Equivalence Definition and 747 Threads

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...

Hi, I'm reading a book on sets and it mentions a set B = {1,2,3,4} and it says that R3 = {(x, y) : x ∈ B ∧y ∈ B} What does that mean? Does that mean every possible combination in the set? Also the book doesn't clarify this completely but for example using the set B say i had another...

Hi, I'm having trouble understanding the concept of equivalence classes and would like some help on what it means to describe an equivalence class. Here is an example that I have deemed to be an equivalence relation but I have no idea about how I can descrive its equivalence class

Hi guys! First time poster, long time lurker! I can't make any sense out of equivalence relations:confused: These kinda questions crop up every year on the exam and I was wondering if someone could help me understand the concept behind them. (i)Show that relation R defined on the of the set S =...

We let C be the set of Cauchy sequences in \mathbb{Q} and define a relation \sim on C by (x_i) \sim (y_i) if and only if \lim_{n\to \infty}|x_n - y_n| = 0. Show that \sim is an equivalence relation on C. We were given a hint to use subsequences, but I don't think they are really necessary...

Homework Statement The problem states that a cube encloses charge. This cube is given in three space by <0,0,0> and <a,a,a>. The electric field is given by: \hat{E}=\frac{4e}{a^{2}e_{0}}[\frac{xy}{a^{2}}\hat{i}+\frac{(y-x)}{a}\hat{j}+\frac{xyz}{a^{2}}\hat{k}]. I am to find the total charge...

Homework Statement Let ## H = \{ 2^{m} : m \in Z\}## A relation R defined in ##Q^{+} ## by ##aRb ##, if ## \frac{a}{b} \in H## a.) Show that R is an equivalence Relation b.) Describe the elements in the equivalence class [3]. The Attempt at a Solution For part a, I think I am able to solve...

i don't have a specific question. i just need an explanation on what this topic is about. i am not understanding it

Homework Statement If you follow this link http://www.math.tamu.edu/~ciken/teaching/spring2014/math302/practice%20midterm%202.pdf There are several optional problems that have been posted for studying for my exam. I figured it would be easier to read the original than have me try to retype...

Hello! :) I have to find an equivalence class $[g] \in \mathbb{Z_{15}}^{*}$ so that each equivalence class $\in \mathbb{Z}^{*}_{15}$ is a power of $[g]$. $\mathbb{Z}^{*}_{15}=\{[1],[2],[4],[7],[8],[11],[13],[14]\}$ I tried several powers of the above classes,and I think that there is no...

Hi guys, please could someone tell me how this is equivalent and/or what the algebraic rule is? how is this: a/as + 1 is equivalent to this: 1/s+1/a Thanks a lot for your time and help

Homework Statement Theorem: Let f:[a, ∞)→ R. The following are equivalent. i) lim ƒ(x) = A as x→∞ ii) For all sequences {xn in [a,∞) with lim xn = ∞ we have lim f(xn) = A. Homework Equations For any ε > 0, |ƒ(x)-A| < ε if x < N The Attempt at a Solution I probably have this wrong, but I...

Greetings All - Per F=BIL I can calculate quantity of Force on coil (or magnet), when I draw certain amount of current from the generator. So I need help in calculating the Force and then weight equivalent of it. Let's say I have Single coil [with 300 turns] generator [wire length = 92...

Homework Statement A photon near the surface of the Earth travels a horizontal distance of 3 km. How far (in meters) does the photon 'fall' in this time? (Hint: think equivalence principle). Homework Equations N/A The Attempt at a Solution My understanding of the equivalence...

Hi, Please don't be spooked by the long post, it's just that it contains two problems (I beg your pardon if I shouldn't have put both in one post, I just figured it'll be better than creating two posts...). I can't figure how to solve these, so if you please could please help me with...

Homework Statement Let ##\mathbb{R}^2 = \{Q = (a,b) | a,b\in \mathbb{R}\}##. Prove that if ##q_1 = (a_1,b_1)## and ##q_2=(a_2,b_2)## are equivalent, meaning ##a_1^2+b_1^2 = a_2^2 +b_2^2##, then this gives an equivalence relation on ##\mathbb{R}^2##. What is ##[(1,0)]...

Hi! How this paper relates to the equivalence principle? http://arxiv.org/pdf/gr-qc/0701084.pdf "in contrast to the situation with static gravitational forces, the effects of accelerative gee-forces on the internal observer are increased"

How does potential energy fit into mass-energy equivalence in SR? As with all forms of energy, a potential energy of ##E## added to static system ought to increase the system's mass by ##E/c^2##. This is often illustrated by saying that a compressed spring has slightly more mass than an...

Homework Statement Write down the Lagrangian of a simple pendulum in terms of it's angle θ to the vertical suspended from a pivot attached to a moving carriage at constant velocity ##v##. Suppose that the carriage is now moving at a velocity ##v(t)=at## so it is accelerating uniformly. Show...

Hi I am reading Stephan Hawking's Universe in the Nutshell and there I didnt understand this sentence "This equivalence didn't work for a spherical Earth because people on opposite sides of the world would be getting farther away from each other.Einstein overcome this idea to make spacetime...

Hey everyone, I have three problems that I'm working on that are review questions for my Math Final. Homework Statement First Question: Determine if R is an equivalence relation: R = {(x,y) \in Z x Z | x - y =5} and find the equivalence classes. Is Z | R a partition? Homework...

I am given that the relation ~ is defined on the set of real numbers by \(x\)~\(y\) iff \(x^2=y^2\). First part of the problem said to prove ~ is an equivalence relation, that wasn't bad. The second part asks to "Describe the equivalence classes". This just seems really vague to me. Is this a...

Homework Statement Let A and B be two sets. Homework Equations Prove that there exists a injection from A to B if and only if there exists a surjection from B to A The Attempt at a Solution I did one implication which is we suppose that f: B→A is a surjection. Then by definition of a...

The following is a question regarding the derivation of Einstein's field equations. Background In deriving his equations, it is my understanding that Einstein equated the Einstein Tensor Gμv and the Cosmological Constant*Metric Tensor with the Stress Energy Momentum Tensor Tμv term simply...

Here is the question in attachment , I make it as the site don't support LaTeX I think! https://www.physicsforums.com/attachment.php?attachmentid=63439&stc=1&d=1383093152

Homework Statement Prove that replacing one equation in a system of linear equations by a non-zero multiple of itself does not change the solution of the system. The Attempt at a Solution I'm still relatively new to proofs, so this is what I have come up with: Let S be a system of...

Homework Statement Let f be a function from E to F . Prove that f is an injective function if and only if for all A and B subsets of P(E)^2. f(A\cap B)=f(A)\cap f(B) The Attempt at a Solution Well since we have "if and only if" that means we have an equivalences so for. \Rightarrow If f...

Homework Statement Prove that limx\rightarrowcf(x)=L if and only if limh\rightarrow0f(x+h)=L. Homework Equations The Attempt at a Solution I think this is a simple problem, but I am getting caught up in the middle, as I'm not sure if my procedure is a valid way to prove the...

On the set of Z of integers define a relation by writing m \triangleright n for m, n \in Z. m\trianglerightn if m-n is divisble by k, where k is a fixed integer. Show that the quotient set under this equivalence relation is: Z/\triangleright = {[0], [1], ... [k-1]} I'm a bit new the subject...

Hi my question is regarding the famous e=mc^2 equation. Clearly the equation has been proven valid through its various practical applications. My question is if energy = mass x the constant of the speed of light squared, where energy (e) is total energy release and mass (m) is total mass...

Homework Statement . Prove that a metric space X is discrete if and only if every function from X to an arbitrary metric space is continuous. The attempt at a solution. I didn't have problems to prove the implication discrete metric implies continuity. Let f:(X,δ)→(Y,d) where (Y,d) is...

Homework Statement Evaluate ∫(x^2-4)^(1/2) / x for x > 2 Homework Equations The Attempt at a Solution I was able to solve this problem via substitution, and my answer is: (x^2-4)^(1/2) - 2arcsec(x/2) + C. However, when I put the question into Wolfram Alpha, it gets this...

Hey, you know the way einstein said that its impossible to tell if you`re in a box that is accelerating or in a gravitational field? But, don`t accelerating charges radiate? so theoretically, by looking at these charges you could in fact tell the difference ? I dunno, maybe I`m missing...

I had a look at an online page for redox titrations (http://www.titrations.info/potentiometric-titration-equivalence-point-calculation). I can extend my understanding of that page far enough to say that for two half-reactions vA A + ve1 e- ⇔ vB B (vSpecies is the stoichiometric coefficient) and...

Hi all, Firstly, I do apologize if this is in the wrong forum or sub-forum, and if the title is a tad misleading, I wasn't quite sure how do phrase it. Onto the post, however, I am sure most if not all of you have seen the energy mass equivalence, e=mc^2 And there is also Einstein's...

If {{a,b},{c}} is the partition of {a,b,c}. When finding the equivalence relation used to generate a partition, is it enough to say {a,b}x{a,b} U {c}x{c}? Thanks Andy

Homework Statement Let A be a set, prove that the following statements are equivalent: 1) A is infinite 2) For every x in A, there exists a bijective function f from A to A\{x}. 3) For every {x1,...,xn} in A, there exists a bijective function from A to A\{x1,...xn} Relevant...

Hello all, I have an equivalence relation that I need some help with. Normally I find these to be fairly simple, however I'm not sure if I'm over-thinking this one or if it's just tricky. For the relation: aRb $\Longleftrightarrow$ |a| = |b| on $\mathbb{R}$ determine whether it is an...

I have a quick question, is the chemical potential $$\mu=\partial F /\partial N$$ where F is the free energy physically equivalent to a potential or energy? For example, in electrostatics, $$V=U/q$$ Does $$\mu_{ext}= U \text{ or } V$$ Also, same thing could be asked about gravity...

can you give an example of symmetric property of equality and transitive property of equality. the generalization of these properties are a bit abstract for me. thanks!

I have done reading on the momentum versus mass of light. However there is one issue which I'm still wondering about: When we use a magnesium lamp which is enclosed by a glas-bulb and ignite it, it will emit light during the chemical reaction. We know that two atoms have a higher mass when...

Hello, I have some questions about the truth tables for impliocation and equivalence. for implication we have: p | q | p=> q T | T | T T | F | F F | T | T F | F | T Here I do not understand the last two lines, how can we say that p implies q when...

Homework Statement Prove that the relation, two finite sets are equivalent if there is a one-to-one correspondence between them, is an equivalence relation on the collection S of all finite sets. I'm sure I know the gist of how to do it, but I'm a beginner in proofs, and I'm not sure if...

Sorry for some probably very basic questions, but here goes. If gravity equals acceleration, how is the Earth's gravity defined by acceleration? If an accelerating body distorts spacetime, as described in Einstein's thought experiment about a light beam shined through an accelerating box...

Homework Statement Let A be the set that contains all rational numbers, but not zero. Let (a,b),(c,d) \in A×A. Let (a,b)\tilde{}(c,d) if and only if ad = bc. Prove that \tilde{} is an equivalence relation on A×A.Homework Equations The Attempt at a Solution The solution just needs to show...