set builder Definition and 12 Threads

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...

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...

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.

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...

"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...

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...

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

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.

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...

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

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...

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 =...