Set Definition and 1000 Threads

Homework Statement 2.) if jimmy piles his baseball cards in stacks of 4, then there is 1 left over. if he piles them in stacks of 7, there are 4 left over. If he piles them in stacks of 9, there are 6 lefty over. If he piles them in stacks of 10, there are 7 left over. compute the smallest...

Hi, i would like to have a hint for the following problem: Let $$v_1, v_2 \&\ v_3 $$ in a vector space V over a field F such that$$ v_1+v_2+v_3=0$$, Show that $\{v_1,v_2\}$ spans the same subspace as $\{v_2,v_3\}$ Thanks in advance

Graph Theory -- Max. Independent set algorithm Homework Statement Design a polynomial time greedy algorithm to compute a maximum independent set for a graph. Explain the algorithm and compute T_w(n). Homework Equations The Attempt at a Solution My terse and informal...

How would I go about proving that if A is a subset of B then the interior points of A are a subset of the interior points of B?

Hey, I was reading about this is in "Additive Combinatorics" (Additive Combinatorics (Cambridge Studies in Advanced Mathematics): Terence Tao, Van H. Vu: 9780521136563: Amazon.com: Books) on pg. 4 when I went to the references and found this paper (http://renyi.mta.hu/~p_erdos/1965-02.pdf) which...

Hello all, I am struggling with this relatively simple task. In a university with 88 students, each student can choose to participate in 3 afternoon activities: activity A, activity B and activity C. Each student can choose to participate in some activities, all or none. 33 students...

Homework Statement Let X be a set containing n elements. If two subsets A and B of X are picked at random, the probability that A and B have the same number of elements is Homework Equations The Attempt at a Solution Total number of subsets possible is 2^n. Now the subsets containing 1...

hi Guys, i Needed your help to prove out the following, thanks in advance; Let u1,u2,...,ut be vectors in $\Re^n$ and $k\in\Re ,k\neq0.$ Prove that $Span\{u_1,u_2,...,u_t\}=Span\{ku_1,u_2,...,u_t\}$

Hi everyone, let's stay I have two inequation set such as: First one is A:= X_1-X_2 \leq 1 X_1 \leq3 X_2 \geq 1 X_1,X_2 \geq 0 Second one is B:= X_1+X_2 \geq 5 X_1\leq5 X_1\geq4 X_2\leq4 X_1,X_2 \geq 0 I had like to write it as a set C := A\oplus B, with C made of linear inequations too. I'm...

Homework Statement Benzoic acid/biphenyl mixture is mixed with diethyl ethe(CH3CH2-O-CH2CH3). The solution is placed in a separatory funnel and sodium hydroxide is mixed in. The bottom layer, H2O, NaOH and benzoic acid is then placed in a flask where it is mixed with HCl, chilled and then...

. . . . . . . . . . Answer GameA. Alexander Pope Q. What drink contains brandy, cream, and holy water?A. Bell & Howell Q. Describe Pavlov's experiment.A. 9W Q. Do you spell your name with a "V", Herr Wagner?A. Plague, Famine, Pestilence, and Death. Q. Name three deductible expenses and a capital...

Hi everyone, :) I encountered the following question recently. :) Now I think this question is wrong. Let me give a counterexample. Take the set of real numbers with the usual Euclidean metric. Then take for example the sequence, \(\{\frac{1}{n}\}_{n=1}^{\infty}\). Then...

Homework Statement Homework Equations The Attempt at a Solution I'm not sure how to prove that it is zero. I don't see what I can do after the second last step.

Homework Statement Let T be a set such that: T=\{t\in\mathbb{R}/t^{2}<2\} Homework Equations a) Justify the existence of a real number a such that a=Sup(T) b) Prove that the proposition a^{2}<2 is false. c) Suppose that a^{2}>2. Prove that we can find a contradiction with a=Sup(T). d)...

Why is the math in the red box necessary? According to this definition, it isn't:

Homework Statement b(B) = cls(B) \ Int(B) where b(B) is the boundary, cls is the closure, and int is the interior of set B. This was not hard for me to prove by picking elements and showing that the sets were contained in one another. However, I decided it would be fun to try to derive it by...

Suppose that A is subset of R (real line) with the property for every ε > 0 there are measurable sets B and C s.t. B⊂A⊂C and m(C\B)<ε Prove A is measurable By definition A is measurable we need to prove m(E)=m(E∩A)+m(E\A) for all E the ≤ is trivial enough to show ≥: Since C is...

Suppose A is not a bounded set and m(A∩B)≤(3/4)m(B) for every B. what is m(A)?? here, m is Lebesgue Outer Measure My attemption is : Let An=A∩[-n,n], then m(A)=lim m(An)= lim m(An∩[-n,n]) ≤ lim (3/4)m([-n,n]) = infinite. is my solution right? I am confusing m(A) < infinite , it...

On the set of Z of integers define a relation by writing m \triangleright n for m, n \in Z. m\trianglerightn if m-n is divisble by k, where k is a fixed integer. Show that the quotient set under this equivalence relation is: Z/\triangleright = {[0], [1], ... [k-1]} I'm a bit new the subject...

Hi, everyone. I once saw a science program with the danish astrophycisist Jens Martin Knudsen, who said that there exists seven absolutely fundamental constants of nature, and if one of these were changed ever so slightly, it would lead to drastic changes in the whole universe. So my...

I have a problem asking to prove the following statement is false: "Every non-empty set of integers has a least element". This seems pretty intuitively false, and so I tried to sum that up in the following way: Suppose we have a subset \(A\) in the "universe" \(X\). Let \(A=\{-n: n\in{N}\}\), a...

How to prove that the limit \lim_{n\to\infty}sin(n)^n n integer towards infinity does not exist ? If n is a real then it's obvious since we can take n=Pi/2*k k being an integer. But if n is a integer then sin(n) is always smaller than 1, hence the power n should tend towards 0. I know this...

Hello, I have a data set that follows an equation similar to sin(x)+x. Just from eyeballing the data, it seems like there should be a pretty simple trigonometric function A*sin(B*x)+C*x. I went to school for engineering so I have some basic/intermediate knowledge of mathematics but it's...

Homework Statement Let S ⊆ R be such that (i) a, b ∈ S ⇒ ab, a + b ∈ S (ii) for all x ∈ R exactly one of the following holds x ∈ S, x = 0, −x ∈ S. Show that S = {x ∈ R ; x > 0} (the set of positive numbers P) 2. Relevant theorems (T1) a² > 0 ∀ a ∈ R. (So a²∈P) (T2) All positive...

naive (intuitive) definition of "set" I happened upon a book by a Joseph Landin, once head of the math department at University of Chicago and subsequently Ohio State University, in which he gives this as a definition of a set and states this property: Shortly thereafter, he writes...

Express the set {X E R: (x+3) (7-x) ((x-2)^2) > 0} as a union of intervals

Here is the question: Here is a link to the question: Show that for any three sets A; B; C , we have: A - (B -C) = (A-B) U (A ? C)? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Suppose that some infinite set S spans V. Then this means every vector in V is expressible as some linear combination of the vectors in S. Does this combination have to be finite? It couldn't be infinite, because that necessarily invokes notions of convergence and norm which do not...

I'm having some set theoretic qualms about the following argument for the following statement: Let V be a vector space of dimension n and let S be a generating set for V. Prove that some subset of S is a basis for V. The argument is as follows: If ##V = \{ 0 \} ## then it is trivial...

Let c_00 be the subspace of all sequences of complex numbers that are "eventually zero". i.e. for an element x∈c_00, ∃N∈N such that xn=0,∀n≥n. Let {e_i}, i∈N be the set where e_i is the sequence in c_00 given by (e_i)_n =1 if n=i and (e_i)_n=0 if n≠i. Show that (e_i), i∈N is a basis for...

A computer consulting firm presently has bids out on three projects. Let Ai = {awarded project i}, for i = 1, 2, 3, and suppose that P(A1) = 0.22, P(A2) = 0.25, P(A3) = 0.29, P(A1 ∩ A2) = 0.07, P(A1 ∩ A3) = 0.09, P(A2 ∩ A3) = 0.05, P(A1 ∩ A2 ∩ A3) = 0.02. The question is to find the...

Homework Statement Prove that if lim n→∞ (p_n ) = p in a metric space then the set of points {p,p_1,p_2, ...,} are closed. 2. Relevant information The definition of close in my book is "a set is closed if and only if its complementary is open." So I want to prove this by contradiction. I...

I am currently trying to understand linear independence and spanning sets. So the question that I have right now is, does a set of five linearly independent vectors always span F^5? Thanks for any help you can offer! Edit: Sorry for the confusion, I really had no idea how to begin this...

Homework Statement Find a set T of natural numbers such that 0 ∈ T, and whenever n ∈ T, then n + 3 ∈ T, but T ≠ S, where S is the set defined: Define the set S to be the smallest set contained in N and satisfying the following two properties: 1. 0 ∈ S, and 2. if n ∈ S, then n + 3 ∈ S...

Homework Statement Show that the set of \mathbb{R}^2 given by S = \{(x, y) \in \mathbb{R}^2 : x > y\} is open. Homework Equations The Attempt at a Solution Why is S the half plane that has boundary given by the line y = -x?

Homework Statement Find the volume obtained by rotating the regon boudned by the given curve about the specified axis Homework Equations The Attempt at a Solution y = secx, y = cosx, 0 <= x < = pi/3 This is what I set up. V = ∏∫ (secx +1 )^2 - (cosx +1)^2 dx I said R...

Homework Statement We have a metric space X=\cup X_k where X_k\subset X_{k+1} and each X_k is open. Show that for any Borel set E, there is an open set U such that \mu (U-E)<\epsilon . (Its supposed to be "U \ E".) Homework Equations \mu is a measure, so probably the important thing...

Homework Statement An interesting example of a ring: Begin with a nonempty set X and form the power set of X, P(X), which is the set of all subsets of X. On P(X), define addition + and multiplication × as follows: For A, B in P(X): A × B = A ∩ B A + B = (A\B) ∪ (B\A), where as...

Suppose we have a perfect set E\subset\mathbb{R}^k. Is there an open set I\subset E?

Homework Statement y = c1e3xcos(2x)+c2e3xsin(2x)+c3+c4x Homework Equations Differential Equations. The Attempt at a Solution I am having trouble what the roots are for the c3, and c4 parts. I know they are a repeated root, but is it just k= 0? It seems like it would work, but I...

Homework Statement Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Homework Equations y = x^2 +1 , y = 9-x^2: about y = -1 The Attempt at a Solution I used disks. I said that r = 1 + ((9-x^2)-(x^2 +1 )) = 9 - 2x^2...

Hi, Using the definition of Hausdorff measure: http://en.wikipedia.org/wiki/Hausdorff_measure I am looking for a simple proof that Hd(C) is greater than 0, where C is the Cantor set and d=log(2)/log(3) Thank's in advance

Is 0 I am told. Is this an axiom, or can it be proven?

Hi, Say y=x2: the solution set is equal to the relation, which is also a set. What's the difference between saying "plot the relation y=x2" and "plot the solution set of y=x2"? Thanks for help.

My question concerns proving the set of non-negative integers of the form $a-dx ~~(a, d, x \in \mathbb{Z}, d \ge 1)$ is nonempty. This is the proof from my book. If $a \ge 0$, then $a = a-d\cdot 0 \in S$. If $a < 0$, let $x = -y$ where $y$ is a positive integer. Since $d$ is positive, we have...

Homework Statement Give S = {(x,|x|,2|x|) | x \in R} \bigcup {(0,2,4),(-1,3,6)}, find span(S) Homework Equations I know that span of a finite set of vectors is given by <a(0,2,4) + b(-1,3,6)+c(x,|x|,2|x|)>, where a,b,c are any real numbers. Can i use that same way to find the span of this...

How do you set a custom security level in Windows 8 to view Latex.

Homework Statement Prove that {m+n, m,n \inZ} is countable Homework Equations The Attempt at a Solution I Can prove it if I make a nxn scheme and put 1,-1,2,-2 along each side. This generates a table which when counted a long first,second etc. Diagonal hits all the numsers in the...

Homework Statement I want to show that the set $$ <1,x,x^2,\cdots ,x^n> $$ forms a basis of the space $$ P_{n} $$ where $$ P_{n} $$ contains all polynomial functions up to fixed degree n. The Attempt at a Solution I have already shown that the set $$ <1,x,x^2,\cdots ,x^n> $$ is linearly...

This proof makes no sense to me. The theorem to be proved is Theorem 44. {x,y} = {u,v} → (x = u & y = v) V (x = v & y = u) where {x,y} and {u,v} are sets with exactly two members, which can be either sets or individuals. The proof relies on: Theorem 43. z \in {x,y} z = x V z = y...