Set Quantification

The concepts and nomenclature of set theory underlie much of the data scientist&s;s daily tasks in processing data sets for exploratory data analysis and database interaction. Sets are unordered collections of elements that usually do not include duplicates. A type of set called a multiset may include duplicates. The elements of sets can exist in groups called subsets . A set with no elements is called the empty set , and the empty set is a subset of every set. The values associated with elements can be numbers, characters, or words. Furthermore, elements may share classifications in common, such as data types, quartile rank, sample batch, etc. When elements of a set are described using qualifiers such as SOME or NONE or ALL, we are quantifying. When predicates are quantified they are known as first-order logic . Quantification is useful in set logic.