What is Set: Definition and 1000 Discussions

Seth, in Judaism, Christianity, Mandaeism, Sethianism, and Islam, was the third son of Adam and Eve and brother of Cain and Abel, their only other child mentioned by name in the Hebrew Bible. According to Genesis 4:25, Seth was born after Abel's murder by Cain, and Eve believed that God had appointed him as a replacement for Abel.

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  1. TheSodesa

    How Do You Calculate Conditional Probability with Complements?

    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...
  2. DeldotB

    Mean and Variance of a data set

    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...
  3. JulienB

    Difference between closed set and open set is a closed set

    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...
  4. B

    Metric Spaces: Interior of a Set

    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...
  5. A

    MHB Finding the zero vector of a sinusoidal set

    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...
  6. S

    Algorithm to find the smallest substring containing a set of....

    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...
  7. M

    MHB Question ' write the elements of set A'

    Any ideas on how to begin Many thanks :)
  8. shawn9521

    I Does light take longer to go a set distance on a train?

    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...
  9. Math Amateur

    MHB Index Set alonside Bigcap and Bigcup - as in Paul Bland's book .... ....

    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
  10. D

    Determining the Max. Set of Linearly Independent Vectors

    (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...
  11. K

    I Open interval (set) end points and differentiability.

    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...
  12. The Bill

    I Radius of the largest ball inside a complex set.

    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...
  13. R

    Set theoretical products

    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?
  14. L

    MHB Proving a Set Theory Statement Regarding Families of Sets

    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...
  15. A

    A Prep for Hawking/Ellis: Point Set Topology Needed

    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...
  16. A

    I Parametric Representation of a Solution Set

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

    I Boundedness and continuous functions

    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...
  18. S

    MHB Finding a set of vectors that span u,v....

    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} =...
  19. rattma

    I Is This Set Theory Notation Correct for Describing Local Maxima?

    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...
  20. R

    Elementary Set Theory (Discrete)

    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'...
  21. K

    A If LHC reports no SUSY by Aug 2016 data set

    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...
  22. J

    Time taken for free falling objects to travel a set distance

    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?
  23. C

    I Proving Set Relationships: A-B ⊂ A & (A∩B)c = A∪Bc

    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.
  24. EnumaElish

    I How is Cantor set similar to coin tosses?

    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?
  25. P

    B What is a clopen set and how can a set be both open and closed?

    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...
  26. N

    MHB Proving No Set Contains All Sets Without Russell's Paradox

    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...
  27. Z

    How to Design and set up a strong electromagnet?

    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...
  28. M

    Using a set square to reduce parallax error

    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...
  29. M

    MHB Algorithm creates representative set of data

    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...
  30. M

    A Algorithm creates representative set of data

    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...
  31. T

    MHB Proving Set Operations [Set Theory]

    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...
  32. M

    Ordered set proof review request

    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...
  33. P

    What is the name for an object that cannot be added to?

    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)?
  34. J

    Does the GCD of a set divide the GCD of any subset?

    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...
  35. kelvin490

    MATLAB How to set zero value boxes transparent in 3D plots?

    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...
  36. DaTario

    I Question about notation in set theory

    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...
  37. I

    Limit points, closure of set (Is my proof correct?)

    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)...
  38. 1

    How do I set up this Legendre Transform for Hamiltonian

    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...
  39. D

    A Why does my chosen basis set for W crash (DFT)?

    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...
  40. J

    Proving a set of matrices is NOT a vector space

    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...
  41. W

    Remembering T-SQL: SET vs SELECT and OBJECT_ID()

    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...
  42. TheMathNoob

    Proof of Partition Property for Subset A in Universal Set U

    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...
  43. M

    MHB Set of nilpotent elements

    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...
  44. M

    Calculation of Permanent set out of stress strain relation

    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.
  45. S

    Why isn't my hash set doing a good job?

    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...
  46. JulienB

    Finding Extrema of a Set: A Derivative Approach

    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...
  47. J

    Proof of Partition of a Set with Nested Partitions | Set Theory Proof 2

    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...
  48. J

    Proving Set Equality: A Simple and Effective Method

    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...
  49. anemone

    MHB Solving Equation In The Set Of Natural Numbers

    Find all the natural numbers $a$ and $b$ such that $(a^2+1)(b^2+1)+45=2(2a+1)(3b+1)$.
  50. Alltimegreat1

    B Possible to see the moons of Jupiter/Saturn with decent set of binoculars?

    Assuming clear night skies
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