Relations Definition and 540 Threads

Homework Statement Determine whether the relations on three sets are Reflexive, Irrelfexive, Symmetric,, Asymmetric, Antisymmetric, Transitive, and Intransitive. The relation \subseteq on a set of sets. Homework Equations The Attempt at a Solution I am having trouble figuring out...

I am taking a philosophy course that covers basic set theory as part of the introduction. I’m not sure in which section of the forum set theory should be, but I think this is the right place. Homework Statement For each of the following relations, indicate whether it is Reflexive...

I am studying set theory and I came across various definitions like equivalence relations, partial order relations, antisymmetric and many more. I am aware mathematicians don't care about real life applications but still - why are we defining so many relations? What is the use of defining...

Determine which of these relations are symmetric 1) x~y if and only if x-y is positive 2) x~y if and only if xy >= 0 3) x~y if and only if x+2y is positive 4) x~y if and only if x+y is positive 5) x~y if and only if x+y is odd I thought all but 1) but this was wrong. The only one I...

Homework Statement This question is about entropy of magnetic salts. I got up to the point of finding H1, the final applied field. The Attempt at a Solution But instead of doing integration I used this: dS = (∂S/∂H)*dH = (M0/4α)(ln 4)2 I removed the negative...

Homework Statement c) Is 'g' a surjective function (onto) ? Justify your answer. Homework Equations Let 'f' be a relation on ℤ (the set of integers) , defined by the entrance requirement : (x;y) ∊ ƒ iff y = x + 15 and let 'g' be the function on ℤ defined by the...

Homework Statement Determine the dom(g) Homework Equations Let 'f' be a relation on ℤ (the set of integers) , defined by the entrance requirement : (x;y) ∊ ƒ iff y = x + 15 and let 'g' be the function on ℤ defined by the entrance requirement : (x;y)...

Preface to my question: I can assure you this is not a homework question of any kind. I simply have a pedagogical fascination with physics outside of my own studies in school. Also, I did a quick search through the forum and could not find a question similar enough to what I want to know, so i...

Let G be a group and let H be a subgroup of G. Define ~ as a~b iff ab-1εH. Define ~~ as a~~b iff a-1bεH. The book I am using wanted us to prove that each was an equivalence relation, which was easy. Then, it asked if these equivalence relations were the same, if so, prove it. My initial...

Homework Statement Given some group G with generators g_{1},g_{2},...,g_{n} as well as a description of the action of g on the elements of some set S={s_{1},s_{2},...,s_{k}}, how in general does one go about finding a complete defining relations (and showing they are complete)? Homework...

If it's a dirac delta doesn't it mean it's infinite when x=y? Or is it a sort of kronecker where it's equal to one but the indices x and y are continuous? I'm confused.

Homework Statement Which of these relations on {0, 1, 2, 3} are equivalence relations? Determine the properties of an equivalence relation that the others lack a) { (0,0), (0,2), (2,0), (2,2), (2,3), (3,2), (3,3) } This one is not reflexive Homework Equations I understand that...

Homework Statement I am working through MacLane/Birkhoff's Algebra, and in the section on Symmetric and Alternating groups, the last few exercises deal with generators and Defining relations for Sn (the symmetric group of degree n). These read: 11. Prove that Sn is generated by the cycles (1...

Homework Statement I need to prove some relations but going round in circles. ## [\hat{J}_z, \hat{J}_+] = \hbar J_+ ## I've got this: ##\left(a_+^{\dagger }a_+-a_-^{\dagger }a_-\right)\left(a_+^{\dagger }a_-\right)-\left(a_+^{\dagger }a_-\right)\left(a_+^{\dagger }a_+-a_-^{\dagger...

Homework Statement Find the general solution to the following recurrence relations (defined n≥2). c) an=6an-1-9an-2+8n+4 Homework Equations The Attempt at a Solution an=6an-1-9an-2+8n+4 8n+4= an -6an-1+9an-2 R2-6R+9=0 R=3,3 So hn=A(3)n+B(3)n Assume pn=Cn+Cn2 → This is where I got...

Hi. I am reading Halmos's Naive Set Theory book. I have the following doubts. 1. In chapter 7. on relations, he says "The least exciting relation is the empty one. (To prove that ∅ is a set of ordered pairs, look for an element of ∅ that is not an ordered pair) ". Whenever someone talks...

Hello, I would like to check my arguments for this problem. Homework Statement Consider the relation R = \{(x,y) \in \mathbb{R} \times \mathbb{R}: x-y \in \mathbb{Z}\} on \mathbb{R} . Prove that this relation is symmetric, reflexive, and transitive. Homework Equations Supposing a relation...

Homework Statement Solve equations 1) and 2) for J_{p+1}(x) and J_{p-1}(x). Add and subtract these two equations to get 3) and 4). Homework Equations 1) \frac{d}{dx}[x^{p}J_{p}(x)] = x^{p}J_{p-1}(x) 2) \frac{d}{dx}[x^{-p}J_{p}(x)] = -x^{-p}J_{p+1}(x) 3) J_{p-1}(x) + J_{p+1}(x) =...

In book http://www.phy.uct.ac.za/people/horowitz/Teaching/lecturenotes.pdf in section 2 it is described transition from Poisson bracket into Canonical Commutation Relations. But it is written The experimentally observed phenomenon of incompatible measurements suggests that position and...

Weinberg in his 1st book on QFT writes in the paragraph containing 2.5.12 that we may choose the states with standard momentum to be orthonormal. Isn't that just true because the states with any momentum are chosen to be orthonormal by the usual orthonormalization process of quantum mechanics...

Homework Statement R = { (1,2), (3,5), (2,2), (2,5) } S = { (2,1), (5,3), (5,1), (5,5) } Explicitly find the relation R^-1 o S^-1 Homework Equations The Attempt at a Solution This was on my test. First I just wrote down the inverses: R^-1 = { (2,1), (5,3), (2,2), (5,2)...

Homework Statement Please see attached thumbnail Here's what I know. 1)Bk is the Hessian 2) sk = \alpha*p 3)pk is the search direction 4) Alpha is the step size Homework Equations yk = \nablaf(xk+1) -\nablaf(xk Bk+1(xk+1-xk) = \nablaf(xk+1) -\nablaf(xk The Attempt at a Solution...

Dear physicist, I designed an experiment for my undergraduate students. As we know, for spin operators, the commutation relation is [Si,Sj]=ihSk We also know, if we use two polarizers which are perpendicular each other, there is no light other side after polarizers. Namely apparatus is...

Hi. I've starting working with vectors in linear algebra but I need to have previous knowledge of equivalence relations so I started studying that but I have a simple doubt with the following relation: $$R = \{ (a,b)/a,b \in A,{\text{ a - b is an integer multiple of 2}}\} $$ In this case could...

Problem regarding "relations and functions". There are 3 very mini problems so I thought it would be rather fine to adjust them in a single thread. Homework Statement (i) Find the range of the function : f(x) = 2-3x , x\inR , x>0 Note : R is universal set containing real numbers in all the...

I need to verify these three work relations and don't know where to even start. Wtotal= ΔK, Wc= -ΔU and Wnc = ΔE The details for the whole problem were A block of mass m1 = 2.40 kg is connected to a second block of mass m2 = 1.80 kg, as shown in the figure. The two masses start from rest...

Hi all! I am searching for an algorithm (most likely already present in the literature) that could solve the following problem: Instance: Properties of sets of elements and relations between sets of elements Question: Find the closure of the properties and relations Possible properties...

Greetings, I wonder if a proof of the relation between the directional cosines of two vectors and cosine between two vectors is available? In order to clarify what I meant I put a screen shot from Vector and Tensor Analysis by Hay.

This question is going to be a bit vague and might lead to nowhere, but still I'll take the risk and try to ask it here. I know in general how to quantize a field, and from the quantized field one gets the quantized Hamitonian thus the time-evolution operator. However, I wonder what're the...

Homework Statement Hi. This is not a homework question per se, but more of a personal question, but I thought I'd post it here. I'm trying to prove the commutation relations of the Pauli-Lubanski pseudovector \begin{equation} W_\mu\equiv-\frac{1}{2}...

I'm confused with a question and wondered if anyone could help explain where I need to go... let x ε R. Prove that x is irrational thenI'm confused with a question and wondered if anyone could help explain where I need to go... let x ε R. Prove that x is irrational then ((5*x^(1/3))-2)/7)...

I need some topics to write about for my research paper. I'm writing about how computer science and technology both force the other to expand. The 3 examples I'm writing about now are hardware/processor enabled security (ie I'm comparing 16bit x86 which had no security to 32bit which did)...

In Tom Stoer's latest thread, he says "there is growing evidence that the incompleteness of the different approaches [LQG / canonical QGR / spin foams] has a common origin", and suprised suggests that "it may be that trying to quantize an effective theory will never work, ie., without...

Homework Statement Let L = Q(t) be the field of rational functions with one variable over Q. Consider the field automorphisms of L defined by a : t -> 1 - t and b : t -> 1/t . Find the relations. I will then be using this to find the size and abstract structure of the subgroup G of Aut(L)...

1. How do angle of launch, range, and flight time relate to one each other? 2.ΔX=vcosθ*t [b]3. According to the equation above,in my opinion as θ increases, range should decrease and time(t) should increase. Is there any other way of knowing the relation?

Homework Statement A plastic ball is inflated enough to produce tangential stresses. σX = σY = 2000Kpa The radial thickness of the material is 1.2mm brfore inflation. Find the thickness after inflation if the tensile modulus of elasticity is 3.4Gpa and the shear modulus is 1.4Gpa...

Homework Statement Using the position space representation, prove that: \left[L_i, x_j\right] = i\hbar\epsilon_{ijk}x_k . Similarly for \left[L_i, p_j\right] . Homework Equations Presumably, L_i = \epsilon_{ijk}x_jp_k . \left[x_i, p_j\right] = i\hbar\delta_{ij} . The Attempt at a...

Homework Statement Consider the polynomials: f(x) = x^{6} + x^{3} +1 and g(x) = x^{2} + x + 1 Denote the roots of f(x) = 0 by x_{1}, ... , x_{6}. Show that \sumg(x_{k}) = 6 , 1\leqk\leq6Homework Equations Vieta relations. The Attempt at a Solution Please correct any initial...

Homework Statement Are these two relations reflexive, antisymmetric, transitive? 1. (w,x)<=(y,z) iff w+x <= y+z 2. (w,x)<=(y,z) iff w+x <= y+z AND w<y Homework Equations The Attempt at a Solution 1. reflexive - yes; antisymmetric - no; transitive - yes; 2. reflexive -...

Ok, so I've been getting confused about some things recently. I've read that fluid flowing in a pipe at higher velocity has less pressure than one flowing slowly. So this means that the less pressure the fluid has, the more momentum it has as it has greater velocity. So suppose I were trying...

Definition: Proth number is a number of the form : k\cdot 2^n+1 where k is an odd positive integer and n is a positive integer such that : 2^n>k My question : If Proth number is prime number are there some other known relations in addition to 2^n>k , between exponent n and coefficient k ?

Homework Statement Let A and B be relations on the set C = {1,2,3,4,5,6}. Prove or disprove the following: If A and B are symmetric, then A U B is symmetric. Homework Equations The Attempt at a Solution The main problem is that I don't know how A U B is defined. In general...

Homework Statement The relation xRy is defined as "x has drawn a picture of y". R is on the set of all people. Is this relation: reflexive, irreflexive, symmetric, asymmetric, antisymmetric, transitive ? Homework Equations What confuses me about this problem is that there is uncertainty...

How can I formally demonstrate this relations with hermitian operators?(A^{\dagger})^{\dagger}=A (AB)^{\dagger}=B^{\dagger}A^{\dagger} \langle x|A^{\dagger}y \rangle=\langle y|Ax \rangle ^* If \ A \ is \ hermitian \ and \ invertible, \ then \ A^{-1} \ is \ hermitian I've tried to prove them...

Hello -- I have some reference object R (e.g. a protein), and I've got two transformations t1 and t2 (e.g. a transformation = quaternion + translation). In my case, t1 and t2 were obtained from symmetry operations. So after applying t1 to R I get object T1, and after applying t2 to R I get...

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 Find : a) acceleration of 1 kg, 2kg and 3 kg blocks and b) tensions T1 and T2 Note: In the figure, 1, 2 and 3 represent the masses of respective blocks in Kg. T1 and T2 represent tension in strings Homework Equations Newton's laws and constraint equations...

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...

Hi My calculus textbook is completely crap at explaining recurrence relations. I know the theorems needed to solve difference equations analytically, but I do not understand why they are true. What websites and/or books can I read to get a better intuitive understanding of recurrence...

Homework Statement [PLAIN]http://img193.imageshack.us/img193/820/unledoxy.png The Attempt at a Solution OKay I could interpret A as something like {{-...,-...}, {-1,-1}, {-1,-2}...{-1,1}...{1,-1}, {1,1}, {2,...}, {..., ...}} Just a lot of combinations of integers without 0...