# 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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 =...