Set Definition and 1000 Threads

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...

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 $s_1-s_2 \in S$ $s_1 \cdot s_2 \in S$ ?

I'm thinking about Cathode Ray Tube (CRTs) television sets. I'm also studying consciousness and attempting to wrap my cognition around Fourier transformations. There are electronics involved. And there is energy and power involved. However, all of it comes together to develop a visual, right...

Homework Statement a.) Is symmetric and transitive, but not reflective: b.) consists of exactly 8 ordered pairs and is symmetric and transitive: The Attempt at a Solution If the question asks me to define some relation, do I need to define some math property like power of some number or...

Let say i have two sets of numbers A and B. and I want to assigne to each number from A two slosest numbers from B. What i would do is to pick an elements from A and then go through the entire B set and find two closest. now if i go the other way arround in orderd to achieve the same result i...

Here is the problem I have faced recently that I cannot deal with yet and I need some help: Given is the - list of elements (numbered): e.g. [1,2,3,4,6,7,8] - the count and size of groups, which can be used to cover the given set of numbers, e.g. groups with group size 2. - I need to find...

Is cardnality of a set refers to the number of elements that set has?

Hey Everyone, A while back I had posted a question here looking for some research ideas for an undergraduate project utilizing the SEM. It had to be microbiology related as I am combing credits for two courses. My project is about testing different antibacterial methods against E. coli...

In showing diam(cl(A)) ≤ diam(A), (cl(A)=closure of A) one method of proof* involves letting x,y be points in cl(A) and saying that for any radius r>0, balls B(x,r) and B(y,r) exist such that the balls intersect with A. But if x,y is in cl(A), isn't there the possibility that x,y are...

On page 113 Munkres (Topology: Second Edition) defines a J-tuple as follows: I was somewhat perplexed when I tried to completely understand the function \ x \ : \ J \to X . I tried to write down some specific and concrete examples but still could not see exactly how the function...

On page 113 Munkres (Topology: Second Edition) defines a J-tuple as follows: https://www.physicsforums.com/attachments/2153 I was somewhat perplexed when I tried to completely understand the function \ x \ : \ J \to X . I tried to write down some specific and concrete examples but still...

First: relating some ideia of set theory and binary logic, like: U = 1 Ø = 0 thus, some identities appears: U ∪ U = U U ∪ Ø = U Ø ∪ U = U Ø ∪ Ø = Ø U ∩ U = U U ∩ Ø = Ø Ø ∩ U = Ø Ø ∩ Ø = Ø 1 + 1 = 1 1 + 0 = 1 0 + 1 = 1 0 + 0 = 0 1 × 1 = 1 1 × 0 = 0 0 × 1 = 0 0 × 0 =...

Hello, and thank you in advanced for this. I am having trouble with setting up most if not all of my integrals when I am trying to find the elements of an inertia tensor. What would I do if i need to find say the tensor for a disk, but i don't know what to take for my three limits to be. i get...

Homework Statement Can you conclude that A = B if we know that (a) A \cup C = B \cup C (b) A \cap C = B \cap C (c) A \cup C = B \cup C and A \cap C = B \cap C Homework Equations The Attempt at a Solution A=B in all three cases, but I can't find a rigorous proof for any of these cases...

Homework Statement Let M and N be two metric spaces. Let f:M \to N. Prove that a function that is locally Lipschitz on a compact subset W of a metric space M is Lipschitz on W. A similar question was asked here...

Hey everyone, Firstly, I apologize if there is a more suitable forum. I think this would be considered a calculus problem, but I'm not sure. I'm trying to develop a RF loss calculator for work that can calculate RF loss over a given length of cable or through a passive device at a given...

Homework Statement I want to extend the below U set of vectors to R4. u1 = (0, 0, 0, -4), u2 = (0, 0, -4, 3), u3 = (3, 2, 3, -2). The Attempt at a Solution For a set of vectors to form a basis for Rn, the vectors must be LI and spans Rn(has n vectors) u1, u2 and u3 are...

Around the 4 minute mark the lecturer makes this statement, but I am not convinced this is true. I accept that (1) if a set is closed, its complement is open. but consider the converse. Consider an open ball S of some arbitrary radius centered at the origin (in whatever dimension d...

Homework Statement In R2 let u = (4, -2), v = (8, 5), w = (4, 1). a)Is the set {u, v, w} a spanning set for R2? b) Are the vectors u, v linearly independent? c) Are the vectors u, v, w linearly independent?The Attempt at a Solution a) u, v and w is a spanning set for the vector space R2...

Homework Statement Let V be the subspace of R3 defined by V = {(x,y,z) | x - y +2z = 0} Then A = {(2,0,-1) , (1,1,0)} B = {(1,3,1) , (3,1,-1)} are both bases for V. Show. The Attempt at a Solution 1) check that both set A and set B of vectors are in R3. V = (x , y ...