Set Definition and 1000 Threads

We can prove that When A and B are two sets(A≠B) (A-B) = (A∩B') = (A-(A∩B)) {We can also confirm them using venn diagram} From first and third relation A-B = A - (A∩B) By cancelling A from both side I get B = (A∩B) Which is only possible when A and B are same set. What is wrong in my proof , is...

I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Chapter 1: Construction of the Real Numbers ... I need help/clarification with an aspect of Theorem 1.3.7 ... Theorem 1.3.7 and the start of the proof reads as follows: n the above proof we...

I am reading Ethan D. Bloch's book: The Real Numbers and Real Analysis ... I am currently focused on Chapter 1: Construction of the Real Numbers ... I need help/clarification with an aspect of Theorem 1.3.7 ... Theorem 1.3.7 and the start of the proof reads as...

Is there a set of $2015$ consecutive positive integers containing exactly $15$ prime numbers?

I have some data collected from experiment and I want to calculate the max and min values for this data. Please note that these data not a result of function. What is the best mathematical way to get the max and min without just picking them by directly observation.

According to this page: https://en.wikipedia.org/wiki/Cantor's_theorem It says: "Cantor's theorem is a fundamental result that states that, for any set A, the set of all subsets of A (the power set of A) has a strictly greater cardinality than A itself." Furthermore, it says: "Cantor's...

Hi, I am working on a problem where I have to find the tightening torque required for rotating the outer sleeve. The Outer sleeve is rotated by human hand ( One hand operation) hence the sleeve torque feel is determined by the set screw. Problem statement: Please refer the image. O-ring 1 at...

I'm a civil/structural engineer and I was just recently thinking about one of the biggest issues for maximizing the efficiency of a wind turbine - the structure itself. The mega turbines that engineers want already have foundations of titanic proportions because as we all know, flag pole...

Hello everyone, I am faced with a problem where I have to power a 30kw drilling pump, with a generator of 45kw (model Gesan), but it does not work. At start-up the current reaches the peak of 190 A and descends gradually, for information the start-up of the pump of the drilling is done by a...

Hello There is the possibility that they help me to solve this demonstration. please AX(BΔC)=(AXB)Δ(AXC)

Homework Statement An experimentalist has measured the u-velocity component of a two-dimensional flow field. It is approximated by u = (1/3)( xy) (y^2) It is also known that the v-velocity is zero along the line y=0. Homework Equations ∇V=du/dx+dv/dy (partial derivatives) The Attempt at a...

Hello all, I have another question about partial order relations, again, a few statements which are either true or false. R is a partial order relation on a set A which is not necessarily finite. 1) With this order, A has at least one maximal and one minimal elements. 2) If with this order...

Hello, I have a question which includes several statements, which I need to decide if they are true or false. I am not sure how to do it, if you could give me hints or "leads", it will mostly appreciated. R is a partial order relation on A, a set of functions from [0,1] to [0,infinity) such...

Homework Statement Let { u, v, w} be a set of vectors linearly independent on a vector space V - Is { u-v, v-w, u-w} linearly dependent or independent? Homework Equations [/B] A set of vectors u, v, w are linearly independent if for the equation au + bv + cw= 0 (where a, b, c are real...

Set up a triple integral for the volume of the solid. DO NOT FIND THE VOLUME. The solid bounded by the paraboloid z = 9 - x^2 - y^2 and the plane z = 0. We are dealing with the xy-plane where z = 0. I know that 0 ≤ z ≤ 9 - x^2 - y^2. The bounds of the integral pertaining to dz are z = 0 to z...

Set up a triple integral for the volume of the solid. DO NOT FIND THE VOLUME. The solid in the first octant bounded by the coordinates planes and the plane z = 4 - x - y. We are dealing with the xy-plane where z = 0. I know that 0 ≤ z ≤ 4 - x - y. The bounds of the integral pertaining to dz...

I have Ettus B210 and trying to add 1 line configuration file "/etc/security/limits.conf" which will allow UHD drive to set priority. So , I typed this command to edit file: gksudo gedit /etc/security/limits.conf and add: #@student hard nproc 20 #@faculty soft...

Homework Statement [/B] A bag has a total of 12 balls, 3 of which are black. If you select 6 balls from the bag. a) How many sets of 6 can be made? b) How many of the sets of 6 contain 3 black balls? c) What is the probability of selecting a set of 6 that contains 3 black balls? Homework...

Homework Statement I am trying to determine whether the closure of a path-connected set is path-connected. Homework EquationsThe Attempt at a Solution Let ##S = \{(x, \sin(1/x) ~|~ x \in (0,1] \}##. Then the the closure of ##S## is the Topologist's Sine Curve, which is known not to be...

When we find solution set of an equation inside a square root why we should assume that inside of square root should be equal to or greater than zero? For example ##\sqrt{5x-4}##. How can I use here equal to or greater than zero symbol? Thank you.

Consider a graphic from May 2004 Physics Today article, Light's orbital angular momentum. Note that for larger l, the "hole" in the beam in the 2nd column gets bigger but the "hole" in the 3rd column basically stays the same size. I would think that both "holes" should grow with increasing l...

This is no homework for me. I am working as a teaching assistant in a lecture about logic and discrete structures for Informatics students. This should be a piece of cake, but I am not exactly sure of the logic behind. 1. Homework Statement Translate into words ∃c . ∀a ∈ A . ∀b ∈ B . ¬(a =...

Homework Statement Show that the collection of all nilpotent elements of a commutative ring ##R## is an ideal. Homework EquationsThe Attempt at a Solution Showing that something is an ideal is somewhat straightforward, but I am a little confused as to what explicitly I have to show. If we...

Homework Statement [/B] Is {n} an open set?Homework Equations [/B] To use an example, for any n that is an integer, is {10} an open set, closet set, or neither?The Attempt at a Solution [/B] I say {10} is a closed set, because it has upper and lower bounds right at 10; in other words, it is...

Homework Statement Hello! I am at the topic on graphing trigonometric functions. Exercises are rather easy at this point, but I have a problem deciphering how authors of the book choose points for x values. Please, take a look at few examples (including screen shots I attach), and, please...

Set up an integral for both orders of integration. DO NOT EVALUATE THE INTEGRAL. Let S S = double integrals Let R = region S S (x^2 + y^2) dA R: semicircle bounded by y = {4 - x^2}, y = 0 I can graph the region but have no idea how to proceed from there. I need solution steps.

Set up an integral for both orders of integration. DO NOT EVALUATE THE INTEGRAL. Let S S = double integrals Let R = region S S y/(1 + x^2) dA R: region bounded by y = 0, y = sqrt{x}, x = 4 I can graph the region but have no idea how to proceed from there. I need solution steps.

Set up an integral for both orders of integration. DO NOT EVALUATE THE INTEGRAL. Let S S = double integrals Let R = region S S xe^(y) dA R: triangle bounded by y = 4 - x, y = 0, x = 0 I can graph the region but have no idea how to proceed from there. I need solution steps.

Set up an integral for both orders of integration. DO NOT EVALUATE THE INTEGRAL. Let S S = double integrals Let R = region S S sinx cos x dA R: rectangle with vertices (-pi, 0), (pi, 0), (pi, pi/2), (-pi, pi/2) I am having such a hard time with the set up. I can graph the region but have...

I have two questions for you. Typically when trying to find out if a set of vectors is linearly independent i put the vectors into a matrix and do RREF and based on that i can tell if the set of vectors is linearly independent. If there is no zero rows in the RREF i can say that the vectors are...

Homework Statement "Determine the max number of elements in a three-element set that is not reflexive, symmetric, or transitive?" Homework Equations ##a R b⇔(a,b)∈R## The Attempt at a Solution Basically, my professor has stated that there are a total number of seven possible elements in a...

Let Q denote the theory of Robinson Arithmetic. A theory T is nice iff T is consistent, is p.r. adequate and extends Q. The fixed-point lemma states that for all nice theories T, for any formula φ, there is a sentence σ such that T ⊢σ↔φ("σ")...

So I know that in general, for the ring of ##n \times n## matrices, if ##AB = 0##, then it is not necessarily true that ##A=0## or ##B=0##. However, in other rings, for example the integers ##\mathbb{Z}##, I know that this statement is true. So what property is the ring of matrices lacking such...

So does anybody watch the TV show http://www.imdb.com/title/tt5114356/']Legion?[/PLAIN] It's set in a/the X-men universe from what I understand (I'm not too well versed in which different universes/spinoffs exist). I don't consider myself to be a cinephile but this show is a work of art if you...

Hey guys! So I'm trying to do this pretty wide diameter in-runner engine, where the rotor is hollow (essentially trying to make a short tube within a short tube :D). After checking out the details between the different types of electric motors (and realizing that I can barely find any...

Homework Statement Find the order of ##Inn (D_4)##, where ##D_4## is the set of symmetries of the square. Homework EquationsThe Attempt at a Solution Is the only way to this by brute force calculation of all of the inner automorphisms, and to see which are distinct?

An orthogonal basis set spanning R4 has four vectors, v1, v2, v3 and v4. If v1 and v2 are [ −1 2 3 0 ] and [−1 1 −1 0 ] find v3 and v4. Please explain this in a very simple way.

Homework Statement In how many ways can you choose 30 balls from an unlimited number of blue, red, green and white balls if you can choose any number of the different coloured balls? Homework EquationsThe Attempt at a Solution What I did is view the problem as choosing from a set of 30 of each...

Let $\beta$ be an ordinal. Prove that $A\cap \bigcup\beta=\bigcup\{A\cap X\mid X \in \beta\}$ I'm not sure on this. It looks a bit like union distributing over intersection. Please help.

Find a function g from {0,1} to B\A such that f^-1(g(x)) = x +2 for x∈{0,1}. Present it in the 2-row form. A = {{1},2,3} and B = {∅,1,{2},3} I know that B\A = {∅,1,{2}} and f is a bijection from A to B\A how do I find such function g? It obviously can't be bijection, how do I match one value to...

Homework Statement Find the coordinates of each member of set S relative to B. B = {1, cos(x), cos2(x), cos3(x), cos4(x), cos5(x)} S = {1, cos(x), cos(2x), cos(3x), cos(4x), cos(5x)} I am to do this using Mathematica software. Each spanning equation will need to be sampled at six separate...

Where exactly on Mars is the best spot to set up camp for a colony? I've been reading about the Hellas Basin, which seems favorable regarding asmospheric pressure and ability to host liquid water (0 to 50 degrees F). However, it's located halfway between the Martian equator and the south pole...

Homework Statement Let ##U = \{(x,y)\in R^2 : xy > 0\}## Show that ##U## is open in the product topology on ##R^2## induced from the standard topology on ##R## Homework EquationsThe Attempt at a Solution Proofs are my downfall. First I've visualised ##U## and it seems to be that it's...

Homework Statement Twelve identical mass-spring combos are lined up and set to oscillation. Two pictures of the same system taken at different times are shown. The crest-to-crest distance is 8.0 cm, and the maximum displacement of all the masses is 1.5 cm. 1) Explain how you can tell that a...

Homework Statement The shows an arrangement of 15 identical disks that have been glued together in a rod-like shape of length L = 1.0000 m and (total) mass M = 100.0 mg. The disks are uniform, and the disk arrangement can rotate about a perpendicular axis through its central disk at point O...

Hello, here's a problem at the boundary between mathematics, programming and chemistry, which I'm struggling with, but I guess can be easily solved by mathematicians/programmers. I'll explain it as concisely as I can, but sorry, it will be a long post, it's not that trivial. In chemistry there...

1. I have to show that S1 = {x ∈ R2 : x1 ≥ 0,x2 ≥ 0,x1 + x2 = 2} is a bounded set.2. So I have to show that sqrt(x1^2+x2^2)<M for all (x1,x2) in S1.3. I have said that M>0 and we have 0<=x1<=2 and 0<=x2<=2. And x2 = 2-x1 We can fill in sqrt(x1^2 + (2-x1)^2) = sqrt (0^2 + (2-0)^2) = 2 < M = 3...

I know that the span of any subset of vectors in a vector space is also a vector space (subspace), but is it true that every vector space has a generating set? That is, the moment that we define a vector space, does there necessarily exist a spanning set consisting of its vectors?

I bought a maths book and have discovered it's somewhat above my level. In particular I'm confused about one bit of notation. I understand the "is a member of" operator when it takes a set as argument (e.g. n ∈ ℝ) but not when the book uses it with functions (e.g. n ∈ f) Does n ∈ f mean that...

Hey! :o Let $E/F$ be a field extension, $S\subseteq E$ and let $t\in E$ be algebraic over $F(S)$. I want to show that there are distinct $s_1, \ldots , s_r\in S$, different from $t$, such that $\{s_1, \ldots , s_r, t\}$ is an algebraically dependent set over $F$. I have done the following...