41 articles
Subset
A subset, also called a set inclusion, is a set all of whose members also belong to another set B, written A ⊆ B; a proper subset leaves at least one member out.
Surjective function
A surjective function, also called an onto function or surjection, is a function in which every element of the codomain is the output of at least one domain element.
Symmetric difference
The symmetric difference, also called the disjunctive union, is the set operation containing elements that belong to exactly one of two sets, corresponding to XOR in logic.
Transfinite induction
Transfinite induction, also called well-ordered induction, is a proof technique extending ordinary mathematical induction from the natural numbers to any well-ordered class, most prominently the ordinal numbers.
Transitive relation
A transitive relation (also called the transitive property) is a binary relation in which aRb and bRc together imply aRc, forming the basis of equivalence relations and orderings.
Tuple
A tuple, also called an ordered n-tuple, is a finite ordered list of elements, written (1, 2, 3), in which order and repetition count; tuples of two and three elements are called ordered pairs and triples.
Uncountable set
An uncountable set is an infinite set too large to count, whose elements cannot be paired with the natural numbers, a fact first shown by Cantor in 1874.
Union (set theory)
The union, or set union, of two sets is the set of all objects belonging to at least one of them, written A ∪ B.
Venn diagram
A Venn diagram, also called a set diagram, represents sets as overlapping closed curves that divide the plane into all 2^n possible intersections; John Venn named and defined it in 1880.
Wacław Sierpiński
Wacław Sierpiński, fully Wacław Franciszek Sierpiński, was a Polish mathematician (1882–1969) who worked in set theory and number theory, founded the journal Fundamenta Mathematicae, and gave his name to the Sierpiński triangle and carpet.
Well-order
A well-order (well-ordering) is a linear order on a set in which every non-empty subset has a least element, exemplified by the usual order on the natural numbers.