Set Theory Ordered Pairs and Cartesian Product with R

Ordered and Unordered Pairs A pair set is a set with two members, for example, [latex]\{2, 3\}[/latex], which can also be thought of as an unordered pair, in that [latex]\{2, 3\} = \{3, 2\}[/latex]. However, we seek a more a strict and rich object that tells us more about two sets...

Algebra of Sets in R

The set operations, union and intersection, the relative complement [latex]-[/latex] and the inclusion relation (subsets) [latex]\subseteq[/latex] are known as the algebra of sets. The algebra of sets can be used to find many identities related to set relations that will be discussed later. We turn now to introducing the relative...

Set Theory Arbitrary Union and Intersection Operations with R

The union and intersection set operations were introduced in a previous post using two sets, [latex]a[/latex] and [latex]b[/latex]. These set operations can be generalized to accept any number of sets. Arbitrary Set Unions Operation Consider a set of infinitely many sets: [latex display="true"] A = \large{\{b_0, b_1, b_2, \cdots \} \large} [/latex] It would...

Set Operations Unions and Intersections in R

The set operations of unions and intersections should ring a bell for those who’ve worked with relational databases and Venn Diagrams. The ‘union’ of two of sets [latex]A[/latex] and [latex]B[/latex] represents a set that comprises all members of [latex]A[/latex] and [latex]B[/latex] (or both). One of the most natural ways to visualize...

Introduction to Set Theory and Sets with R

Sets define a ‘collection’ of objects, or things typically referred to as ‘elements’ or ‘members.’ The concept of sets arises naturally when dealing with any collection of objects, whether it be a group of numbers or anything else. Conceptually, the following examples can be defined as a ‘set’: {1, 2, 3,...