What is Equivalence: Definition and 744 Discussions

In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The relation "is equal to" is the canonical example of an equivalence relation.
Each equivalence relation provides a partition of the underlying set into disjoint equivalence classes. Two elements of the given set are equivalent to each other, if and only if they belong to the same equivalence class.

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  1. J

    Gravity / equivalence principle

    This may be stupid question... Equivalence principle - there is no experiment in a closed laboratory to determine if the lab is accelerating or at rest in a uniform gravitational field. It seems, then, that it is a fundamental property of the universe that one can always consider themselves...
  2. B

    The Equivalence of Mass and Energy

    I was working on the following problem: An electron and a positron each have a mass of 9.11 x 10-31 kg. They collide and both vanish, with only electromagnetic radiation appearing after the collision. If each particle is moving at a speed of 0.30c relative to the laboratory before the...
  3. James R

    Proving Double Sum Equivalence

    Does anybody know how to prove the following? \sum\limits_{n=0}^{\infty} \sum\limits_{m=0}^{\infty} f(n,m) = \sum\limits_{p=0}^{\infty} \sum\limits_{q=0}^{p} f(p,p-q) f(n,m) is any function of n and m. Note the change of the limiting values on the sums.
  4. K

    Understanding Equivalence Relations in Math: Examples and Explanation

    ok i don't know why i can't grasp this and i feel so stupid... here's an example in the book which i do get... Let S denote the set of all nonempty subsets of {1, 2, 3, 4, 5}, and define a R b to mean that a \cap b not equal to \emptyset. The R is clearly reflexive and symmetric...
  5. P

    Proving Equivalence of y is Rational, y/3 is Rational, 2y+5 is Rational

    Well I have to prove the following statements are equivalent: a. y is a rational number b. y/3 is a rational number c. 2y+5 is a rational number So a -> b -> c -> a I'm not quite sure how you are suppose to prove something is rational however. I started like this: * y = q/r Where q &...
  6. T

    Gravity: Equivalence or Equal? | Tony's New Theory

    Hi. New to this forum. Great place. A long time ago when I first read about equivalence in relation to gravity I thought it seems too much like a coincidence. I thought if it smells like a duck, looks like a duck, and quacks like a duck, chances are its a duck. I mean what if gravity is indeed...
  7. P

    Equivalence relations problem #2 (alg)

    R = the real numbers A = R x R; (x,y) \equiv (x_1,y_1) means that x^2 + y^2 = x_1^2 + y_1^2; B= {x is in R | x>= 0 } Find a well defined bijection sigma : A_\equiv -> B like the last problem, I just can't seem to find the right way to solve this??
  8. P

    Equivalence relations problem (algebra)

    Z = all integers A = Z; m is related to n, means that m^2 - n^2 is even; B = {0,1} I already proved that this is a equivalence relation, but i just don't know how to; I need to find a well defined bejection sigma : A_= -> B I hope this makes sense.. i wrote it up as well as I...
  9. Oxymoron

    Difficulty with EASY equivalence statement

    I want to be able to prove that S=T \, \Leftrightarrow \, \langle Sx\,|\,x \rangle = \langle Tx\,|\,x \rangle given that S,T \in \mathcal{B(H)} and x \in \mathcal{H}. If S and T are bounded linear operators and I suppose that S = T then I have to be able to prove that \langle...
  10. S

    Proving Equivalence and Function Equality in Real Analysis

    Hey guys, wasn't sure what forum to post this in. So if this is the wrong forum, I apologize. Anyway, I have a problem in Real Analysis that I can't quite get. Here it is: Let f:A->B and R is a relation on A such that xRy iff f(x) = f(y). a.) Prove R is an equivalence relation b.) Show...
  11. N

    Proving Equivalence Relations: Intersection of Two Sets

    Hi All I have a problem with Set theory. I am given to prove the following; Is the intersection of two equivalence relations itself an equivalance relation? If so , how would you characterize the equivalnce sets of the intersection? Regards, Nisha.
  12. M

    What are the criteria for proving equivalence of Cauchy sequences?

    Question: Prove that if a Cauchy sequence x_1, x_2,... of rationals is modified by changing a finite number of terms, the result is an equivalent Cauchy sequence. All the math classes I have taken previously were computational, and my textbook contains almost no definitions. So, I...
  13. J

    G-equidecomposable and equivalence relation

    G acts via isometries on a set X, and A,B are subsets of X. Prove that the relation A~B is an equivalence relation on subsets of X iff A and B are G-equidecomposable. I think this has to do with the Banach-Schroder theorem, but am not sure. I know it is a definition in group theory, but...
  14. H

    Schrödinger equation and equivalence principle

    May be this is a silly question, but if one converts the nonrelativistic Schrödinger equation for a free particle to an uniformly accelerated frame, is the result the same as the Schrödinger equation for a particle within a gravitational potential? I was trying some simple calculations but did...
  15. N

    Question about the equivalence principle

    - Albert Einstein, Relativity: The Special and General Theory, Section 23 I'm confused about how gravity could account for all of the observations of the observer on the rotating disc. If the observer dropped a ball, he would see it fall away from the disc initially, as expected if there was...
  16. L

    To show that equivalence classes of ker f are concentric circles

    I just want to make sure that I am doing this right or if I am on the right track. To find a map f :R ---> R so that ker f ={(x,y): x^4=y^4} pi_R: (x,y) ---> {(x,y): x^4=y^4} pi_R: x ---> {R(x): x^4 is an element in X} pi_R: Y ---> {R(y): y^4 is an element in Y} Define f: R x R --->...
  17. H

    The energy-momentum tensor and the equivalence principle

    Is it correct that the only way to have a theory of gravitation that fulfills the equivalence principle is to make use of a tensor as the source of gravity (and not a scalar or a vector, for example)? How can this be proven?
  18. Chronos

    Equivalence without relativity

    Here is a very interesting read on SR. Were Gould not the author, I probably would have glossed and flossed this paper. http://www.arxiv.org/abs/astro-ph/0504486 E = mc^2 Without Relativity Authors: Andrew Gould
  19. P

    Does the equivalence principle hold for charged particles?

    I'm new here so this may be an old question. The equivalence principle states (roughly) that one can't distinguish between an accelerating frame and a uniform gravitational field. But an accelerated charged particle radiates. Thus the EP seems to imply that a stationary charged particle in a...
  20. W

    Equivalence between path integral formulation and matrix formulation

    Does anyone know where to find the "direct" (not by prove they are both equal to Schrodinger formualtion )proof?
  21. V

    Why is the Principle of Equivalence considered a theorem?

    I was reading the Principle of Equivalence which says that inertial mass is equal to the gravitational mass, though I am not very clear that why it should be written as a theorem. Here is what I read and the subsequent confusions that formed :- First, to define the inertial mass, you fix a...
  22. U

    On the dynamic equivalence of the corpuscular theory and space-time mediation of lig

    In the Compton Effect Revisited The Proper Interval Locality Interpretation (http://www.electrodynamics-of-special-relativity.com/Compton-Effect ) we showed that a zero interval strike from a bound electron in a remote quantum system was the equivalent of being struck locally by a photon since...
  23. B

    Creating Equivalences in Logic - Is There a Reason?

    I've wondered about this. The book for my logic course (now done with) had no rule for creating equivalences. If you had A <--> B, by the system in the book you couldn't replace occurrences of A with B and occurrences of B with A. You'd have to break down A <--> B with material equivalence...
  24. W

    Does light bending doubly violate the equivalence principle?

    The equivalence principle (EP) - which is the basis of general relativity – states that you cannot distinguish between an object’s behaviour in a uniform gravitational field from that in a uniformly accelerating frame. If light travels vertically in a gravity field it loses or gains energy, and...
  25. C

    Special Relativity - Transformations and Equivalence Principle

    I am going to try to explain relativity without light or maxwell's equation. Light or Maxwell's equation or electromagnetism has nothing to do with relativity. a) The speed of light (and not light itself - note the difference) has something to do with it. b) The fact that M&M used light...
  26. phoenixthoth

    Equivalence of C & D: A Question

    One question for now: 1. If C is a full subcategory of D and D is a full subcategory of C, what can be said, if anything, about C and D being either equal or equivalent in some way?
  27. S

    Graviton and the equivalence principle

    I posted this in general physics, but I didn't get an answer, so I'll try again here: Einstein's theory of general relativity was motivated by his equivalence principle, that no experiment can distinguish between an accelerated frame and a still frame under the influence of gravity. But if...
  28. S

    The gravition and Einstein's equivalence principal

    the graviton and einstein's equivalence principle Einstein's theory of general relativity was motivated by his equivalence principle, that no experiment can distinguish between an accelerated frame and a still frame under the influence of gravity. But if the gravitational force is mediated by...
  29. quasar987

    Exploring Mass-Energy Equivalence and Nucleons

    I was thinking just a moment ago and fragments of random knowledge and ideas gathered to make this question... If I remember my college physics class correctly, an evidence of the mass-energy equivalence is that in an atom, the sum of the rest masses of the nucleons is greater than the rest...
  30. S

    Exploring Quotient Spaces: Visualizing Equivalence Classes

    Hi I just wanted to know what a qoutient space is . Is there a physical picture to it? How can one imagine what an equivalence class,equivalence relation is?
  31. L

    The Equivalence Principle-bending of light

    The Equivalence Principle--bending of light Hi everyone! I have learned the general relativity, but I have a few problems which I don't understand. Can someone help me? I am recently learning the Equivalence Principle and the bending of light. I have read the following paragraphs in a...
  32. J

    Equivalence Point Calculation: Joe's Question

    Hi ppl, I was wondering. I have found the Equivalence point from the graph of volume versus pH for a given titration. To determine the Half equivalence point for to calculate Pka=Ph, do I half the pH or the volume which I found for the Equivalence point initially? Thanks for any help, Joe
  33. Garth

    A New Test of the Equivalence Principle?

    The Eotvos type experiments test the equivalence principle by comparing the inertial accelerations of bodies of different compositions within a gravitational field. In short they test whether feathers and cannon balls fall at the same 'rate'. But has anybody tested whether particles and...
  34. E

    Dought regarding equivalence principle

    i have some doughts regarding the principle of equivalence.we have seen that the inertial mass and gravitational mass are same.now consider the nucleus where in nucleons are binded due to which there wiil be mass reduction,this is inertial mass.then how come there is decrease in gravitational...
  35. K

    Equivalence and derivation of general relativity

    derivation of general relativity Can the theory of general relativity be deduced without appealing to the ideas of special relativity? Quantum mechanics didn't need special relativity to come into existence even though QM eventually incorporated it.
  36. Loren Booda

    Equivalence principle + light speed postulate =

    It seems to me that Einstein's equivalence of gravitational acceleration and non-gravitational acceleration, when combined with his constancy of light speed in vacuuo, should yield a constancy of gravitational speed in vacuuo.
  37. Garth

    Questions of the equivalence principle

    Being full of doubts I have some questions of the equivalence principle. 1. In the presence of gravitational fields the Einstein Equivalence Principle (EEP) is a necessary and sufficient condition for the Principle of Relativity, (PR). Here I summarise PR as the doctrine of...
  38. G

    The equivalence of observed separation and relativistic velocity.

    The final conversatation between Doc Al and Russ_Watters in post 78 in the Speed of light thread went as: Reading this last post led me to question whether the conversation between Doc Al and Russ_Watters ought not be left unanalyzed. I had finished reading the entire thead earlier and began...
  39. E

    Hoffman.comHow does matter get converted into energy?

    Is there any model to describe the mechanism that allows matter to be converted into energy? If a mass is suddenly converted into its energy equivalent what is the nature of this energy?
  40. Antonio Lao

    Force and Spacetime Equivalence

    The Principle of Equivalence between inertial mass and gravitational mass used by Einstein to formulate his general theory of relativity is a prelude to another equivalence principle. This is the equivalence between a fundamental force and the geometry of spacetime. The forces used in this...
  41. E

    Equivalence Relations question

    I am not exactly clear on what an equivalence relation. If A is a set, then a relation on A is a subset R. The relation R is an equivalence relation on A if it satisfies the reflexive property, symmetric property, and transitive property. What types of relations are we talking about. And when...
  42. C

    About Feynman-Kac equivalence between PDE and SDE

    Hi, I am quite new to the concept of stochastic equations. I am learning of it from some financial textbooks, however they lack a bit in the approach. Let me see if i understood Feynman-Kac: for every PDE in N dimensions (with second derivatives equivalent by unitary/orthogonal...
  43. C

    Find all equivalence classes. Questions about functions

    Questions about functions: Let A be a set and let f: A -> A be a function. For x,y belongs to A, define x ~ y if f(x) = f(y): a. Prove that ~ is an equivalence relation on A. This is my guess, but I am not sure whether I'm right: Proving reflexiveness: If (x,y) belong to A, then f(x)...
  44. W

    Ring Theory: Equivalence Relations

    Hello, I have a question regarding equivalence relations from my ring theory course. Question: Which of the following are equivalence relations? e) "is a subset of" (note that this is not a proper subset) for the set of sets S = {A,B,C...}. Example: A "is a subset of" B. Now...
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