Set Definition and 1000 Threads

Hi, How and why set of natural numbers is closed?

Homework Statement given set C = {(x,y)|x,y are integers, x^2 + |y| <= 2} Suppose they are uniformly distributed and we pick a point completely at random, thus p(x,y)= 1/11 Homework Equations Listing it all out, R(X) = {-1,-2,0,1,2} = R(y) The Attempt at a Solution My problem is that when I...

Homework Statement Find the Acceleration of the system and the tensions in the three ropes. *If you can't see the picture there's a triangle (ABC), a train of four objects and three pulleys (one exactly at each corner). Side AC (hypotenuse) at the bottom, side AB to the left and side AC to the...

Homework Statement A and B are both spans. A = span(a1,a2,a3) B = span(b1,b2) Then how many elements would AUB have? Homework Equations N/A The Attempt at a Solution [/B] I'm almost certain the answer is 2, with the two elements being span(a1,a2,a3) and span(b1,b2) but I'm unsure as to...

As I understand it a coordinate origin is just chosen for convenience. So how can we state the Earth revolves around the sun when you could make coordinate origin at any point in the universe??

In SR, an event is a particular point in space and time.For simplicity, we only use one dimension of space. We have x'=γ(x-vt) if when x, t = 0 , x', t' = 0Let's say we have a bunch of inertial frames, all moving at different speeds, but all sharing a common origin x, t = 0 From the POV of...

My linear algebra is a bit rusty. Let ##A=\{\bar{v}_1, \dots, \bar{v}_1\}## be a set of vectors in ##R^n##. Can dim(span##(A))=n## without spanning ##R^n##? I guess I'm unclear on how to interpret the dimension of the span of a set of vectors.

I was wondering, why is the set of complex numbers needed to solve problems that the set of reals doesn't permit to ? I mean, in relation to the fundamental theorem of algebra, that is.

We know that in the space of functions, its possible to find a complete set so that you can write for an arbitrary function f, ## f(x)=\sum_n a_n \phi_n(x) ## and use the orthonormality relations between ## \phi##s to find the coefficients. But is it possible to find a set of functions ##...

The question: Parametrize the solution set of this one-equation system. x_1 + x_2 + ... + x_n = 0 My question (please look at the photo): I understood why we have the first row, but what's the point of the other rows?

Homework Statement Determine the largest set on which the function is analytic. f(z) = (z2-2)e-xe-iy Homework Equations z=x+iy f(x+iy) = U(x,y) + iV(x,y) Ux=Vy Uy=-Vx The Attempt at a Solution I think I'm right in saying that f(z) is analytic if the CR equations (provided above) are...

Homework Statement I solved the problem myself but i have a question about the algebra Homework Equations n(A ∪ B ∪ C) = n(A) + n(B) + n(C) -n(A ∩ B) -n(A ∩ C) -n(B ∩ C) + A ∩ (B ∩ C) = n(A ∪ B) -n(A ∩ C) -n(B ∩ C) + A ∩ (B ∩ C) The Attempt at a Solution I knew i needed...

Hello, I will be doing an experiment to separate N2 from O2 in air using membrane separations. I need to write my own experimental procedure to find the objectives of the experiment. Here is our experimental set up I'm trying to figure out how to do objective i. I need to figure out the...

Hi, I'm reading The Martian by Andy Weir (fantastic book). A character, describing how a Mars mission works, says of fueling their ascent vehicle: "Through a neat set of chemical reactions with the Martian atmosphere, for every kilogram of hydrogen you bring to Mars, you can make thirteen...

Homework Statement Homework Equations y (x,y) = 2YmSin(kx)Cos(wt)The Attempt at a Solution I am having trouble at setting up the standing wave equation for this problem. Once I set up the equation, I know that part a b c d is just plugging in the numbers. From what I learned, I know that...

Been working this problem for hours and can't seem to get it right. Any assistance would be greatly appreciated! Note: Green colored text is the editable text public class CheckingPasscodes { public static void main (String [] args) { boolean hasDigit = false; String passCode =...

Homework Statement Determine whether the given set is open or closed (or neither): {(x,y,z) ε R^3, 1<x^2+y^2<4} Homework EquationsThe Attempt at a Solution I believe that the set is open due to the only bounds being inequalities that are less than, not less than or equal to, but that seems...

Suppose that set A have unique element...Can we say that cardinality(A)=1 or $cardinality(A)\le1$ ? Which one is true ?

Hi. I'm having trouble understanding the logic behind finding a set of u for u(u-1) > 0. To solve these, I tend to factor as much as possible, then equate each expression to 0 (in this case to > 0) and solve, changing the > to < if I must divide by a negative number. I get u >0 and u > 1 but the...

Hello! I have the following problem: Three brothers are aged 6, 10 and 14 years old. Will they ever, in the future, have a prime number birthday the same year? Looking at all of the prime numbers between 1 and 100, it seems that they won't. So I guess this is the same thing as saying: are...

I am trying to gain an understanding of the basics of elementary algebraic geometry and am reading Dummit and Foote Chapter 15: Commutative Rings and Algebraic Geometry ... At present I am focused on Section 15.1 Noetherian Rings and Affine Algebraic Sets ... ... I need someone to help me...

I am trying to gain an understanding of the basics of elementary algebraic geometry and am reading Dummit and Foote Chapter 15: Commutative Rings and Algebraic Geometry ... At present I am focused on Section 15.1 Noetherian Rings and Affine Algebraic Sets ... ... I need someone to help...

How is a general path called instead of being a continuous function from an interval to some topological space, where we replace the domain from an interval to a compact set, is there a name for such a function? Perhaps I should add that the compact set is also convex.

I'm trying to figure out what the vertical bars in |A∪B| mean given that A and B are both sets. I tried searching for it, and can't seem to find the meaning of it. Is it supposed to be absolute value of all the elements of the union of sets A and B?

1. The problem statement, all variables and given/known Prove that if a set ##X\subseteq G## is finite then it's Normalizer in G, ##N_G(X)## is also equal to the set: ##A=\{g\in G : gXg^{-1}\in X\}## Homework Equations Given ##X\subseteq G##, then the normalizer of X in G is defined as...

http://www.stuff.co.nz/world/europe/71871827/queen-elizabeth-ii-set-to-become-longest-reigning-uk-monarch

Most definitions of a matrix that I have seen involve entries that are elements of a field. What if I have a unorderd set with no operations defined on it, say a set of different colored marbles or a set of historical events. Can I have a matrix whose entries are elements of such a set?

Homework Statement Show that the set of limit points of the set ##A \subseteq \mathbb{R}## given by ##L## is a closed set.2. Relevant theorems Definition: A closed set F (subset of R) is such that it contains its limit points. Definition: A limit point x of a set A (subset of R) is such that...

Homework Statement Let ##A, B, C## be sets with ##A \subseteq B##. Show ##(A-B)\cup C=(A\cup C)-(B\cup C)## Homework Equations None. The Attempt at a Solution So, generally, one shows two sets to be equal by showing that each is a proper subset of the other. I started with the LHS. Thus...

Hi. I hope this is not too far into philosophy. Set Theory is commonly accepted as the foundations of Mathematics. Is it possible to develop a different type of Mathematics by using Fuzzy sets or Rough sets instead?

Homework Statement Let A and B be two events such that P(A) = 0.4, P(B) = 0.7, P(A∪B) = 0.9 Find P((A^c) - B) 2. Homework Equations I can't think of any relevant equations except maybe the Inclusion Exclusion property. P(A∪B) = P(A) + P(B) - P(A∩B) This leads us to another thing P(A∩B^c)...

Homework Statement Hello, I need some help on the following. I am BRAND new to set theory and this was in my first HW assignment and I am not sure where to start. The question is as follows: Let A and B be parts of a set E Let P(E)\rightarrow P(A) X P(B) be defined by f(X)=(A\cap X,B\cap X)...

Dear Everyone, I have some help setting up a system of linear equation. The problem states, Two planes start from Los Angeles International Airport and fly in opposition directions. The second plane starts $\frac{1}{2}$ hour after the first plane, but its speed is 80 kilometers per hour...

Hello, I didn't know where to put my question, but I think here is the best section for it. http://im60.gulfup.com/apkrpJ.png The problem isn't that I can't solve it, I actually did but I don't understand the concept ! -- I don't remember anything from my high school stat and I didn't do...

Homework Statement The following doesn't come from a textbook, and I am very uncertain whether it is true or false. Suppose that ##B \subseteq \mathbb{C}## is a convex set, and consider the set ##L_B := \{|b|: b \in B \}##. Homework EquationsThe Attempt at a Solution My question is, will...

Homework Statement Show that the set ##\{\mathbf{v}_1⊗\mathbf{v}_2⊗...⊗\mathbf{v}_p:\mathbf{v}_k\in V_k\}## of tensor products of vectors is strictly less than ##V_1⊗V_2⊗...⊗V_p##. Homework EquationsThe Attempt at a Solution Truly, I don't see any difference between the sets. They seem...

So when I took linear algebra I was asked to show the well-known properties of orthogonality in the functions cos(mx) and sin(mx)... With this I mean all the usual combinations which I don't see why I should point out explicitly. The inner product in the vector space was defined...

I have the following set of equations from which I need to find δ and φ uniquely (i.e without quadrant ambiguity). In other words I need to have expressions for tan δ and tan φ involving A,B,C and D which are known quantities. A=1-sin(squared) δ/2 x sin 4φ B=1+sin(squared) δ/2 x sin 4φ C=...

Prove or disprove the following statement: If p(a)=p(b)=q then p(a∩b)≤q2 We know nothing know about event a , b. The Attempt at a Solution I tried this but don't know correct or not Can some one help me let a, b are independent event 0<q<1 then p(a∩b) = p(a) p(b) = q*q = q^2 [/B]

So I have an integral: ## \delta W=\int_{-\Delta}^\Delta\left[x^2\left(\frac{d\xi}{dx}\right)^2−D_S\xi^2\right]dx ## Here ##\xi## is a function of ##x## and ##D_S## is a constant. ##\Delta## is just some small ##x##. Now I need to set the variation of ##\delta W## to 0. Do do this I...

Homework Statement $$ A \subset B \Rightarrow A \cap C \subset B \cap C $$ 2. Homework Equations [/B] $$ A \subset B \Leftrightarrow A \cup B \subset B$$ $$ A \cap C \Leftrightarrow A \cap C \subset A \wedge A \cap C \subset C$$ The Attempt at a Solution For sets A and C $$A \cap C...

I am a new user of Multisim and I am trying to make a buck converter. In other softwares, such as pspice I was able to control the switching frequency by editing properties but in Multisim, most of the switches are user interactive. I want to set frequency of 50 Hz in a switch. Kindly help me...

Homework Statement Prove that ##A\cap(B\Delta C)=(A\cap B)\Delta(A\cap C)## Homework EquationsThe Attempt at a Solution [/B] L.H.S.=##A\cap(B\Delta C)## =##A\cap[(B - C) \cup (C - B)]## =##A\cap[(B \cap \bar{C}) \cup (C \cap \bar{B})]## =##[A\cap (B \cap \bar{C})] \cup [A\cap (C \cap...

I read somewhere that mathematical functions can be implemented as sets by making a set of ordered tuples <a,b> where a is a member of A and b is a member of B. That should create a function that goes from the domain A to the range B. But set theory has functions too, could they be sets too...

Should I sharpen up on using set builder notation? Like, will I ever need it in physics or calculus? I'm currently refreshing my skill at writing in Interval notation for inequalities and the like.

So I was originally in Neuroscience and took a physics course and ended up loving it so much I switched over. Nonetheless, I'm pretty much starting from the beginning. I was wondering if this overall schedule throughout my degree would be good for potentially going into grad school for...

If G is a finite set closed under an associative operation such that ax = ay forces x = y and ua = wa forces u = w, for every a, x, y, u, w ##\in## G, prove that G is a group. What I attempted: If we can prove that for every x ##\in## G, x##^{-1}## is also ##\in## G, then by the closure of the...

I've just started self-studying measure theory by reading Pugh's Mathematical Analysis. I'm trying to understand his argument for why the exclusion of a zero set does not change the outer measure: $m^*(E\setminus Z)=m^*(E)$: (Pugh's arugment): Let $Z$ be a zero set, $E\subseteq\mathbb{R}$, and...

Hello, I can't wrap my mind around this: inf∅= ∞ sup∅= - ∞ Thank you in advance.

Dear everyone... I am trying to set up a RF lab at home to help me do DSP projects with very low frequency, as low as possible. Anyone who has experiences about RF lab, please give me some ideals and what machines from basic to advance will be needed for the lab? Thank you, Nate Duong.