Set

A set is a collection of distinct objects, called its elements, considered as a whole. Its identity depends only on which elements it contains, not their order or repetition.

Element (mathematics): An object that belongs to a set. Set membership is expressed by saying that an element belongs to a set.
Union (set theory): The set containing elements that belong to at least one of two or more sets. Union combines sets while retaining each element only once.
Georg Cantor: A German mathematician who founded modern set theory and developed the theory of infinite cardinalities. His work made sets and comparisons of infinity central mathematical objects.
Function (mathematics): A relation assigning exactly one output to each input in a specified domain. Functions are defined through relationships between sets of inputs and outputs.
Subset: A set whose every element also belongs to another set. Subsets capture containment between sets.
Intersection (set theory): The set containing elements shared by two or more sets. Intersection isolates the common membership of sets.
Richard Dedekind: A German mathematician whose work helped establish rigorous foundations for arithmetic and the real numbers. His treatments of infinite collections helped shape early set-theoretic thinking.
Relation (mathematics): A set of ordered tuples that specifies which objects are related. Relations use sets of tuples to encode connections among objects.
Empty set: The unique set containing no elements. It is the simplest set and a subset of every set.
Set difference: The elements of one set that do not belong to another set. Difference removes from a set the elements selected by another.

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