Equivalence Definition and 721 Threads

If I have a subset, how do I define an equivalence relation. I understand it has to satisfy three properties:transitive, symmetric and reflexive, but I'm not sure how to give an explicit definition of the equivalence relation, for example on I where I=\{(x,y) : 0 \le x\le 1 \ \& \ 0 \le y \le 1\}

This is a question from A consise introduction to pure mathematics (Martin Liebeck) Hi guys, just stuck on one problem was wondering if someone could lend me hand. Let ~ be an equivalence relation on all intergers with the property that for all "m" is an element of the set of intergers ...

Homework Statement Define a relation on R as follows. Two real numbers x, y are equivalent if x - y \epsilon Z . Show that the set of equivalence classes of this relation is bijective to the set of points on the unit circle. Homework Equations N/A? I don't think there are any special...

This is a question from A consise introduction to pure mathematics (Martin Liebeck) Hi guys, just stuck on one problem was wondering if someone could lend me hand. Let ~ be an equivalence relation on all intergers with the property that for all "m" is an element of the set of intergers ...

Of all things I'm concerned, this one should be the most confusing ever. I'll tell how... E=mc2 That is, energy is an object's mass times the speed of light squared. Mass is w*g, and g is 9.81 for so long you're on Earth. Then, the speed of light is 299,792,458 m/s*299,792,458 m/s, which...

Homework Statement Is it always true that lim f(x) x-->infinity = lim f(1/t)t --> 0 lim f(x)x--> 0 = lim f(1/n)n-->infinity The Attempt at a Solution How can you begin to prove or disprove these statements if you don't know what f is doing to x. In other words, lim f(x) could not...

Homework Statement For the linear circuit shown, given that the current I in the 0.9 K\Omega is 10mA when Vs = 100V: (a) Predict I using the proportionality property for: Vs = 25V, -12V, and 145 V respectively. (b) Use Thevenin’s theorem across terminals a and b. Find I in terms of Vs and...

Homework Statement Hi, new to the Physics Forum and desperately need some help with a math analysis problem... Prove that {x|x>1} and {x|0<x<1} are equivalent sets by writing a function and show that it is one-to-one and onto. Homework Equations The Attempt at a Solution

Statement: Prove or Disprove: A relation ~ on a nonempty set A which is symmetric and transitive must also be reflexive. Ideas: If our relation ~ is transitive, then we know: a~b, and b~a \Rightarrow a~a. Therefore our relation ~ is reflexive, since b~c and c~b \Rightarrow b~b, and c~a...

Hello! I'm a bit lost on these questions pertaining to equivalence relations/classes. If someone could run me through either, or both, of these questions, I'd be very thankful! I'm completely lost as to what to do with the z in terms of set S... Homework Statement Show that the given...

I am not sure that I am using the correct term of "equivalence" for this question, but here goes. If I were traveling at the speed of light and tried to shine a flashlight forward, would it send out a light beam? Would the same thing not happen if I were standing on the event horison of a Black...

Homework Statement is the relation \propto deifined on RxR defined by (x,y) \propto (a,b) \Leftrightarrow x^{2} + y^{2} = a^{2} + b^{2} an equivalence relation? The Attempt at a Solution I know i have to show that they hold true for the 3 properties 1 reflexive 2 symetric 3...

Let H be a separable Hilbert space and let {e_k} be a Hilbert basis (aka total orthonormal sequence) for H. Then |||u|||_1:=\sum_{k=1}^{+\infty}\frac{1}{2^k}|(e_k,u)| is a norm. If {f_k} is another Hilbert basis, we get another norm by setting...

The equivalence principle is a straightforward application of Newton's third law, isn't it? There's nothing new in it

A relation R on R^2 is defined by (x_{1},y_{1})\mathit{R}(x_{2},y_{2})\;\;\;if\;\;\;x_{1}^{2}+y_{1}^{2}=x_{2}^{2}+y_{2}^{2} How do you show that R is an equivalance relation?

Hi, Im only starting to learn about naive set theory from a book , so pardon me if my answer to the question is really obvious.. Prove that .. A\subseteqB , if and only if A\capB =A,if and only if A\cupB=B, if and only if A-B=empty set.. I was thinking of using venn diagrams to...

As most of you probably know, the WEP states that the intertial mass and gravitational mass of any object are equal. This principle has base in Galileo's observations, that all free-falling objects have a constant acceleration. What I would like to get clear is the order of arguments that leads...

According to the Equivalence Principal, the effects of Gravity are locally indistinguishable from those of Acceleration. QUESTION: Since Gravity curves Space, a la the Flamm Paraboloid, does acceleration do the same ? Acceleration does impose a comparable Time Dilation effect, from the...

The Equivalence Principle suggests the possibility that a 'kinematic' paradigm might produce exactly the same cosmic observations as the standard 'expanding space' paradigm. In my view, functional equivalence demands that the 'kinematic' paradigm make the same observational predictions as the...

Can someone give me an explanation or possibly a proof that \int^{a}_{b}f(x)dx= \displaystyle\lim_{m\to\infty}\sum^{m}_{k=1}f(x^{*}_{k})\Delta x

Is it possible to eliminate Gravity completely even locally as equivalence principal says? I think this is not possible,since in a curved spacetime, Riemann tensor cann't be made zero in any frame. Then in what sense equivalence principal(which says that for a freely falling observer in a...

I obtained an analytical description of time dilation and length contraction which describes why these occur at high speeds. However there was no such analysis of Einstein's famous equation E=m(c squared). Instead, a derivation that I found in http://www.karlscalculus.org/einstein.html starts...

Suppose I set up two labs, Alice on Earth and Bob in a region of intergalactic space (or maybe in a void) where the Riemann tensor is zero. I accelerate Bob's lab at 32.2 ft/sec/sec. Both measure the Riemann tensor using identical equipment. Alice will get a nonzero value for some components...

Is there a way to figure out the number of equivalence classes for all graphs of order n, size k?

An idea crossed my mind on how to explain the weak equivalence principle(WEP) without using the gravitational law: F=G m1m2/r2 Part of what WEP sais is that assuming we are in a uniform gravitational field, if we let two objects of different masses, they will fall with exactly the same speed...

Homework Statement We have an equivalence relation such that A <-> B. Prove that the equivalence relation is true. The Attempt at a Solution Let P: A -> B Q: B -> A Let's prove the relation by contradiction. Assume \neg A -> \neg B The previous assumption is the same as Q. Thus, we have...

Does fact that QFT in imaginary time is equivalent to QSP represents the proof that many-particle quantum physics is equivalent to quantum theory of fields? To elaborate a little, I had some discussion with some engineers, and when I was explaining them Standard Model I had to invoke concepts...

let the relation \propto on a set S have the properties (i) a \propto a for every a \in S (II) if a \propto b and b \propto c then c \propto a show that \propto is an equivalence relation on S. Does every equivalence relation on S satisfy (i) and (ii) I'm not sure where to start this i know...

These two terms would be the simplest terms in the set theory as they are on the first chapter in my textbook. But why can't i understand it? In my textbook it says A relation R in a set is a set of ordered pairs, so any subset of a set of ordered pairs will be a relation. This includes the...

Homework Statement Prove that if (a1, b1) ~ (a2, b2) and (c1, d1) ~ (c2, d2), then (a1, b1) + (c1, d1) ~ (a2, b2) + (c2, d2) and (a1, b1) \bullet (c1, d1) ~ (a2, b2)\bullet (c2, d2). Let [a, b] denote the equivalence class with respect to ~ of (a, b) in Z x (Z-{0}), and define Q to be the...

Homework Statement 1. Suppose A-B is equivalent to B-A. show that A is equivalent to B. 2. if A,B and C are nonempty and A cross B is equivalent to A cross C then B is equivalent to C Any help would be appreciated, thanks! The Attempt at a Solution I tried constructing a bijection, but that...

Homework Statement Suppose that A is a nonempty set and R is an equivalence relation on A. PROVE that there is a function f with A as its domain such that for x and y in A, xRy (x is related to y) if and only if f(x)=f(y) Homework Equations Equivalence relations are relations that...

I'm reading in a textbook (Gravity by J. Hartle) that gravitational time dilation is implied by the equivalence principle. The following thought experiment is described. A vertical rocket at rest in a uniform gravitational field (no tidal effects) is compared to a rocket constantly...

What is an appropriate statistical test for equivalence of two population means? I'd like the null hypothesis to be that the populations are different. The problem with the t-test is that the null hypothesis says that the populations are the same. It is more appropriate in my application...

I'm having a bit of difficulty in showing the following is an equivalence relation: z~w iff \frac{z}{w} \in \mathbb{R} \forall z,w \in \mathbb{C}*=\mathbb{C} \backslash \{0\] clearly z~z is ok as 1 is real then i considered \frac{z}{y} \in \mathbb{R} and tried to show y divided by z is...

My notes say that a photon traveling from a high altitude to an observer at low altitude appears to have a higher frequency i.e. gravitational blue shift. now I am having trouble getting this: the strong equivalence principle says we can substitute this "laboratory" with a laboratory that...

Hi, everyone: I have been looking for a while without success, for the definition of equivalence for unimodular quadratic forms defined on Abelian groups . I have found instead ,t the def. of equivalence in the more common case where the two forms Q,Q' are defined on vector...

Homework Statement 1. Prove that if ca=cb (mod m) and gcd(c,m)=1, then a=b (mod m) 2. Prove that if a=b (mod m), then gcd(a,m)=gcd(b,m)Homework Equations The Attempt at a Solution I can't figure out how to get started on these, especially the last one. Is it just a matter of expanding definitions?

Ok, well I'm sorry if this is the wrong section but it has to do with energy and nuclear physics. I have to present why we should use nuclear energy, though no one in the class knows a lot about it. I am going to be using the example of getting nuclear energy from U-235/92. I have the formula...

Homework Statement Are the statements A and B equivalent with each other? A. Suppose that n is an integer which is not a perfect square. B. If n >= 1, then \sqrt{n} is either an integer or is irrational. The Attempt at a Solution I am keen on saying that the two statements are not...

Given two units of measurements with the same physical dimensions (LMT), are they redundant? For example, Einstein's stress-energy tensor of GR uses units of pressure and energy density which are clearly distinguished in most interpretations. However both pressure and energy density have the...

Homework Statement Determine if this is an equivalence relation. Either specify which properties fail or list the equivalence classes: A = {0, 1, 2...} R = {(m,n) | m^2 ≡ n^2 mod 3} Homework Equations m^2 ≡ n^2 mod 3 The Attempt at a Solution I've determined that it is...

Equivalence of inertial & gravitational mass--I need a sanity check. Einstein, in his 1916 book Relativity, illustrates the equivalence of gravitational and inertial mass using the example of a braking train. The example begins with the train at rest (of course) and the scenery moving to the...

Hello, I would like to know if there are experimental tests of the Equivalence Principle in the realm of electrodynamics. The book by http://books.google.com/books?id=BhnUITA7sDIC&pg=PP1&dq=Theory+and+Experiment+in+Gravitational+Physics&lr=#PPP1,M1" contains a lot of material about the...

I read the textbook 5 times now and I can't seem to figure out what the equivalence class suppose to be and how to find it, and i don't understand quotient set either (more importantly how to find it). I'm not familiar with any Equivalences at all if anyone can help me with it that would be...

In Modern Quantum Mechanics, Sakurai say that at quantum level the gravity is no more geometrical because the schrodinger equation depend on the fraction \frac{m}{\hbar}. Can someone explain better this claim or link me some detailed paper on this argument?

The book I'm reading on special relativity is a ficitonal conversation between Newton and Einstein. Einstein is explaining relativity to Newton. Its a very good book in my unprofessional opinion, but one thing I'm having problems with is energy-mass equivalence. I'm not having trouble with...

Homework Statement A car is traveling at 12ms^-1. To the passenger in the car the wind appears to be blowing at 8.0ms^-1 at right angles to the road. What is the magnitude and direction of the velocity of the wind with respect to the ground. Homework Equations I can think of two...

I was wondering whether or not astronauts who weighed differently on Earth would weigh differently on a spaceship accelerating to simulate gravity. Do the astronauts who have more mass experience a greater force in the ship like the would on Earth or does each astronaut weigh the same on the ship?

Homework Statement (S \wedge T) \wedge \neg (S \wedge T) (S \vee T) \Rightarrow (S \wedge T) Are the two (predicates?) logically equivalent? Homework Equations Not sure, but I believe that logical equivalence means that two predicates give the same output on the same input...