Equivalence Definition and 721 Threads

Homework Statement Consider the relation on \mathbb{N} given by aRb if there exists k \in \mathbb{Z} such that a/b = 2k. Give an example of two different equivalence classes (that is, find x, y \in \mathbb{N} such that Ex \neq Ey, where Ex and Ey are the equivalence classes of x and...

Homework Statement Prove or disprove that: \frac{{\sum_{i=0}^{ord_N (2) - 1}} (2^i \bmod N)}{N} Is equal to the number of odd residue classes of 2^x \bmod N for all odd numbers N greater than 1. Homework Equations Residue Classes are the residues that are generated by a function...

\exists{x}(P(x)\Rightarrow{Q(x)})\equiv{\forall{x}P(x)\Rightarrow{\exists{x}Q(x)}} I am able to derive this equivalence by using the standard equivalences of symbolic logic, but when I try to verify this semantically, with an example, I just can't see why these two expressions are equivalent...

Hi, So I came across this article on the internet, and it was about the Equivalence Principle. So I were interested and read it all, and in the article it said that the EP might be only approximately true. What interested me more about the article was it said that any theory of quantum...

Hello all . Is the paragraph right ? I think there are three mistakes in the sentences . First mistake is that mass and matter is not same and the text is not right . Second mistake is that energy can not transform to massive particles but it can convert to massive particles , because massive...

I've been giving some thought to the new scientist article about the equivalence principle. What initially seems like a very simple issue is remarkably tantalising. (please note- I'm not a physicist so this may be quite stupid) This led me on a little to the question of gravity and direction...

What’s your understanding of the principle of equivalence? In the literature, I find two meanings: (1) Gravitational mass is numerically equal to inertial “mass.” (This is a postulate.) (2) A mass at rest in a frame is equivalent to being in a “gravitational field” in an accelerated frame...

Homework Statement 'Show that row equivalence is an equivalence relation'. Homework Equations The definition for 'row equivalence' given in the text is, 'two augmented matrices corresponding to linear systems that actually have solutions, are said to be (row) equivalent if they have the...

\RightarrowHomework Statement I'm given two statements, p and (q\Rightarrowr) and I need to prove that the two statements are equivalent. So I need to show that p \Leftrightarrow(q\Rightarrowr) I know that p\Rightarrow(q\Rightarrowr) \Leftrightarrow (p\wedgeq)\Rightarrowr but I don't know...

Homework Statement I've been trying to prove the equivalence between the two statements for quite a while now, any ideas? (A+C)(B+C') = BC + AC' Homework Equations The Attempt at a Solution I used the distributive property to simplify the LHS to AB + BC + AC' Unsure what...

Homework Statement let X = {1,2,3,..,10} define a relation R on X x X by (a,b)R(c,d) if ad=bc. show that R is an equivalence relation on X x X. Homework Equations The Attempt at a Solution I think that the R have to be reflexive (because ad=bc). Eg. one of the subset is (1,1)...

Homework Statement A particle of mass ##m## is projected from ##x(0) = x_o## in the vertical direction, with an initial velocity, ##\dot{x}(0) = v_o##. It is subject to gravity and linear drag, mk|v|, against the motion. 1) Show that the body follows ##v(t)## such that:$$v(t) = -g/k + (v_o...

Hello hello, I'm not looking just for an answer per say, but am also wondering the thought process in solving problems such as the following: Hopefully this doesn't take up too much of someones time. Determine whether the following equations are logically equivalent: 1) (∃x)( P(x) →...

I have just began my journey in General Theory of relativity through the book of Weinberg-Gravitation and cosmology principles and applications of the general theory of relativity I don't know if this topic is just a repeat of an older one, if it is please let me know the link to it... I...

If 25.00 mL of 0.20 mol/L HCO2H(aq) is titrated with 0.26 mol/L NaOH(aq) determine the pH at halfway to the equivalence point. So far I have: Moles of HCO2H = 0.005 mol; at half way = 0.0025 I don't know the next step.

Homework Statement I have a lagrangian written as: \mathcal{L}_H = \text{Tr}\left[\,(D_\mu \Phi)^\dagger D^\mu \Phi\right] - \mu^2 \text{Tr}\left[\,\Phi^\dagger \Phi\right] - \lambda (\text{Tr}\left[\,\Phi^\dagger \Phi\right])^2 Where the field is: \Phi \equiv \frac{1}{\sqrt{2}}(i...

Does a uniformly accelerated charged particle radiate em waves? The equivalence principle says that a particle in uniform acceleration is equivalent to a particle at rest in a gravitational field. A particle at rest in a gravitational field is clearly not going to radiate em waves therefore by...

Simple algebra to find the strict mass–energy equivalence formula, and I can't do it! find ((m^2)*(c^4)=(E^2)-(p^2*c^2)) from (E=m*c^2*y) (p=m*y*v) (y=1/(1-(v^2/c^2))^(1/2)) Yeh i can find the m^2c^4 parts and the E^2 obvioulsy. but then i am stuck with E^2(v^2/c^2) when instead i want...

I'm reading a book wherein the Earth's rotation is supposedly slowing down. The author claims that a ball thrown in the air would fall faster and harder... But if the rotation slows, wouldn't the equivalence principle say that the smaller acceleration could also be interpreted as a smaller force...

I was having a discussion with an individual who was claiming that information is a form of energy. I disagreed with that claim. Over the course of the conversation, he provided me with the following article http://physicsworld.com/cws/article/news/2010/nov/19/information-converted-to-energy...

Homework Statement An unknown amount of mass lost from a fusion reaction is converted to energy. Determine the amount of mass equal to 17.6 MeV of energy. Homework Equations E=mc2? The Attempt at a Solution 17.6=m(931.5) m=0.01889u Not sure if this is correct

We recently started learning about special relativity. Today my teacher said that ET = E0 + EK when talking about masses in motion. So what is the name for the energy stored in mass? We have already learned about kinetic, gravitational, elastic, magnetic and I'm sure I forgot a few.

Given a group G acting on a set X we get an equivalence relation R on X by xRy iff x is in the orbit of y. My question is, does some form of "reciprocal" always work in the following sense: given a set X with an equivalence relation R defined on it, does it always exist some group G with some...

Homework Statement Normed space (l^\infty,\|\cdot\|_\infty) with subspace S\subset l^\infty consisting of convergent sequences x=(x_n)_{n\in\mathbb{N}}. Given a sequence of maps A_n:l^\infty\to\mathbb{R} defined as $$A_n(x)=\sup_{i\in\mathbb{N}}\frac{1}{n}\sum_{j=0}^{n-1}x_{i+j}$$need to...

Homework Statement The question is let E1 and E2 be equivalence relations on set X. A new relation R is defined as the E1 o E2, the composition of the two relations. We must prove or disprove that R is an equivalence relation.Homework Equations The Attempt at a Solution I know that we must...

Homework Statement Let f:X→Y where X and Y are sets. Prove that if {S\alpha}\alpha\inI is a collection of subsets of Y, then f-1(\cup\alpha\inIS\alpha)=\cup\alpha\inIf-1(S\alpha) Would I prove this by showing set inclusion both ways? And any hints on how to begin? Thanks.

Show that if R1 and R2 are equivalence relations on a set X, then R1 is a subset of R2 iff every R2-class is the union of R1 classes. Attempt: I don't understand that if R2 has elements nothing to do with the elements of R1, how can an R2 class be a union of those elements belonging to an R1...

Homework Statement While doing a physics assignment today, I came up with an expression in my answer that appears to be equivalent to sin(θ), however, i couldn't find a way to manipulate the expression to prove that it was. Could anyone point me in the right direction as to a way that I could...

Homework Statement Fe[3+]+V[2+]-->Fe[2+]+V[3+] If you start with 0.1000 M solutions and the first-named species is the titrant, what will be the concentration of each reactant and product at the equivalence point of the titrations above? Assume that there is no change in [H+] during the...

1. Energy is proportional to mass. 2. Mass (of nucleus) is proportional to volume. 3. Volume can be determined from cross-sectional area. If this is the case, then is E=mc^2 equivalent to kE=(pi)r^2 where r is the radius of the nucleus and k is some constant?

Is it true that: If A is not equivalent to its subset A1. Then A is not equivalent to any subset of A1?

Hi. I've seen a video by MinutePhysics that talked about the mass-energy equivalence equation, usually known as E=mc^2. It said that there is an extra part to it, and I didn't really understand what it meant. (E^2)=((mc^2)^2)+((pc)^2) seems to be the full one (p being momentum) So...

Hello I have a problem in understanding wave functions Let q \mapsto \phi(q) a position wave function for a single particle of mass m The equivalent momentum wave function is said to be computable with using Fourier transform: \psi : p \mapsto \int_q \phi(q) \cdot e^{-i/\hbar \cdot \langle p...

Homework Statement Find the digital filter equivalence of the circuit in a difference equation formHomework Equations Is this the difference equation form?The Attempt at a Solution If that is the proper form.. I think this is how to solve it? I got this example from my textbook I'm just not...

It would be helpful if someone could please explain topological equivalence of functions in simple words? I am working on dynamical systems and chaos theory.In the underlying material,topological equivalence has taken a more complex definition involving orbits.Please be kind enough to explain...

I have read the basis of the the equivalence principle, that inertial mass = gravitational mass, and that it leads to the conclusion that any acceleration = equivalent gravitational field intensity. (I believe 'gravitational field intensity' is the same as 'gravitational acceleration'.)...

This really isn't a homework question per se, but I really don't want to post in the big boys' fora. I am learning about basic modern physics at school, as the title suggests, but I am very confused on one matter. Take the tritium nucleus as an example. If tritium nucleons are separate...

I am having a difficult time seeing how \sum_{n=0}^{\infty} ((-1)^n + 1)x^n is equivalent to 2\sum_{n=0}^{\infty} x^{2n}

Suppose a square matrix A is given. Is it true that the null space of A corresponds to eigenvectors of A being associated with its zero eigenvalue? I'm a bit confused with the terms 'algebraic and geometric multiplicity' of eigenvalues related to the previous statement? How does this affect the...

Ok, I am barely beginning to understand the subject. I understand that the relation ≥ on N(naturals) is reflexive, not symmetric, and transitive. I don't understand why it is transitive though. Can someone explain? Also, I understand why x2 = y2 is reflexive and symmetric, but I don't...

I was just wondering if our use of a flat Minkowski background metric when looking at gravitational radiation in the weak-field limit is essentially done so that locally, for example with detectors on Earth, we can treat spacetime as being flat, but on a larger scale we use the equivalence...

While I was looking up E=mc^{2}, I have learned such formula only applies to stationary objects and for kinetic object, the formula is this: E_{r}=\sqrt{(m_{0}c^{2})^{2}+(pc)^{2}} Where E_{r} is relativistic energy and m_{0} is rest mass In the formula, what is p and what is (pc)^{2}...

Our math Teacher asked us to find how many equivalence relations are there in a set of 4 elements, the set given is A={a,b,c,d} I found the solution to this problem there are 15 different ways to find an equivalence relation, but solving the problem, i looked in Internet that the number of...

Our math Teacher asked us to find how many equivalence relations are there in a set of 4 elements, the set given is A={a,b,c,d} I found the solution to this problem there are 15 different ways to find an equivalence relation, but solving the problem, i looked in Internet that the number of...

Mass energy equivalence question Hi I'm just wondering how energy is equivalence to the mass if E=mc ^2. I don't understand why you must times it by the speed of the light^2. And if the mass is proportional to the gravity, is it right to consider gravity as energy?

Homework Statement ~ is a equivalence relation on integers defined as: a~b if and only if 2a+3b is divisible by 5 What is the equivalence class of 0 Homework Equations The Attempt at a Solution [0] = {0, 5n} n is an integer My reasoning for choosing 0 is that if a=0...

Homework Statement Relation on set of integers. a~b if and only if 2a+3b is divisible by 5 show that ~ is an equivalence relation Homework Equations The Attempt at a Solution I have already proved that the relation is reflexive and symmetric, but I'm unsure of my approach...

Equivalence Principle: A hint on how to start! Hi, I have no idea where to start. 1. Statement Problem Let X be a non empty set with a equivalence relation ~ on it. Prove that for all x,y\inX, [x]=[y] if and only if x~y. Homework Equations For the Equivalence Relation to exist, it...

imagine we rotate a vector centered at the origin with euler angles alpha,beta,gamma. now the question is, can we do this rotation by the means of defining a vector N(which its length is 1).and rotating the vector zeta radians counter clockwise around N? I think it must be possible and I want...

Since all the observables in QM is on the form \langle \alpha |A| \beta \rangle where A is an observable, one can transform the observables and states like A \to A' = UAU^{-1} \ \ \ |\beta \rangle \to |\beta '\rangle = U |\beta \rangle where U is a unitary transformatioin. These...