35. P

    Question about Dr. Chinese's example of Bell's Theorem

    Hello, this could be a basic question. I saw the link http://www.drchinese.com/David/Bell_Theorem_Easy_Math.htm" on one of the threads. Following the table there the probability of complete match between two detectors happens twice out of 8 times. i.e. 1/4. How how can we say that it...
  36. N

    Hi guysIn my statistics book there is an example. They say that we

    Hi guys In my statistics book there is an example. They say that we see 3 occurrences of type A, and theoretically expect 7. This is a difference of 4, since we know that the standard deviation is 1.65 (they calculate it), then the difference is 2.4 standard deviations. Looking at a table of...
  37. S

    Finding the set of interior points, the closure, and an example

    Suppose that S=[0,1)U(1,2) a) What is the set of interior points of S? I thought it was (0,2) b) Given that U is the set of interior points of S, evaluate U closure. I thought that U closure=[0,2] c) Give an example of a set S of real numbers such that if U is the set of...
  38. Saladsamurai

    Power Series Following an example problem

    Homework Statement I am following along in an example problem and I am getting hung up on a step. We are seeking a power series solution of the DE: (x - 1)y'' + y' +2(x - 1)y = 0 \qquad(1) With the initial values y(4) = 5 \text{ and }y'(4) = 0. We seek the solution in the form y(x) =...
  39. R

    Can you think of a counter example (real analysis)

    Homework Statement X and Y are two closed non-empty subsets of R (real numbers). define X+Y to be (x+y | x belongs to X and y belongs to Y) give an example where X+Y is not closed Homework Equations The Attempt at a Solution i tried X=all integers and Y=[0 1] but that didnt work out. i know...
  40. F

    Linear Independence: Polynomial Example

    Hello everyone. I was going through my Linear Algebra Done Right textbook that threw me off. I hope this forum is appropriate for my inquiry; while there is no problem I'm trying to solve here, I don't know whether just asking for clarification would belong to the homework forum instead. If...
  41. D

    Example of a pure existence metaproof

    Example of a "pure existence metaproof" http://en.wikipedia.org/wiki/Existence_theorem A pure existence theorem is a theorem which states the existence of something, but the proof of the theorem does not indicate a construction of the thing in question. As the article mentions, this is...
  42. L

    Needing a solid example of a composite mass value

    Hi. I am having a bit of trouble working through all the formulas for calculating the total composite mass of moving particles. If I could just fill in this 'black and white' and very intuitive example then I will be able to use it as a guide to test everything I'm doing. If we have 2...
  43. S

    How is the k.p method used in semiconductor systems?

    Hi, I am trying to find a worked example of the k.p. method for a semiconductor. I understand the theory, but would like to find an example of its implimentation for a simple system just to help with my understanding of it. Many thanks in advance
  44. M

    An example of a close and bounded set that is not compact

    Take the discreet metric on an infinite set A. I understand that its closed (because it contains all of its limit points), but I don't understand why its bounded and why its not compact. Also, when they say "an infinite set A" do they mean a set that extends to infinite (say, [1,n] for...
  45. E

    Topology/Analysis: example of a particular set

    Homework Statement Give an example of a nonempty set A in R such that A = Bd(A) = Lim(A) = Cl(A). Bd(A) is the boundary of A, Lim(A) is the set of limit points of A, Cl(A) is the closure of A. Homework Equations Bd(A) = A - Int(A), Int(A) is the interior of A Lim(A) = is the set of...
  46. atomqwerty

    An example of moving towards a light source

    Hi, I've a question that I'll illustrate by presenting the following example: Let's imagine Einstein in a car that's moving away from a clock. This clock 'send' a light beam with the information 'It's 12 o'clock'. If the velocity of this car is close to c, I understand that Einstein will...
  47. strangerep

    Non-convergence counter example?

    Non-convergence counter example?? (This question occurred to me in the context of quantum field theory, but since it's purely mathematical, I'm asking it here...) Consider the universal vector space \Xi of arbitrary-length sequences over C (the complex numbers). Denote \delta_k ~:=~...
  48. M

    Example of a differentiable structure on R

    Consider the manifold of the real-line R with a differentiable structure generated by the map x^3 : M \rightarrow \mathbb{R} . This example is given in a textbook I'm looking at, but I don't really understand how this can work. The inverse map is clearly not smooth at x=0. Do they mean that...
  49. K

    Applications of Resonance in Real Life, Example?

    I wonder how and where does resonance is applied in our real life. Any example?
  50. N

    Is sexual reproduction an example of convergent evolution?

    Second thread on the evolution of like, in the Archaen and Proterozoic eons. There are many kinds of eyes, and many have arisen quite independently; the classic example of convergent evolution. Did sexual reproduction arise more than once, independently? Is it too an example of convergent...
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