Set Definition and 1000 Threads

Homework Statement [/B] P(A | \overline{B}) = ? Homework Equations Multiplicative rule: \begin{equation} P(A | B) = \frac{P(A \cap B)}{P(B)} \end{equation} Additive rule: \begin{equation} P(A \cup B) = P(A) + P(B) - P(A \cap B) \end{equation} Difference: \begin{equation} A \backslash B = A...

Homework Statement In this problem we will be generating and analyzing lists of normally distributed random numbers. The distribution we are sampling has true mean 0 and standard deviation 1. If we sample this distribution N=5 times, what do we expect the mean to be? How about the standard...

Homework Statement Hi everybody! I'd like to check with you guys if I tackled that problem correctly. I might have a few theoretical questions along the way :) Prove that the difference ##A \setminus B## of a closed set ##A \subset \mathbb{R}^2## and an open set ##B \subset \mathbb{R}^2## is...

Homework Statement Let ##(X,d)## be some metric space, and let ##A## be some subset of the metric space. The interior of the set ##A##, denoted as ##int A##, is defined to be ##\bigcup_{\alpha \in I} G_\alpha##, where ##G_\alpha \subseteq A## is open in ##X## for all ##\alpha \in I##. The...

Hi everyone, Thank you in advance for taking the time to read my question and for your help. I really appreciate it. The question is set out as follows: Given the set 𝑆 = {𝑎 sin (𝑥+𝑏) | 𝑎, 𝑏 E R}. The addition of elements 𝒔1, 𝒔2 ∈ 𝑆 is defined as follows: 𝒔1 +𝒔2 =𝑎1 sin (𝑥+𝑏1)+𝑎2 sin...

characters in a specified amount. I've been working on this for 10+ hours and can't seem to get it right. It passes all the unit tests I've written, but when I use it in the context of the program I'm writing it fails. The idea is like ACTAGACC { A : 2, C : 1} ------> 4, because smallest...

Any ideas on how to begin Many thanks :)

Edit: Sorry, the title should say LIGHT, not time! << Mentor Note -- Title updated >> Let's say you're on a train, in the back of a car. The train is stationary. You shine a laser to the front of the car, and you can measure the time it takes for the laser to reach the wall. Now, if the train...

When I write \bigcap_\Delta M_\alpha I get \bigcap_\Delta M_\alpha ... ...How do I get the index set \Delta alongside \bigcap as in the following text from Paul Bland's book "Rings and Their Modules" ... ... ?Hope someone can help ... Peter

(sorry for the horrible butchered thread title... should say "determination", not "determining") 1. Homework Statement In "Principles of Quantum Mechanics", by R. Shankar, a vector space is defined as having dimension n if it can accommodate a maximum of n linearly independent vectors (here is...

When we talk about differentiability on a Set X, the set has to be open. And if a set X is open there exists epsilon> 0 where epsilon is in R. Then if x is in X, y=x+ or - epsilon and y is also in X But this contradicts to what i was taught in high school; end points are excluded in the open...

I've been thinking about notions like the following: "How far can one be from the nearest road while in a particular country." "What's the 'maximum thickness' of a subset of \mathbb{R}^n?" "What mountain range has the biggest circular region entirely within it?" These sorts of questions lead...

Homework Statement Let S be any set and T = ∅. What can you say about the set S×T? Homework EquationsThe Attempt at a Solution The solution is that S×T=∅. I'm not quite sure why this is though. Is it because there isn't anything in T to give an ordered pair so S×T is empty?

I was wondering if anyone could please check my work and reasoning for this problem. Thank-you! (Also, would this be considered a direct proof? How might a contradiction and IFF proof look like and compare?) Problem: Suppose F, G1 and G2 are nonempty families of sets. Prove that if F ⊆ G1 ∩ G2...

I'm trying to prepare to read The Large Scale Structure Of Space-time by Hawking and Ellis. I've been reading a General Topology textbook since the authors say "While we expect that most of our readers will have some acquaintance with General Relativity, we have endeavored to write this book so...

How did he found x = 1, y = 0, z = 0 and x = 1, y = 1, z = 2?

I am working my way through elementary topology, and I have thought up a theorem that I am having trouble proving so any help would be greatly appreciated. ---------------------- Theorem: Let A ⊂ ℝn and B ⊂ ℝm and let f: A → B be continuous and surjective. If A is bounded then B is bounded...

Find a set of vectors {u, v} in $\mathbb{R}^4$ that spans the solution set of the equations: $x - y + 2z - 2w = 0$ $2x + 2y -z + 3w = 0$ ($u$ and $v$ are both $4 \times 1$) $u = ?$, $v = ?$ I put the matrix in RREF to get $\begin{bmatrix}1&0&3/4&-1/4\\0&1&-5/4&7/4\end{bmatrix} =...

Hi, Is the following notation correct? X = {xt> max(xt-k,...,xt-1,xt+1,...,xt+k)|(t-k,...,t+k) ∈ T2k+1∧ k ∈ ℕ\{0}} where T = [1,n]∩ℕ denotes the time periods over which x runs. I basically want to say that X is the set of points that are local maxima in a neighbourhood of k points to the right...

Homework Statement Suppose A⊂B⊂C. What is A/B, A/C, and A∪B Homework EquationsThe Attempt at a Solution This isn't really a homework question, I am just trying to get some exposure to discrete math before I take it in the fall. The set differences A/B and A/C are both empty sets and the 'or'...

according to blogger Tommaso Dorigo the LHC "What to expect for ICHEP I believe that if the machine keeps delivering at this pace, by mid-July CMS and ATLAS could have in their hands some 10 inverse femtobarns of 13-TeV collisions. Those data, three to four times larger in size that what was...

The time taken for a free-falling object to fall a set distance (on earth) is, according to Wikipedia, described by the equation: t = √(2d/g). Why is the distance doubled in this equation/ how is this derived?

Can some please explain to me how to solve these two questions? Let A, B and C be any sets, prove that: (a) A-B ⊂ A (b) (A∩B) complement = A complement ∪ B and (A∪B) complement = A complement∩ B complement.

The wikipedia page on the Cantor set states that it is a model for an infinite series of coin tosses. In what sense are recorded coin outcomes similar to a set of points on the real line?

I feel like I ask too many questions here, so I'm sorry about that. But, anyway, what is a clopen set? I was watching something the other day that a friend sent me, and, out of the blue, the guy starts referring to a set as being "clopen" with no explanation. I tried to break all the definitions...

Greetings: I am attempting to prove that no set contains all sets without Russell's paradox. What I have thus far is this: Let S be an arbitrary set and suppose S contains S. If X is in S for some X not=S, then S - S cannot be empty. But this is a contradiction; hence if S contains S, then...

Hello guys. I am new member of this forum and I am looking for some guidance on a certain project. Now, the reason I am posting is that I need your help with a project I am currently just starting and of which unfortunately I have little details figured out as well, so please bear with me if you...

Homework Statement In one of my revision guides, there is an experiment for calculating the acceleration of free fall using the electromagnet and trap door arrangement. The biggest error is in the measurement of the height over which the ball falls. The guide says: "You could reduce the error...

Hi all, I have algorithm to analyze and make it easier to implement in programming language (Python). We have table with data and we want to select only representative part. It looks like: ID_PRODUCT | CARDINALITY | SET VARIANCE WITH THIS ELEMENT AND ABOVE 10 ---------------- 110...

Hi all, I have algorithm to analyze and make it easier to implement in programming language (Python). We have table with data and we want to select only representative part. It looks like: ID_PRODUCT | CARDINALITY | SET VARIANCE WITH THIS ELEMENT AND ABOVE 10 ---------------- 110...

Could someone help me in this by simplifying/Proving the equation using Theorems/ Rules on Operation of Sets (i.e Commutative property, idempotent, assoc, dist. , definition of union , def. intersection , DeMorgan ,etc.). Letting A, B and C be three sets .. Prove/Disprove : Any solution...

Homework Statement , relevant equations, and the attempt at a solution are all in the attached file. I was reading through Invitation to Discrete Mathematics and attempted to solve an exercise that involved a proof. I've typeset everything in LaTeX and made a PDF out of it so that it does not...

What is the name for an object that cannot be added to (for example, a circle can only have 360 degrees; any more degrees and it is no longer merely a circle)?

Homework Statement If A is a set of integers and B is a set properly contained in A, does the greatest common denominator of all of the integers in A divide the greatest common denominator of all elements in B? Homework Equations None. The Attempt at a Solution Obviously gcd(A) divides any...

I used a function called ind2patch to make a big 3D block which contains a number of smaller blocks in 3 dimensions. Each small block has a value which the magnitude is represented by a color.One example is shown below: However, most of the boxes have very low or zero value and I don't need to...

Hi All, Sorry, to begin with, if the question seems to be out of place. My question has to do with the notation (#) for the number of elements in a set: $$ N = \# \{ v_i \in V \vert v_i v_j \in E \} $$ Is it well known? If written in a scientific communication, must one offer a description of...

Homework Statement Let ##E'## be the set of all limit points of a set ##E##. Prove that ##E'## is closed. Prove that ##E## and ##\bar E = E \cup E'## have the same limit points. Do ##E## and ##E'## always have the same limit points? Homework Equations Theorem: (i) ##\bar E## is closed (ii)...

Homework Statement Im trying to understand the Legendre transform from Lagrange to Hamiltonian but I don't get it. This pdf was good but when compared to wolfram alphas example they're slightly different even when accounting for variables. I think one of them is wrong. I trust wolfram over the...

Hello, I am trying to optimize a molecule with the chemical formula C60H52O18P4S4W2. I have tried using different Basis Sets on my input file but I keep getting the following error: " Standard basis: Aug-CC-pV5Z (5D, 7F) Atomic number out of range in CCPV5Z. Error termination via Lnk1e in...

Homework Statement Show that the following is NOT a vector space: {(a, 1) | a, b, c, ∈ ℝ} {(b, c) Note: this is is meant to be a 2x2 matrix. This may not have been clear in how I formatted it. 2. The attempt at a solution I am self-studying linear algebra, and have had a difficulty...

Hi, I wonder if someone remembers their T-SQL. We have this statement: Just curious: I remember using SET where SELECT appears. Is this SELECT used in order to assign values to many variables simultaneously? Also, Is there a reason to use two separate DECLARE statements , or could we just use...

Homework Statement Assume {B, C, D} is a partition of the universal set U, A is a subset of U and A is not a subset of B complement, A is not a subset of C complement, A is not a subset of D complement. Prove that {A ∩ B, A ∩ C, A ∩ D} is a partition of A. Homework EquationsThe Attempt at a...

Hey! :o I am looking at the following exercise: An element $r\in R$ is called nilpotent if $r^n=0$ for some integer $n=1,2, \dots $. Show that if $r$ is nilpotent then $1-r$ is invertible in $R$. Show that if $R$ is commutative then the set $N(R)$ of nilpotent elements is an ideal of...

Hi, I have been given a relation between stress and strain which is strain=(stress/70000)(1+(3stress/(1890)) the dia of round bar is 10mm and length is 3mm and that's all the data i have and I am required to find out permanent set.

So I created my own implementation of a hash set of strings and am XORing the characters as a hashing function: private int _GetBucketNumber ( string s, List<List<string>> Buckets ) { // s: string whose index to look up // Buckets: source buckets...

Homework Statement Hi everybody! It's kind of the first time that I try to solve this type of problem, so I'd like to see what you guys think about it and if I am heading in the right direction: Examine if the set {(x2 + x + 1)/(x2 + 1) : x∈ℝ} has a maximum and/or a minimum, and calculate...

Homework Statement . Let A be a set and {B1, B2, B3} a partition of A. Assume {C11, C12} is a partition of B1, {C21, C22} is a partition of B2 and {C31, C32} is a partition of B3. Prove that {C11, C12, C21, C22, C31, C32} is a partition of A. Homework EquationsThe Attempt at a Solution I know...

Homework Statement Attached is the problem Homework EquationsThe Attempt at a Solution So I have to show that each side is a subset of the other side Assume x∈ A ∪ (∩Bi) so x∈A or x∈∩Bi case 1 x∈ ∩ Bi so x∈ (B1∩B2∩B3...∩Bn) which implies x∈B1 and x∈B2 ... and x∈Bn so x∈B1∪A and x∈B2∪A...

Find all the natural numbers $a$ and $b$ such that $(a^2+1)(b^2+1)+45=2(2a+1)(3b+1)$.

Assuming clear night skies