Equivalence Definition and 748 Threads

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...

Homework Statement Hi I have justed switched to a new subject and have some question. 1) Show that if X is a topology space then there exist an equivalence relation if and only if there exist a connected subset which contains both x and y. 2) Show that the connected components are a...

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...

Homework Statement Taking e to be small, we have been given these two formulas to prove m1 = \frac{-1+\sqrt{1-4e}}{2e} = \frac{-1+(1-2e+O(e^2))}{2e} = -1+ O(e) m2= \frac{-1-\sqrt{1-4e}}{2e} = \frac{-1-(1-2e+O(e^2))}{2e} = -1+ O(1) Homework Equations The Attempt at a Solution...

It is my understanding that the Equivalence Principle postulates that if I were standing in a closed room, I would not be able to distinguish whether the downward force that I felt was caused by (1) the presence of a massive body such as the Earth exerting a downward gravitational force or (2)...

Let A be a set. For every set B and total function f:A->B we define a relation R on A by R={(x,y) belonging to A*A:f(x)=f(y)} *belonging to - because i don't know how to make the symbole... Prove that f is one-to-one if and only if the equivalence classes of R are all singletones

I've been trying to put this together in my head for a while and it doesn't come out. For example, if there are more stars on one half of the sky, does it mean that a thrown object will travel faster in that direction? If the object is at the edge of the universe, does it mean it will not be...

Ok so I was answering a question about a spacecraft accelerating through deep space with observer A in the front and observer B in the rear. I was asked to explain why a phton sent from A to B would appear blue shifted to B - simple enough I just plugged in a positive velocity to the...

Hello, I can answer some basic questions about GR, but I don't teach it, and I am not proficient in it. Yesterday a student asked a question that I felt I couldn't do justice to. Can you help? I had the student email the question so I could ask around. So far I haven't gotten any useful...

I can't figure out how to show that the Clausius entropy \Delta S= \int_{T_1}^{T_2} \frac{dQ}{T} is equivalent to the Boltzmann entropy S=kln \Omega at thermal equilibrium. Does anyone know how to do this?

One ton of Uranium used at a typical 1 GW reactor is equal to how many tons of coal being burned in a 1 GW coal fired plant?

Hi all. First post so please forgive the noobness. I have been listing to an audio book of "A briefer history of time" by that well known genital man and I have hit upon something I don't understand. My understanding of the Principle of Equivalence is that you will not be able to tell if you...

Hi all, There are a few doubts I hope I can get enlightened. If we were in a lab in outer space, free of gravitational influence and the lab accelerates downwards, what will we experience? do we 'move' to the top of the lab? What I'm confused about also is, why is that when you have an...

Hi, When I was just walking through the hallway of my department I found an exercise sheet asking the student to examine the following proof. Assume R\subset M\times M is a binary, symmetric, transitive relation. Then for any a,b \in M with a\sim _R b it follows by symmetry that b\sim _R a...

Homework Statement On set PxP, define (m,n)\approx(p,q) if m*q=p*n Show that \approx is an equivalence relation on PxP and list three elements in equivalence class for (1,2) Homework Equations The Attempt at a Solution I will appreciate any help how to start this problem...

Homework Statement Find relations that satisfying just Reflexive just Symmrtic just Transitive (R) & (S), but not (T) (R) & (T), but not (S) (S) & (T), but not (R) Homework Equations S=Z (a,b) \inR if <=> a>b (T) but, not (S) & (R). the ex is given in the class, but...

I'm curious about the famous formula, e=mc^2 . Since mass can be measured in any of several unit systems, shouldn't the formula read e\propto mc^2 ? Thanks!

Homework Statement question 1: Define ~ on Z by a ~ b if and only if 3a + b is multiple of 4. question 2: Let A = {1,2,3,4,5,6} and let S = P(A) (the power set of A). For a,b \in S define a ~ b if a and b have the same number of elements. Prove that ~ defines an equivalence...

Homework Statement Prove that when R and S are equivalence relations, then SR is equivalance relation when SR=RS. Homework Equations The Attempt at a Solution I want to know what sets should i take for the relations ? is it ok when i take R a a subset of X x Y and S as a...

This thread discusses an interesting point Jonathan Scott brought up at https://www.physicsforums.com/showthread.php?t=264782&page=2. A naive application of the equivalence principle (EP) would suggest that a free falling charge does not radiate, and that a charge on the surface of the Earth...

Please be nice to me, I'm new here. Anyway, help to solve this maths problem would be much appreciated: Homework Statement Work out a detailed proof (below) that the relation on the integers defined by p~q if and only if 7|p-q is an equivalence relation: a) the relation is reflexive b) the...

From equivalence principle, being on Earth is equivalent to being on lift accelerating at 9.8 m/s2...so if we are in a lift and that accelerates at 9.8 m/s2 then at some time we will cross the velocity of light.. my questions are 1) is Earth accelerating ? 2) what happens if the velocity...

Homework Statement Use the equivalence principle to explain the observation that a helium balloon leans forward in a forward-accelerating car. Homework Equations I don't think equations are needed. The Attempt at a Solution I'm completely confused on this question

Homework Statement There's this one exam problem that I cannot solve... Here it goes: Consider the set Z x Z+. Let R be the relation defined by the following: for (a,b) and (c,d) in ZxZ+, (a,b) R (c,d) if and only if ad = bc, where ab is the product of the two numbers a and b. a) Prove that...

Homework Statement A 20.00 ml stock sample of HBr is diluted to 50 mL. If 18.76 ml of 0.1345 M KOH was required to reach the equivalence point, what is the concentration of the stock HBr solution? Homework Equations KOH + HBr --> KBr + H20 M = conc. = mol./L n = V * conc. The...

Is the time dilation between two frames at different distances from a mass equivalent by some constant of proportionality to the time dilation between two frames in relative motion? For example: where r0 is the Schwarzschild radius and r is a radial coordinate greater than r0, this would be...

I was revising linear algebra and came across the topic of 'constructing complementary subspace given a subspace' - and since the proof (that used Zorn's lemma) of its (complementary subspace's) existence was not constructive, the author defined an equivalence relation in constructing a...

some of you will probly find this easy but this my first assignment after learning what a logical equivalence is so I can't warp my head around it. there are 2 problems I need help with. Homework Statement Find a compound proposition logically equivalent to p V q using only the logical...

My understanding is that, according to the Equivalence Principle, accelerated motion is indistinguishable from that of being in a gravitational field. So then, at the Event Horizon of a black hole, where gravity is too great for light to escape, wouldn't that be equivalent to accelerated motion...

For an weak acid/strong base titration, the pH at equivalence can be estimated by pH = pKa + pHtitrant/2. Can someone explain where that equation comes from? Thanks.