Set Definition and 1000 Threads

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 ...

I am having difficulty with the following Exercise due next week. Prove that the set of all 2-element subsets of ##N## is denumerable. (Exercise 10.12 from Chartrand, Polimeni & Zhang's Mathematical Proofs: A Transition to Advanced Mathematics; 3rd ed.; pg. 262). My idea so far was...

I don't like Jech's textbook on set theory because he gives these definitions written in this bizarre language and he doesn't restate the definition in colloquial English. That mathematicians feel its unnecessary to give colloquial examples of their definition or examples, in my opinion, is a...

Homework Statement My textbook gives me this definition of a connected set. http://media.newschoolers.com/uploads/images/17/00/69/80/76/698076.png I have been working through my practice problems and I got to one that asked me to sketch the set given by|z+2-i|=2and note whether it is...

We define by recursion the set of sets {An:n∈ℕ} this way: A_0=∅ A_n+1=A_n ∪ {A_n}. I want to prove by induction that for all n∈ℕ, the set A_n has n elements and that A_n is transitive (i.e. if x∈y∈A_n, then x∈A_n). My thoughts: for n=0, A_1 = ∅∪ {∅} = {∅} then, for n+1: A_n+2...

Homework Statement Can you conclude that A = B if A and B are two sets with the same power set? Homework Equations The Attempt at a Solution I know intuitively that A and B have to be equal, because all the individual entities in the power set (you know what I mean) have to be in...

I'm trying to round out my math skills in order to apply to graduate school for physics and I've already taken all of the calculus offered along with linear algebra, power series etc... I'm wondering which would be better should I choose to take a math course this term: abstract algebra or set...

I'm an undergraduate studying math taking intermediate proof-writing courses, and there are certain basic identities of set theory and functions that still confuse me - i.e., I have to reprove them or think about them carefully every time. Examples: (A\times B)\cap (C\times D)=(A\cap C)\times...

Homework Statement Three tests are available to identify six different substances. Test 1 is true in the presence of substance 1,2,3, and 4 Test 2 is true in the presence of substance 3,4, and 5 Test 3 is true in the presence of substance 2,5, and 6 Using set notation to denote the...

Why do I run into trouble if I try to define the set of all groups? I get that defining the set of all sets could lead to paradoxes. But how is it that defining the set of all groups somehow leads to the same kind of problems? If I define the set of all groups as all the ordered pairs (x,y)...

Hi. I was tasked with organising a tournament with the following set up: 8 players 7 rounds each round, each player is paired with another, and plays another pair; so each round has 2 games played (ie, a&b vs c&d ; e&f vs g&h) However there were the following constraints: Each player must be...

Homework Statement Homework Equations A set is closed if it contains alll of its boundary points. A boundary point is a point where an open ball around that point has one point inside the ball that's in the set, and one point in the ball that's not in the set.The Attempt at a Solution As seen...

Please give me example of antipodal set in infinite dimensional?

Homework Statement In each of the two following open sentences P(x) and Q(x) over a domain S are given. Determine all ##x \in S## for which P(x) → Q(x) is a true statement. ## P(x): x \in [-1, 2]; Q(x): x^{2} \leq 2; S=[-1,1] ## Homework Equations According to truth values for →: a...

As a mathematician, what may you say are the beauties that you see in the Mandelbrot set??

I understand the definition of real numbers in set theory. We define the term "Dedekind-complete ordered field" and prove that all Dedekind-complete ordered fields are isomorphic. Then it makes sense to say that any of them can be thought of as "the" set of real numbers. We can prove that a...

I've been asked to fit the histogram with a Poisson distribution as part of a mostly independent learning thing. The data was produced through a stochastic simulation. Can someone get me started on how I would go about finding the expected distribution? If you need additional information...

Homework Statement Show that S is open if and only if ∀x ∈ S, ∃ a open ball B(x; r)(r > 0) such that B(x; r) ⊂ S And what we have is , let X be normed space, S ⊂X , Then S is close if and only if $$∀{x_{n}}⊂X, s.t. x_{n}->x \in X$$, x∈ S. A set S is open if and only if X\S is close...

Hey guys, I have just moved into a new place for my university studies. There are smoke detectors in the apartment(kitchen living room and bedroom), I never had those things in apartments that I use to live. I am quite worried about the one in the kitchen, because I heard that while cooking a...

So when we have an open cover of a set X means we have a collection of sets \{ E_\alpha\}_{\alpha \in I} such that X \subset \bigcup_{\alpha \in I} E_\alpha . My question comes from measure theory, on the question of finite \sigma -measures, The definition I'm readying says \mu is \sigma...

Homework Statement Determine the interior, the boundary and the closure of the set {z ε: Re(z2>1} Is the interior of the set path-connected? Homework Equations Re(z)=(z+z*)/2 The Attempt at a Solution Alright so z2=(x+iy)(x+iy)=x2+2ixy-y2 so Re(x2+2ixy-y2)= x2-y2 >1 So would...

Homework Statement Check if the following set of vectors are linearly dependent or independent: A) V1= \stackrel{1}{1} V2= \stackrel{1}{3} B) V1= \stackrel{\stackrel{1}{2}}{3} V2= \stackrel{\stackrel{2}{1}}{3} C) V1= \stackrel{1}{3} V2= \stackrel{2}{1} V3= \stackrel{-1}{2} Homework...

Find a countable set that is also open or prove that one cannot exist

Lemma: If A is an at most countable alphabet, then the set A^* of strings over A is countable. Proof begin: Let p_n be the n^{th} prime number: p_0 = 2, p_1=3, p_2=5, and so on. If A is finite, say A = {a_0, a_1, ... , a_n}, where a_0, a_1, ... , a_n are pairwise distinct, or if A is countable...

I know eigenvectors corresponding to different eigenvalues are linearly independent but what about a set ${e_{1},...,e_{n}}$ of eigenvectors corresponding to different eigenvalues?

Homework Statement Homework Equations I have to use these set identities: The Attempt at a Solution Pretty sure this is impossible since it's an inequality.

Homework Statement Question #2. Homework Equations The Attempt at a Solution I've drawn a venn diagram for the left-hand side and the right-hand side and I can see that they're not equal but how do I provide a counter-example for this? Wouldn't a counter-example require an infinite number...

Homework Statement Homework Equations The Attempt at a Solution $$A-(A\cap B)=A-B\\ A\cap (A\cap B)^{ C }=A\cap B^{ C }\quad (set\quad difference\quad law)\\ A\cup [A\cap (A\cap B)^{ C }]=A\cup [A\cap B^{ C }]\quad (applied\quad A\cup \quad to\quad both\quad sides)\\ A=A\quad (absorption...

Homework Statement Homework Equations I have to use these set identities: The Attempt at a Solution Pretty sure this is impossible because there's no identity for the Cartesian product.

Homework Statement Let K \subset \mathbb{R^n} be compact and U an open subset containing K. Verify that there exists r > 0 such that B_r{u} \subset U for all u \in K . Homework Equations Every open cover of compact set has finite subcover. The Attempt at a Solution I tried...

Now i think i derived this correctly, but I'm not sure if it's correct, can anyone give me a confirmation? ##n-1/2=x## Where ##x## is the result of subtracting 1 from the observations and then dividing by 2. Then ##x+1=Median## Thank you :) Edit: Oops, this is the handicapped...

What is the precise definition of the open set? The definition I have been using until now has been that an open set is a set such that all of its points have some neighborhood that's contained in the set. The definition of neighborhood as far as I know is a collection of all the points within...

Hi Can you please help me with this problem? "What is the maximum size of a set A of logical expressions that only use →, p, q : each pair of elements of A are not equivalent?" I've found 6 different possible truth values. Is this the maximum size? If yes, how do I prove it? Thanks!