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. parshyaa

    I Is It Valid to Cancel Sets in Set Theory?

    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...
  2. Math Amateur

    I The Set of Positive Integers - a Copy of the Natural Numbers

    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...
  3. Math Amateur

    MHB The Set of Positive Integers as a Copy of the Natural Numbers ....

    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...
  4. lfdahl

    MHB Set of 2015 Consecutive Positive Ints with 15 Primes

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

    I Max and min values -- Finding them in a data set

    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.
  6. jaketodd

    I Cardinality of the Power Series of an Infinite Set

    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...
  7. P

    How to calculate the Torque for a Set screw

    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...
  8. I

    Why is there only one set of blades per wind turbine?

    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...
  9. bachir1994

    Choice of a generator set for a drilling pump

    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...
  10. D

    MHB Demonstration of set operation

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

    When can the velocity gradient be set to zero?

    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...
  12. Y

    MHB Partial Order Relation where the Set is not Necessarily Finite

    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...
  13. Y

    MHB Partial Order Relation on a Functions Set

    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...
  14. SetepenSeth

    Linear Algebra - Linear (in)dependence of a set

    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...
  15. harpazo

    MHB Finding Bounds for a Triple Integral: Solids Bounded by a Paraboloid and Plane

    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...
  16. harpazo

    MHB Finding Bounds for a Triple Integral in the First Octant

    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...
  17. N

    How to add confg file to allow UHD drive set priority?

    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...
  18. V

    How many sets of 6 can be made from a set of 12

    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...
  19. B

    Path-Connected Sets and Their Closures: A Counterexample?

    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...
  20. M

    B Why Must the Expression Inside a Square Root Be Non-Negative?

    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.
  21. Spinnor

    I Is there a problem with this set of plots?

    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...
  22. Smalde

    Basic set theory with quantors question

    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 =...
  23. Mr Davis 97

    Showing that a set is an ideal

    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...
  24. S

    Simple open set topology question

    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...
  25. Vital

    Graphs of sin and cos, how to set points for x values

    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...
  26. harpazo

    MHB How Do You Set Up Double Integrals Over a Semicircular Region?

    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.
  27. harpazo

    MHB How Do You Set Up Double Integrals for Different Orders of Integration?

    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.
  28. harpazo

    MHB How do I set up double integrals for different orders of integration?

    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.
  29. harpazo

    MHB Double Integral Setup for a Rectangular Region

    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...
  30. cathal84

    I Proving a set is linearly independant

    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...
  31. Eclair_de_XII

    How can relations on three-element set have seven elements?

    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...
  32. N

    Help me Prove that such a set does NOT exist

    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")...
  33. Mr Davis 97

    I Distinctiveness of the set of nxn matrices as a ring

    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...
  34. J

    Experience the Artistry of "Legion": TV Show Set in the X-Men Universe

    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...
  35. yavorh

    BLDC: Required voltage to get set rpm at given amps

    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...
  36. Mr Davis 97

    Finding the order of the set of inner autos of D_4

    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?
  37. Minal

    A Find vectors in Orthogonal basis set spanning R4

    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.
  38. L

    Combinatorics: a set of 30 from unlimited objects

    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...
  39. F

    MHB How to Prove a Set Theory Ordinal Relationship?

    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.
  40. FallArk

    MHB Find g: Solving a Set Theory Problem

    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...
  41. C

    Linear Algebra - Finding coordinates of a set

    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...
  42. L

    B The Best Spot to Set Up a Colony on Mars

    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...
  43. sa1988

    Prove Set U is Open | Product Topology on R^2

    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...
  44. J

    Spring set makes up a traveling wave

    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...
  45. OrlandoLewis

    Moment of inertia of a set of spinning disks

    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...
  46. L

    I Desymmetrization of a combinatorial set

    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...
  47. C

    How to prove a set is a bounded set?

    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...
  48. Mr Davis 97

    I Existence of spanning set for every vector space

    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?
  49. Jehannum

    I What does n ∈ f mean in set theory notation?

    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...
  50. M

    MHB It is an algebraically dependent set over F

    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...
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