What is set builder: Definition and 12 Discussions

In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy.Defining sets by properties is also known as set comprehension, set abstraction or as defining a set's intension.

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  1. V

    Are both sample spaces the same or do they mean different things?

    I came up with two different forms of the sample space S, but I am not sure if they mean the same thing or the first one could mean something different. H stands for heads showing up and T stands for tails showing up. $$ S = \{ \{i,j\}: i \in \{H,T\}, j \in \{H,T\} \} $$ $$ S = \{ (i,j) : i...
  2. D

    I Set Builder Roster methods

    How do the roster method and set builder methods when combined give modern meaning to traditional topics? For example: Find the roots of x^2-4x+3=0 Suppose we have no knowledge of the algebraic techniques for solving this equation. Had we wished to write the solution set for this equation using...
  3. JR Sauerland

    Set builder notation: is it ever used?

    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.
  4. H

    How to define a set without set builder notation

    How do you define a set without using set builder notation? For example, let's say that I want to define set S as: S={x ∈ ℕ ∣ 0<x<5} Then S={1,2,3,4} However, suppose that I wanted to define S without set-builder notation, as below? ∀x(x ∈ ℕ ^ 0<x<5 ⟺ x∈S ) Would these two...
  5. S

    Set builder notation and proofs

    "set builder" notation and proofs I'm curious about the references to "set builder" notation that I see in forum posts. Is this now a popular method of teaching elementary set theory and writing elementary proofs? I haven't looked at materials for that subject in the past 20 years. The...
  6. J

    Set builder notation question.

    Homework Statement Use the set-roster notation to indicate the elements in each of the following sets. Homework Equations S = {n ∈Z |n(-1)k, for some integer k} The Attempt at a Solution Here is how I read this: "S is the set of all n’s that are a member of the integers...
  7. N

    Set theory - set builder notation

    Homework Statement X={8^n-7n-1/n belongs to N} Y={49(x-1)/x belongs to N} Homework Equations Then, x is subset of y ] or y is subset of x or x=y,none of these
  8. K

    Home work with set builder notation

    Ok, I am needing help turning (2, 5, 10, 17) into set builder notation. I know to get these you add odd numbers 3, 5, 7 but I can't wrap my mind around putting this into notation.
  9. R

    Set Builder Notation: Domain of f, g & h

    Hi! We have 3 functions; f=http://img59.imageshack.us/img59/8682/fovgdt3.png ,[/URL] g=\frac{1}{\sqrt{(2x2 - 1)(x2-1)}} and h= \frac{\sqrt{2+x}+x(x^2-1)}{(x^2-1).\sqrt{2+x}} And we want to write the domain of these functions in the set builder notation, which I'm not very familiar with...
  10. L

    Need help with Set Builder Notation? Learn the basics and get tips here!

    Set Builder Notation? Does anyone know the basics of set builder notation. Any tips and tricks?
  11. E

    Quick set builder notation question

    I've seen a lot of variety in the way different books/people use set builder notation. Is their any "standard"? For example, I've seen: {x | x < -2 or x > 2 } And somtimes: {x | x < -2 U x > 2 } And also: {x | x < -2 } U {x | x > 2} Is anyone of these more "correct" than the others...
  12. G

    Set Builder Notation: POS_λ(\alpha) Explained

    How would you describe this set in plain English: \text{POS}_\lambda(\alpha) = \alpha_\lambda^0 \cup \{\kappa - \{\lambda\}|\kappa \in \alpha_\lambda^+\} where: \lambda is a literal \kappa is an \vee clause with the set \kappa = \vee_{j\leq m}\;\lambda_j represented as \kappa =...