Equivalence Definition and 721 Threads

In the solution to a differential-equation problem -- proof of the existence of an integrating factor -- the following statements are made regarding a general function "u(xy)" [that is, a function of two variable that depends exclusively on the single factor "x*y"]...

Homework Statement Give the equivalence classes of the relation aRb if and only if a^4 ≡ b^4 (mod 30) on the set {1, 2, 3, . . . , 15}. Homework Equations Definition of modular arithmetic. Definition of equivalence class. The Attempt at a Solution I can successfully do this problem using...

Mentor Note: This thread has been separated out of a previous one to keep discussion of this particular topic open, since the previous thread has been closed. Sorry, the opportunity to ask questions is just too hard to resist. I'm still searching for the right understanding of equivalence. Or...

Its given in my textbook that equivalence of gas = (volume of gas) / (Volume of 1 eq. gas at NTP) How do i calculate volume occupied by 1 equivalent of gas? Example: What would be the volume occupied by 1 eq. of CO2 (Its given 11.2l in my book) Is there a formula for this?

Homework Statement If a relation R on N × N is (a,b)R(c,d) iff ad(b+c) = bc(a+d) Homework Equations -- The Attempt at a Solution I got the reflexive and symmetric parts but not the transitive part... here's what i have ## (a,b)(c,d)∈R and (c,d)(e,f)∈R## To prove ##(a,b)(e,f) ∈ R## .i.e...

We know that different models of the Reals are elementary equivalent but not isomorphic. In the hyperreals, we have that the Archimedean principle does not hold but it does hold in the standard Reals ( i.e., the hyperreals allow for the existence of indefinitely-small and indefinitely -large...

I am attempting to do a lab that requires the determination of an unknown diprotic acid using a titration curve. I have graphed my data but I am unsure what point to use as my eq. point. In my lab manual it says I may use the second or first eq. point but the second is often clearer. I am not...

Hello, I've to construct a proof of the following statement: Prove that if S is a set and S_1... S_k is a partition of S, then there is a unique equivalence relation on S that has the S_i as its equivalence classes. I'm really not sure how to go about this proof at all, so any help would be...

Prove that the following is an equivalence relation on the indicated set. Then describe the partition associated with the equivalence relation. 1. In Z, let m~n iff m-n is a multiple of 10.2. The attempt at a solution Reflexive: m-n = 0 0 ∈ Z, and 0 is a multiple of every number...

Heloo! :o I am looking at the equivalence between a NFA and a DFA. NFA: Q={q1,q2} DFA: Q`=P(Q} When $a\in \Sigma, Q_I, Q_j \in Q`$ which is sufficient and necessary condition so that $ Q_I \overset{a}{\rightarrow}Q_j$?

http://<a href="http://imgur.com/UwulXqg"><img src="http://i.imgur.com/UwulXqg.png" title="source: imgur.com" /></a>[/PLAIN] 1. Homework Statement Find equivalent capacitance of this formation from a to b, C1=4.1 uF, C2=6.86 uF, C3=5.03 uF, C4=5.92 uF http://imgur.com/UwulXqg Homework...

In formulating GR, Einstein was motivated by the otherwise strange coincidence of the equivalence of gravitational and inertial mass. He removed this by discovering that trajectories determined by gravitation are actually inertial. However, gravity's source is still the tensor T, which is...

Homework Statement I know that the principle of equivalence states that a person in a window-less box will not be able to tell if s(he) is in a stationary box on Earth or in a box that is accelerating upward at a constant rate. I am assuming that the acceleration of the rocket is 9.8 m/s^2...

Imagine an electric dipole with charges ##+q##, ##-q##, mass ##m## and size ##d##. Assume this dipole is oriented horizontally and is sitting at rest on top of some weighing scales on earth. As the charges are at rest the weight of the dipole is just ##-mg##. But by the principle of...

Apologies if this is in the wrong forum, but I chose to post here as the question pertains to equivalence relations and classes. Sorry if it's such a trivial question, but what is the mathematical difference between equivalence and equality? My understanding is the following, but I'm a little...

I'd like to see for myself the Equivalence Principle. Would there be a commercially available test kit like perhaps a small iron and cotton enclosed in vacuum tubes and they are to fall at same time and hit the bottom at same time with indicator lights to tell if they hit at same time or at bit...

Homework Statement Let * and = be defined by a*b means a - b is an element of the integers and a = b means that a - b is an element of the rationals. Suppose there is a mapping P: (* equivalence classes over the real numbers) --> (= equivalence classes over the real numbers). show that this...

I understand that a tangent vector, tangent to some point p on some n-dimensional manifold \mathcal{M} can defined in terms of an equivalence class of curves [\gamma] (where the curves are defined as \gamma: (a,b)\rightarrow U\subset\mathcal{M}, passing through said point, such that \gamma (0)=...

I am new to relativity, so bare with me. I do not want to argue against it; however, one must admit it is a rather awesomely unwieldy theory. In my self education on the subject, I am bothered by the Equivalence Principle, mainly this: An elevator accelerating through space is no different from...

Here are the 2 situations: Situation A: a person floating in space far away from any mass (i.e. the person is in zero-gravity environment) Situation B: a person undergoes a free-fall from the top of a roller coaster (assuming that there's no air resistance) My question is, would the person in...

Homework Statement This is not a homework problem per se, but I have been working on it for a few days, and cannot make the logical connection, so here it is: -- The problem is to show that ##\frac{1}{4\pi} \int_{-\infty}^{\infty} \frac{ e^{-\sqrt{\xi ^2 + \alpha^2 } |y-y'| + i \xi (x-x')...

This is probably a stupid question, but is there an equivalence between matter, energy and space time? Like for instance if you had a ball of 1 kilogram, could you convert it into volumetric space and have everything around it be further away? When two or more objects are going further away from...

Might sound like a stupid question, but if somebody could give me a mathematical description of the difference between equality and equivalence that might be really interesting.

Say we have an elevator moving through deep space at a constant velocity. We have a light emitter at the "top" of the elevator pointing towards a detector at the bottom of the elevator. We shine the light and notice that the frequency at which the light was emitted at the top is the same as...

http://www.sciencedaily.com/releases/2014/12/141219085153.htm It says "Here's a nice surprise: quantum physics is less complicated than we thought. An international team of researchers has demonstrated that two peculiar features of the quantum world previously considered distinct are different...

\begin{equation*}Let\text{ } (X,\mathcal{A} ,\mu ) \text{ }be \text{ }a \text{ }complete\text{ } \sigma -finite\text{ } measure\text{ } space \\and \text{ }Y \text{ }be \text{ }a \text{ }separable\text{ } Banach\text{ } space\text{ } supplied \text{ }with \text{ }the \text{ }norm\text{ }...

So I'm looking to find the distance light has traveled since matter - dark energy equivalence. Assume dark energy dominance from equivalence. Space-time has flat geometry and Ω0m = 0.315 , Ω0 = 1 Thus: Ω0Λ will equal Ω0 - Ω0m= 0.685 ρ0m (1 + zeq)3 = ρ0Λ where: ρ0m = ρ0c * Ω0m and: ρ0Λ =...

~(P<->Q) ⊣ ⊢ (P<->~Q) I'm suppose to write the proof for this equivalence but I can't figure it in either direction The closest I got was (P->~Q) from ~(P<->Q) but I can't figure anything else out

Hello! (Smile) We are given the set $E=\{d,e,f \}$, $d,e,f$ different from each other and the relation $I_{E}=\{ <x,x>: x \in E\}$. Prove that $I_{E}$ is a set. In addition, show that the relation $I_{E}$ is an equivalence relation in $E$ and find all the equivalence classes. That's what I...

Hi again! (Smile) If $\rho$ is an equivalence relation, could you explain me why the following relations stand? (Thinking) $I_A \subset \rho$ $\rho^{-1}=\rho$ $\rho \circ \rho \subset \rho$

Desloge (1989) published the article: ## '##Non-equivalence of a uniformly accelerating reference frame and a frame at rest in a uniform gravitational field## '##. His result, briefly resumed: a uniform gravitational field is not flat, is quite interesting. But the way he proves the result is...

Does anybody knows how you can reach one form of the divergence formula from the other? Or in general, why is the equivalence true?

The question was : describe the first law of thermodynamics. I said matter can't be created or destroyed. I got marked wrong, my argument will be that the laws of thermodynamics can be written in different ways. Einstein famous equation relates matter and energy. There is also the matter-energy...

Homework Statement For the circuit shown below, find the R equivalent resistance between terminals A and B. http://puu.sh/bX1Sp/33db39d1c0.png Homework Equations parallel and series circuit definition[/B]The Attempt at a Solution I admit that I don't even know where to begin with this...

Hello! In http://my.ece.ucsb.edu/York/Bobsclass/201C/Handouts/Chap1.pdf, pages 19-20, the Love's Theorem in Electromagnetism is declared. In presence of some electric sources \mathbf{J} and magnetic sources \mathbf{M} enclosed by an arbitrary geometrical surface S, which produce outside S a...

In the Wikipedia entry on mass-energy equivalence*, there is a reference to an elementary derivation of mass-energy equivalence in an article by Rohrlich (AJP 1990), which apparently expands on the original thought experiment by Einstein (ie observer in middle of moving train, light pulses...

Someone noted that the famous muon half-life experiment, supporting time dilation in SRT, seems to violate the equivalence principle of GRT. The very large radial acceleration in the experiment does not appear to cause any additional slowing. The acceleration does not seem to have an equivalent...

Hi, I have to prove the following logical equivalence using algebraic substitutions: (p v ~q) v ~q → (r v p) ∧ ~q ≡ ~r v q → (q v p) ∧ (~p v ~q) I've already done the truth table for this problem and proved they are logically equivalent but am not sure how to go about using algebraic...

The problem comes up as part of a final master's project in FEM analysis. The project consists in calculating the oscillation response of the World Trade Center towers after the plane impacts. The particular problem I'm having trouble is that I need to transform the plane impact of which mass...

Hi pf, I have recently watched a YouTube physics video from SixtySymbols channel which is a channel of short physics videos presented by professors of physics from Nottingham University. The video (pasted below) argues that because of inertial mass and gravitational mass being equivalent this...

I am not well versed in the idea of Higgs mechanism. However, I was wondering if it does explain the problem of equivalence of gravitational and inertial mass. Also, what is the modern accepted definition of mass?

Short answer: Mass and energy are NOT equivalent in general. Confusion can arise due to multiple definitions of mass (see our https://www.physicsforums.com/threads/what-is-relativistic-mass-and-why-it-is-not-used-much.796527/ ), but using the modern convention of identifying the word "mass"...

[SIZE="4"]Definition/Summary A relation on a set A is a set of ordered pairs (a,b) of elements ofA (a subset of A \times A). An equivalence relation \sim\ \subseteq A \times A is a relation which is reflexive, symmetric and transitive. In other words, the relation \sim on A is an...

Suppose we have a class equivalence relation ~ on a proper class C. Can we form the class of equivalence classes C/~? What axioms do we need, assuming we base ourself on NBG? I can't seem to prove that this class exists with the axioms stated. I.e., the proposition that there exists a class D...

I want to show that the group SU_L(N)\times SU_R(N) is the same as SU_V(N)\times SU_A(N) - i.e. that it is possible to rewrite the transformation: \begin{cases} \psi_L \to \psi'_L=V_L\,\psi_L\\ \psi_R \to \psi'_R=V_R\,\psi_R \end{cases} , where V_L and V_R are N\times N SU(N)...

Homework Statement Show that for a set A\subsetN, which is numerically equivalent to N=Z+, and the set B = A \cup{0}, it holds that A and B are numerically equivalent, i.e., that A \approxB Hint: Recall the definition of A≈B and use the fact that A is numerically equivalent to N. Note...

I am reading Paolo Aluffi's book Algebra: Chapter 0 which takes a (moderately) category theory oriented and infused approach to algebra. I am studying chapter 1: Set Theory and Categories and need help with formulating a definition of an epimorphism and with then proving it to be surjective...

"Resistors resist the passage of current through them." Then why the current through each resistor same in series combination? Suppose 'I' current is passing through a system of two resistors connected in series. 1. Won't the first resistor - which is directly connected to the positive...

Homework Statement We say that two sets A and B have the "same powerfulness" if there is a bijection from A to B. Show that the relation "have the same powerfulness" is an equivalence relation between sets. Homework Equations An equivalence relation satisfy the following: xRx...

I am looking for literature on a certain topic in mathematics inspired by string theory of which I have heard bits and pieces. Since I am not at all familiar with string theory and haven't found anything online, I was hoping someone more knowledgeable might recognize some of the keywords I...