Set Definition and 1000 Threads

Hi I am trying to find the equations of a charged particle inside a dipole & quadripole. Practically, I need to write a simulation program for it which assumes a beam passing through a dipole-quadripole-dipole which are setting around an arc. Is there some recommended literature ? Of course...

For those who have read Halmos, in Section 6 Ordered Pairs (page 23 in my book), he gives a non-trivial exercise to find an intrinsic characterization of those sets of subsets of A that correspond to some order in A. I'm curious what that characterization is. A is suppose to be a quadruple...

Hi - Glad to have found this forum. I am looking for a book which contains LOTS of Set Theory word problems with solutions. Anyone aware of a good resource? Thanks in advance.

Homework Statement Theorm 1: If M is a monoid, the set of M* of all units in M is a group using the operation of M, called the group of units of M. My question is this always a "real" group? for example, is this 'group' always closed under the binary operation? Homework Equations...

Homework Statement Prove that the set of all algebraic numbers is a countable set. Solution: Algebraic numbers are solutions to polynomial equations of the form a_0 x^n + a_1 x^(n – 1) + . . . + a_n = 0 where a_0, a_1, . . . , a_n are integers. Let P = |a_0| + |a_1| + . . . + |a_n| + n...

Let B be the non empty sets, B ={(x,y):y = e^x, x belongs to set of real numbers} Write the set in roster form.

Homework Statement (Verbatim) A particle moves with speed .9c along the x'' axis of frame S'', which moves with speed .9c in the positive x'-direction relative to frame S'. Frame S' moves with speed .9c, in the positive x-direction, relative to S. a.) Find the speed of the particle relative to...

I am going through section 14 in chapter 3 in Mary Boas' "Mathematical Methods for the Physical Sciences 3rd ed" Example 1 is clear, but this line is confusing in example 3 (I don't understand why it shows that these are not an element of the set). I have pasted example 1 for reference...

I know that we can easily construct a set whose cardinality is strictly greater than that of the set of real numbers by taking P(\Re) where P denotes the power-set operator. But as far as I am aware there aren't really any uses for this class of sets (up to bijection), or any intuitive ways of...

I am going through James Binney's course on Quantum Mechanics. I love all of the little misconceptions he points out along the way. One thing he mentions in his text and the lectures is found on page 20 and 21 starting with the heading "Commutators" eq. 2.21. He states that non commuting...

Homework Statement For the set S = (-1)^n * (3 + 5/n) I have determined that the maximum is 3 + 5/2 and the minimum is -8. However I am not sure if it is closed; given that it has a maximum and minimum, does this mean by definition that the set will be closed? Homework Equations...

Homework Statement Is {(1; 1; 0);(0; 0; 2);(0; 0; 1);(1; 2; 3)} a spanning set for R3The Attempt at a SolutionThis is supposed to be easy but the answer sheet might be wrong. The answer I have says it is and then proceed to say that (0;0;2) is linearly independent. But it isn't because...

Homework Statement For a set of vectors in R3, is the set of vectors all of whose coordinates are integers a subspace?The Attempt at a Solution I do not exactly understand if I should be looking for a violation or a universal proof. If x,y, z \in Z then x,y,z can be writted as...

I have a problem with this excercise. Ironically I think I can manage the part that is supposed to be hardest, here is the problem: Let (V,||\cdot||), be a normed vector-space. a), Show that if A is a closed subset of V, and C is a compact subset of V, then A+C=\{a+c| a \in A, c \in C\} is...

Hi, I was wondering, how can a null set be a subset of other sets? Could anyone explain the idea in non technical terms, I'm just a beginner. :) Thank you!

Homework Statement 8. Let ##A## be a non-empty subset of ##R## which is bounded above. Define ##B = \{x ∈ R : x − 1 ∈ A\}##, ##C = \{x ∈ R : (x + 1)/2 ∈ A\}.## Prove that sup B = 1 + sup A, sup C = 2 sup A − 1. The attempt at a solution Note that ##sup A## exists. Let ##x ∈ B##; then ##x − 1...

Hi! So let's say we measured the angular momentum squared of a particle, and got the result ##2 \hbar^2##, so ##l=1##. Now we have the choice of obtaining a sharp value of either ##L_z, L_y## or ##L_x##. Okay, fair enough. But I have two questions: 1) The degeneration degree is ##3## because...

Homework Statement I hope this does not violate copyright or anything but this problem originated from an assignment from Introduction to Mathematical Thinking in Coursera. I could not post there because the class ended and the discussion board there is dead. Let C be the set of all cars, let...

Homework Statement Let S be the set of functions from a set A to {0,1} Prove that |P(A)|= |S| Homework Equations P(A) is the power set of A The Attempt at a Solution I have no idea how to do this... If A is finite then A has n elements, and we can write out the elements from one to...

The intuitive picture I have of giving a set a topology, is that of giving it a shape in the sense of connecting the points and determining what points lie next to each other (continuity), the numbers of holes of the shape, and what parts of it are connected to what. However, the most...

Hi, this issue came up in another site: We want to compute ( not just ) the deRham cohomology of ## X=\mathbb R^2 - ##{p,q} , but also an explicit generating set for ## H^1 (X) = \mathbb Z (+) \mathbb Z## in deRham cohomology . Only explicit generating set I can see here is {(0, +/-...

I have a set of differential equations with the basic form: dy_n/dt = t*(a_(n-1)*y_(n-1)+b(n+1)*y_(n+1)-2c_n*y_n) So the time depence is a simple factor in front of the coefficient matrix. Does this set of differential equations have closed form solutions?

Homework Statement Let A=\mathbf{C}-{z:Re(z) and Im(z) are rational}. Show that A is a connected set. Homework Equations My book gives the definition of a disconnected set as a set that satisfies three conditions. A set A is disconnected if there exist two open sets U and V in \mathbf{C}...

Set Theory -- Uncountable Sets Homework Statement Prove or disprove. There is no set A such that ##2^A## is denumberable. The Attempt at a Solution A set is denumerable if ##|A| = |N|## My book shows that the statement is true. If A is denumerable, then since ##|2^A| > |A|, 2^A ##...

Homework Statement Describe the set {x:|x2-5|<4} Homework Equations The Attempt at a Solution I know this is simple stuff but I'm confused as to what way I'm supposed to answer this. My current answer is: |x2-5|<4 -4<x2-5<4 -4+5<x2<4+5 1<x2<9 1<x<3 Is that all the...

What is set associated mapping and What are the difference between direct and set associated mapping

Hi all, Im new here :-) So I am designing a simple Wien bridge oscillator, and need it to be set to a specific frequency. This is my circuit: Where C1 = C and C2 = C and R3 = R and R4 = R Im using ω=1/(C2R2) where C = my capacitor values and R = my Resistor values. My problem is, however...

Is anyone pumped? Because I'm pumped and you should be pumped. GET PUMPED! My last chance to get a 2300, fingers crossed.

How do you define a set without using set builder notation? For example, let's say that I want to define set S as: S={x ∈ ℕ ∣ 0<x<5} Then S={1,2,3,4} However, suppose that I wanted to define S without set-builder notation, as below? ∀x(x ∈ ℕ ^ 0<x<5 ⟺ x∈S ) Would these two...

Homework Statement a) Consider the relation S defiend on the set {t : t is a person} such that xSy holds exactly if person x is taller than y. Determine if the relation S is reflexive, symmetric and transitive. Is the relation S an equivalence relation? Homework Equations Recall that...

Homework Statement Let [a,b] \subset \mathbb{R} be a compact interval and t0 \in [a,b] fixed. Show that the set S = {f \in C[a,b] | f(t_0) = 0} is not dense in the space C[a,b] (with the sup-norm). Homework Equations Dense set: http://en.wikipedia.org/wiki/Dense_set sup -...

Why is the characteristic function* of a ball in Rn continuous everywhere except on its surface?My lecturer said that a circle is a 'set of discontinuities' - what exactly does that mean? (some context: we're looking at how we can integrate over a ball. Previously we've only looked at Riemann...

Homework Statement Let ##A\subset E^n## be a set with volume and ##f:A\to\mathbb{R}## a continuous function. Show that if the set ##\{x\in A:f(x)=0\}## has volume zero, then the set ##\{x\in A:f(x)>0\}## has volume. Homework Equations None The Attempt at a Solution A proposition...

Can a measurable function be a.e. equal to a non-measurable function? Let ##(X,\Sigma,\mu)## be an arbitrary measure space. Let M be the set of measurable functions from X into ##\mathbb C##. I know that M is closed under pointwise limits. I'd like to know if M is also closed under the types...

Hello everyone, I need to find a way to measure and plot the impedance of a set of chokes across a frequency range of 10kHz. Any ideas how I can do that? I have a frequency generator, a variable power supply and an oscilloscope with a spectrum analyzer.

For reference, my class is using The Joy of Sets by Keith Devlin. I've been asked to solve this as a practice problem, but this stuff is really confusing over the first read or two and I've yet to see any example proofs and I think I'll just mess it up. A link to the book can be found here if...

Is the set of the natural Nos complete?

1. Suppose A \ B\subseteqC\capD and x\inA. Prove that if x \notinD then x\inB 2. None 3. Proof: Suppose A \ B\subseteqC\capD, x\inA, and x\notinD. It follows that our first assumption is equivalent to A due to our third assumption. Thus, B\subseteqC\capD is disjoint and either x\notinB\subseteqC...

Are set operations on a set ##X## defined as operations on ##2^X##? In other words a binary operation on ##X## is an operation ##\omega:2^X\times{}2^X\rightarrow{}2^x##? Surely the basic set operations could be defined that way, but then some weird non-standard operation like...

I've been trying to think of the grammatically correct way to translate A\cupB and A\capB. So, let's say A is the set of all animals and B is the set of all boats. Then, A\cupB is the set of all entities which are either animals or boats (or both). And A\capB is the set of entities...

Definition of maximal, greatest, minimal and least elements of a set: http://i.stack.imgur.com/PnI9V.png Since c is a minimal element but c is not a least element, this implies that there is one element that is not comparable to c. What is that element? What about d and i?

Homework Statement Let V be an inner product space. Show that if w is orthogonal to each of the vectors u1,u2,...,ur, then it is orthogonal to every vector in the span{u1,u2,...,ur}. Homework Equations The Attempt at a Solution Not sure how to show this, if w is orthogonal to...

Homework Statement Determine whether set S = {2a,-4a+5b,4b| aε R ^ bε R} is a subspace of R3? If it is a subspace of R3, find the dimension? Homework Equations dimension= n if it forms the basis of Rn, meaning that its linear independent and span(S) = V The Attempt at a...

Homework Statement Let A=\{f:\mathbb{Z}\to\mathbb{Z}: f(n)\neq 0 \text{for a finite number of n}\}, prove that A is countable. Homework Equations I'm considering using that it would be equivalent to prove that the set A'=\{f:\mathbb{N}\to\mathbb{N}: f(n)\neq 0 \text{for a finite number...

In order to increase production rate a reactor set point was increased from 160 psig to 190 psig. The reactor pressure transmitter was recalibrated from 0-200psig to 0-300 psig what is the percent span for old and new set points. Can you please explain to me how to find the answer. The book says...

Hello all, I'm a bit stumped when it comes to formal proofs. I PART A: "Let A,B ⊆{1,2...n} be two sets with A,B > n/2. Prove that the intersection of A ∩ B is nonempty." This part I used contradiction, but didn't get everything. I assumed that if the intersection of A and B was empty, then A∪B...

hey all, I am currently studing logic and set theory. My professor solved this question in a way that seems quit strange to me- Hope you could be of help. I attached the question in image file so signs won't be lost

I have faced the following problem recently: We have a sequence A of M consecutive integers, beginning at A[1] = 1: 1,2,...M (example: M = 8 , A = 1,2,3,4,5,6,7,8 ) We have the set T consisting of all possible subsequences made from L_T consecutive terms of A, which do not overlap. (example...

is empty set part of every set?? you have a power set of s represented by p(s) and s is { x is integer and either x=<-2 or x>=5} and you have another set d = {{-3 -2 1}, {4}, {6, 7}, {-5, 6, 9}} when you are asked for intersection of p(s) and d in a plain maths question am I...

Hey again! :) I have a question.. If I have to show that a set $S$ is a ring,do I have to show all the axioms or is it enough to show the criteria: $s_1,s_2 \in S$ and $s_1-s_2 \in S$ $s_1 \cdot s_2 \in S$ ?