Binary Relation
A binary relation on a set A is a relation from A to itself.
Definition · Example · CSE Use →Discrete Mathematics
Definitions, examples and Computer Science applications for this mathematics subject.
All TermsAlgebra 16Algorithm Math & Complexity 10Arithmetic 1Calculus 16Discrete Mathematics 15Functions 15Geometry 2Geometry & Trigonometry 5Graph Theory & Trees 15Graphics & Machine Learning Math 5Linear Algebra 15Logic & Boolean Algebra 20Number Theory 15Numerical Methods 10Probability 15Set Theory 15Statistics 15Trigonometry 1
Binomial Coefficient
A binomial coefficient counts the ways to choose k objects from n without order.
Definition · Example · CSE Use →Combination
A combination selects objects without regard to order.
Definition · Example · CSE Use →Equivalence Relation
An equivalence relation is reflexive, symmetric and transitive.
Definition · Example · CSE Use →Factorial
The factorial of n is the product of all positive integers from 1 to n.
Definition · Example · CSE Use →Inclusion-Exclusion Principle
The inclusion-exclusion principle counts a union by adding set sizes and subtracting overlaps.
Definition · Example · CSE Use →Mathematical Induction
Mathematical induction proves a statement for all integers by establishing a base case and an inductive step.
Definition · Example · CSE Use →Partial Order
A partial order is a reflexive, antisymmetric and transitive relation.
Definition · Example · CSE Use →Permutation
A permutation is an arrangement of objects in which order matters.
Definition · Example · CSE Use →Pigeonhole Principle
The pigeonhole principle says that placing more objects than containers forces at least one container to hold multiple objects.
Definition · Example · CSE Use →Poset
A poset is a set together with a partial order relation.
Definition · Example · CSE Use →Recurrence Relation
A recurrence relation defines terms of a sequence using earlier terms.
Definition · Example · CSE Use →Relation
A relation from A to B is any subset of the Cartesian product A × B.
Definition · Example · CSE Use →Sequence
A sequence is an ordered list of values, often indexed by integers.
Definition · Example · CSE Use →Strong Induction
Strong induction assumes all earlier cases up to n are true to prove the next case.
Definition · Example · CSE Use →