Aaron Schlegel's Notebook of Interesting Things

A pair set is a set with two members, for example, {2, 3}, which can also be thought of as an unordered pair, in that {2, 3}={3, 2}. However, we seek a more a strict and rich object that tells us more about two sets and how their elements are ordered.

The set operations, union and intersection, the relative complement − and the inclusion relation (subsets) are known as the algebra of sets. The algebra of sets can be used to find many identities related to set relations.

Set unions and intersections can be extended to any number of sets. This post introduces notation to simplify the expression of n-sets and the set union and intersection operations themselves with R.

The set operations 'union' and 'intersection' should ring a bell for those who've worked with relational databases and Venn Diagrams. The 'union' of two of sets A and B represents a set that comprises all members of A and B (or both).

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.