What is Equivalence: Definition and 744 Discussions
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The relation "is equal to" is the canonical example of an equivalence relation.
Each equivalence relation provides a partition of the underlying set into disjoint equivalence classes. Two elements of the given set are equivalent to each other, if and only if they belong to the same equivalence class.
Homework Statement
A particle has a mass of 4.032u. What is its mass in MeV/c2
Homework Equations
The Attempt at a Solution
4.032u = 4.032 * 1.66*10-27 = 6.69*10-27 kg
Energy equivalent, E = mc2: = (6.69*10-27)*(3*108)2 = 6.02 *10-10J
J→eV (divide by 1.6∗10-19) )=3.76∗109...
Hi all,
Let λ>0 and define an equivalence relation on ℝn-{0} by
(x~y) \Leftrightarrow (there is an s\inZ such that λsx=y)
I would like to know what the quotient space ℝn-{0}/~ looks like. I know that it is a set of equivalence classes.
To understand it better I wanted to see how it...
So this is problem 11.1 out of Jackson Electrodynamics:
Two equivalent intertial frames K and K' are such that K' moves in the positive x direction with speed v as seen from K. The spatial coordinate axes in K' are parallel to those in K and the two origins are coincident at times t=t'=0. (a)...
Homework Statement
Determine whether the given relation is an equivalence relation on the set. Describe the partition arising from each equivalence relation:
xRy in ℝ if x≥y
Homework Equations
Reflexive: for all x in X, x~x
Symmetric: for all x,y in X, if x~y, then y~x
Transitive...
Homework Statement
I'm trying to prove that Electric field away from a line segment of charge, is equivalent to the field away from a point charge, provided I observe from far enough.
Homework Equations
Ignoring all the constants:
potential_line = log( (sqrt(r^2 + a^2) + a) /...
Homework Statement
Let 1\leq s<r<\infty. For what pairs s,r the norms \left\|\cdot\right\|_{s},\left\|\cdot\right\|_{r} are equivalent?
Homework Equations
I have already proven that \left\|\cdot\right\|_{s}\leq (b-a)^{\frac{r-s}{rs}}\left\|\cdot\right\|_{r} and that...
URGENT HELP: Equivalence of NFA's with plugin DFA's
Homework Statement
Hello guys!
I have been thinking about this problem for weeks and I'm still not sure if the problem is decidable or not. Basically it asks there are NFA's with states that can be substituted to DFA's. Given two such NFA's...
This really isn't one specific problem per se as it is more of a conceptual issue, so I apologize for breaking away from the given format.
I've worked through three problems involving a circuit where a thevenin equivalence circuit is required between two points, and all sources are dependent...
Hello! I've found this paper, wherein page 33 states that the reverse Poincaré inequality gives
\forall v \in H^1_0(\Omega) , \|v\|_{L^2(\Omega)} \leq C(\Omega) \|\nabla v\|_{L^2(\Omega)}
This I can follow - it gives a norm equivalence between the norm of a vector and the gradient of its...
A charged battery should have a mass a little greater than a depleted battery. Surely that is measurable. So does a live person have greater mass than his or her dead equivalent? Surely that is a 2nd law of thermodynamics that would be revealing. Or is the entropy of life so small that it is...
NOte this is not a homework nor related to any course nor any test problem etc. - entirely my own interest and study.
Re\: text by Biedenharn and Louck "Angular momentum in Q.Physics" . I derive an expression for the norm squared wrt a certain expression in Boson calculus. You don't really...
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...
Homework Statement
Define a relation ~ on ℝ by
a~b if and only if a-b∈Q.
i) Show that ~ is an equivalence relation.
ii) Show that
[a]+=[a+b]
is a well-defined addition on the set of equivalence classes.
Homework Equations
Q represents the set of rational numbers.
An Equivalence...
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
Show for the z-component of the curl of a vector function that the integral off this over an infinitesimal rectangle in the x-y plane is equal to the contour integral of the original vector function around the perimeter.
Homework Equations
Short of explaining how to...
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...
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...