Equivalence Definition and 721 Threads

given closed subsets, A and B, of R^d with A bounded prove the equivalence of: 1) There exists a pair of sequences x_n in A and y_n in B such that |x_n - y_n| -> 0 as n -> infinity 2) A intersection B is non empty. I have attempted this question but am a bit stuck on proving 1 implies 2...

Homework Statement Let f : A → B be a function and let Γ ⊂ B × B be an equivalence relation on B. Prove that the set (f × f)^-1 (Γ) ⊂ A × A (this can be described as {(a, a′) ∈ A × A|(f(a), f(a′)) ∈ Γ}) is an equivalence relation on A.Homework Equations The Attempt at a Solution Let...

Firstly: Does anyone know at our current level of technology what "small enough not to detect tidal forces" equates to? Near the surface of the earth(as it probably depends on the amount of curvature of space). Secondly: Does anyone know at out current level of technology what the minimum...

show that P \leftrightarrow Q is equal to (P\wedgeQ) \vee (\negP \wedge\negQ) (P→Q) \wedge (Q→P) (\negP\veeQ) \wedge (\negQ\veeP) [\neg(P\wedge\negQ)\wedge\neg(Q\wedge\negP)] \neg[(P\wedge\negQ)\vee(Q\wedge\negP)] I don't know which law to use from this point on to prove the...

Hi friends, sorry that i have posted so many threads recently regarding complex analysis. i am trying hard to understand as much as possible.anyway i was wondering if anyone had any good geometric interpretation for the equivalence between a differential being exact and it being path...

(x1, y1)Υ(x2, y2) ⇔ x1 × y2 = x2 × y1 for all x1, x2 ∈ Z and y1, y2 ∈ Z+ have been shown to be an equivalence relation in tutorial. Specify the equivalence class [(2; 3)] as induced by Υ. i don't understand what it means by 'Specify the equivalence class [(2; 3)] as induced by Υ.'...

Homework Statement If f ∈ C(R) with f(0) ≠ 0, show that there exisits a g ∈ C(R) such that [fg] = [1], where [1] denotes the equivalence class containing the constant function 1. Homework Equations The Attempt at a Solution Let f ∈ C(R) such that f:R → R is defined as f(x) = 1/x...

Homework Statement prove that if a~a' then a+b ~ a' + b Homework Equations The Attempt at a Solution I can prove that if a=a' then a+b = a' + b but how can I apply this to any equivalence relation

Homework Statement Define a relation on R as follows. For a,b ∈ R, a ∼ b if a−b ∈ Z. Prove that this is an equivalence relation. Can you identify the set of equivalence classes with the unit circle in a natural way? Homework Equations The Attempt at a Solution I have already proven that this...

let be the function \sum_{\rho} (\rho )^{-1} =Z and let be the sum S= \sum_{\gamma}\frac{1}{1/4+ \gamma ^{2}} here 'gamma' runs over the imaginary part of the Riemann Zeros then is the Riemann Hypothesis equivalent to the assertion that S=2Z ??

Homework Statement Prove: If E1, · · · , Ek are the disjoint equivalence classes determined by an equivalence relation R over a set X, then (a) X = union of disjoint equivalence classes Ej (b) R = union of disjoint (Ej x Ej) Homework Equations R is a subset of X x X The Attempt at a Solution...

I'm not sure if I did these 2 questions correctly, so would someone please check my work for any missing ideas or errors? Question 1: Homework Statement Prove: For every x belongs to X, TR∩S(x) = TR(x) ∩ TS(x) Homework Equations The Attempt at a Solution TR(x) = {x belongs to X such that...

Homework Statement Given: R is an equivalence relation over a nonempty set X Prove: dom(R) = X and range(R) = XHomework EquationsThe Attempt at a Solution I have the following thoughts: About the given: Since R is an equivalence relation over X by hypothesis, R satisfies: Reflexivity: <x,x>...

Homework Statement Given: A relation R over N x N ((x,y), (u,v)) belongs to R. i.e (x, y) ~ (u,v) If max(x,y) = max(u,v), given that max(x,y) = x if x >= y = y if x < y Prove that R is an equivalence relationHomework Equations I know that to prove an equivalence...

Homework Statement Suppose R and S are relations on a set A, and S is an equivalence relation. We will say that R is compatible with S if for all w,x,y,z ∈ A, if (w,y) ∈ S and (x,z) ∈ S, then (w,x) ∈ R iff (y,z) ∈ R. Prove that if R is compatible with S, then there is a unique relation T...

I've always been interested in Physics so have finally decided to do a Physics degree. I've been reading various things to help prepare myself and have just been reading about the laws of thermodynamics and mass-energy equivalence. As I'm reading through different articles about these subjects...

Homework Statement Suppose B ⊆ A and define a relation R on P(A) as follows: R = {(X,Y) ∈ P(A) x P(A) | (X∆Y) ⊆ B} a) Show that R is an equivalence relation on P(A). b) Prove that for every X ∈ P(A) there is exactly one Y ∈ [X]R such that Y ∩ B = { }. *P(A) is the powerset of A...

Can anyone please help me with this because I'm really getting confused. Thanks! In R, we know that fine topology is equivalent to the Euclidean topology as convex functions are continuous. Now if instead of R we consider a subset of it say [0,1], the fine topology induced on [0,1] would...

Homework Statement Decide if the following are Equivalence relations and if so describe their classes i) a\equiv b if 2 divides a^2+b^2 ii) a\equiv b if 2b\geq a Homework Equations The Attempt at a Solution ii) isn't an equivalence relation. it is reflexive but not...

Homework Statement Deciede if the following are equivalence relations on Z. If so desribe the eqivalence classes i) a\equiv b if \left|a\right| = \left|b\right| ii) a\equiv b if b=a-2 Homework Equations The Attempt at a Solution i) \left|a\right| = \left|a\right| so its...

Let Q be the group of rational numbers with respect to addition. We define a relation R on Q via aRb if and only if a − b is an even integer. Prove that this is an equivalence relation. I am very stumped with this and would welcome any help Thank you

Let me restate my problem in a more clear way i think. Situation A: a accelerated rocket in flat spacetime. the observer in the rocket could think he is in a gravitation field equivalently.All experiments he do are like in a gravitation field downward. SituationB: a apple falls down under...

Pair-production is the event when a particle and anti-particle is created from a single photon. We don't see 2 or more photons participating in a single pair-production event. Further, it seems in all the events of energy-mass conversion, photons act independently. Two or more photons can...

defining a tangent vector v as the equivalence class of of curves: v = [\sigma] = \left. \frac{df(\sigma)}{dt} \right|_{t=0}, i want to show that this definition is independent of the member of the equivalence class that i choose. where \sigma represents a function from the reals to the...

My book says that you cannot use the Henderson-Hasselbalch equation to find the pH at the equivalence point when titrating a weak acid with a strong base... I was wondering why not? it says that instead you must use the Kb of the conjugate base and that we find that from the Kw and the Ka...

Read about this experiment and the results obtained: http://www.physorg.com/news/2011-07-gyroscope-unexplained-due-inertia.html What's going on here? Why is the laser gyro accelerating? If this effect proves to be reproducible, would it not indicate the violability of the so-called...

Bosoms (energy'ish) are 1 spin integers, Fermions (mass'ish) are 1/2 spin integers. KE=1/2MV^2 E=1MV^2 I've only been trying to wrap my puny mind around spin for longer than 10 years, these spins creates magnetic poles right? In all 3 dimensions?

Are there any good, preferably tutorial, papers on equivalence classes with regards to theories of physics, and how they relate to units? Specifically, I'm looking for something that discusses that if you formulate the laws of physics in feet, then convert the units to inches, you haven't...

Hello, In a previous discussion of Pair production I was shocked by what I heard and I have some questions from the general explanation of the subject. So you can make fermions out of bosons? You can make rest mass out of energy? Does this mean that not just relativistic mass, but...

Homework Statement This was done in a lab, we titrated 0.2M NaOH with an unknown concentration of acetic acid. I've used excel to graph my first derivative of the data. Homework Equations (change in pH)/(Change in volume) The Attempt at a Solution My professor talked about drawing two trend...

Homework Statement Lets say I have the word mississippi . Would I then say that I have 11 elements in my multiset . And would I say that I have 4 equivalence classes because I only have 4 different letters. If I had the set A={1,2,3,} Would I say this has 3 different...

I was reading WikiPedia's entry on this, and there was one paragraph that surprised me: E = mc2 has sometimes been used as an explanation for the origin of energy in nuclear processes, but mass–energy equivalence does not explain the origin of such energies. Instead, this relationship merely...

I found 2 tables describing raising precision in experiments performed to investigate Equivalence Principle: http://en.wikipedia.org/wiki/Equivalence_principle#Tests_of_the_weak_equivalence_principle http://en.wikipedia.org/wiki/Hughes%E2%80%93Drever_experiment#Modern_experiments I can't...

Please help me prove that the following properties are equivalent Nested Interval Property Bolzano-Wierstrass theorem Monotonic sequence property LUB property Heine-Borel theorem archimedean property and cauchy sequence line connectedness...

I understand energy mass equivalence, but when mass is changed to energy what happens to it's gravitational field?

in my textbook it say that a frame which move at constant velocity in deep space and a frame under free fall in uniform gravitational field will be Equivalent. There is no experiement that observer can do to see whether he is in which of the two frame. But it later say that light bent in...

From another thread this question came up: What about tidal forces? Although they could be incredibly small (and I don't think anyone denies they exist) you could conceive of a test in a closed room that detects tidal forces (if it is gravity) and when it doesn't detect them it is uniform...

Hello everyone! I am not able to understand Chemical Equivalence? The bookish language is very hard to understand... If someone could explain me the Concept Of Equilvalence, it would be very helpful for me... Thanks, Pranav

A charged particle is held at rest inside a box in gravity-free space. The box is accelerated uniformly. The charge theoretically radiates electromagnetic power. Now picture the same box held at rest in a gravitational field. Does the charge radiate?

Hello all. I've been thinking a lot about the Equivalence Principle as it has been taught to me: "The effects of the acceleration (vector) a of a referential are indistinguishable of those of a gravitational field (vector) g=-a". The same book has the phrase: "There is no experience that...

I am just trying to understanding of the equivalence principle and was hoping someone would be kind enough to sense check my thoughts below. 1) If I was in a rocket ship accelerating at a rate of 1g relative to the earth, the clock on my ship would tick at the same rate as a clock on the...

Many textbooks state the principle of equivalence as such: There is no experiment that can be done inside a small closed space, such as a box, that would allow an observer inside the box to distinguish between being in a uniformly accelerated box or being in a box that is at rest on the surface...

Homework Statement Let f: R -> R, x -> x^2 What does the partition for the equivalence relation of this function look like? Homework Equations The Attempt at a Solution Uh...I have no idea. Sorry, the book only has examples of like integers from modulo n, if anybody could...

Homework Statement Suppose there exist three functions: f:A\stackrel{1-1}{\rightarrow}B g:B\stackrel{1-1}{\rightarrow}C h:C\stackrel{1-1}{\rightarrow}A Prove A\approxB\approxC Do not assume the functions map onto their codomains. Homework Equations The Attempt at a Solution I took a...

In another thread, it's considered a generally accepted fact that the WEP is not valid anymore the way it was initially postulated: I find this surprising, because such a change in the principles of the theory should be more stressed in introductory GR textbooks, and kind of disturbing...

Homework Statement The spontaneous fission rate for U-238 is roughly 1 fission per gram per 100 seconds. Show that this rate is the equivalent to a half-life for spontaneous fission of ~5.5x1015 years Homework Equations none that I can find in my book The Attempt at a Solution I'm...

Homework Statement [PLAIN]http://img15.imageshack.us/img15/1/unledjs.png Homework Equations The Attempt at a Solution Hi, If anyone could help me with this I would be very glad! I have said that M=(aij) and M^T=M^-1 therefore if e1 relates v, where v=(x,y,z) then...

Homework Statement 1. What volume of .022M HCl must be added to the 110ml buffer solution to completely react with the ammonia (NH3) to reach equivalence. Then, what is the pH of this at the equivalence point. Buffer solution (equilibrium): [SIZE="4"]NH3 + H20 ⇌ NH4+ + OH- Other Info...

Homework Statement Hecht in his optics mentions that Asin(kx-wt+pi) is equivalent to Asin(wt-kx) w=greek omega Homework Equations What is the fundamental reason behind this? The Attempt at a Solution I have a hunch it's plain trigonometry applied, but none of the things that I can...

Homework Statement Prove or disprove and salvage if possible: for [a], [b] ∈ Zn for a positive integer n, if [a]·[b]=[0], then either [a]=[0] or [b]=[0]. The Attempt at a Solution I've managed to disprove the statement: Let n=6,[a]=3,and[b]=[4]. The[a]·[b]=[ab]=[3·4]=[12]...