Sets

• Set (mathematics) – Collection of mathematical objects
  • Element (mathematics) – Any one of the distinct objects that make up a set in set theory
  • Venn diagram – Diagram that shows all possible logical relations between a collection of sets
  • Empty set – Mathematical set containing no elements
  • Subset – Set whose elements all belong to another set
  • Union (set theory) – Set of elements in any of some sets
    • Disjoint union – In mathematics, operation on sets
  • Intersection (set theory) – Set of elements common to all of some sets
    • Disjoint sets – Sets with no element in common
  • Complement (set theory) – Set of the elements not in a given subset
  • Symmetric difference – Elements in exactly one of two sets
• Ordered pair – Pair of mathematical objects
• Cartesian product – Mathematical set formed from two given sets
• Power set – Mathematical set containing all subsets of a given set
• Simple theorems in the algebra of sets
• Naive set theory – Informal set theories
• Multiset – Mathematical set with repetitions allowed

Functions

• Function – Association of one output to each input
• Domain of a function – Mathematical concept
• Codomain – Target set of a mathematical function
• Range of a function – Subset of a function's codomain
• Image (mathematics) – Set of all values of a function
• Injective function – Function that preserves distinctness
• Surjection – Function such that every element has a preimage (mathematics)Pages displaying short descriptions of redirect targets
• Bijection – One-to-one correspondence
• Function composition – Operation on mathematical functions
• Partial function – Function whose actual domain of definition may be smaller than its apparent domain
• Multivalued function – Generalized mathematical function
• Binary function – Function that takes two inputs
• Floor function – Nearest integers from a numberPages displaying short descriptions of redirect targets
• Sign function – Mathematical function returning -1, 0 or 1
• Inclusion map – or inclusion function, or canonical injectionPages displaying wikidata descriptions as a fallback
• Pigeonhole principle – If there are more items than boxes holding them, one box must contain at least two items
• Relation composition – Mathematical operationPages displaying short descriptions of redirect targets
• Permutations – Mathematical version of an order changePages displaying short descriptions of redirect targets
• Symmetry – Mathematical invariance under transformations

Arithmetic

• Decimal – Number in base-10 numeral system
• Binary numeral system – Number expressed in the base-2 numeral systemPages displaying short descriptions of redirect targets
• Divisor – Integer that is a factor of another integer
• Division by zero – Class of mathematical expression
• Indeterminate form – Expression in mathematical analysis
• Empty product – Result from multiplying no factors
• Euclidean algorithm – Algorithm for computing greatest common divisors
• Fundamental theorem of arithmetic – Integers have unique prime factorizations
• Modular arithmetic – Computation modulo a fixed integer
• Successor function – Elementary operation on a natural number

Elementary algebra

Elementary algebra – Basic concepts of algebra

• Left-hand side and right-hand side of an equation – Mathematical NomenclaturePages displaying short descriptions of redirect targets
• Linear equation – Equation that does not involve powers or products of variables
• Quadratic equation – Polynomial equation of degree two
• Solution point – Mathematical formula expressing equalityPages displaying short descriptions of redirect targets
• Arithmetic progression – Sequence of numbers
• Recurrence relation – Pattern defining an infinite sequence of numbers
• Finite difference – Discrete analog of a derivative
• Difference operator – Pattern defining an infinite sequence of numbersPages displaying short descriptions of redirect targets
• Groups – Set with associative invertible operation
• Group isomorphism – Bijective group homomorphism
• Subgroups – Subset of a group that forms a group itselfPages displaying short descriptions of redirect targets
• Fermat's little theorem – A prime p divides a^p–a for any integer a
• Cryptography – Practice and study of secure communication techniques
• Faulhaber's formula – Expression for sums of powers

Mathematical relations

• Binary relation – Relationship between elements of two sets
• Heterogeneous relation – Relationship between elements of two setsPages displaying short descriptions of redirect targets
• Reflexive relation – Binary relation that relates every element to itself
• Reflexive property of equality – Relationship asserting that two quantities are the samePages displaying short descriptions of redirect targets
• Symmetric relation – Type of binary relation
• Symmetric property of equality – Relationship asserting that two quantities are the samePages displaying short descriptions of redirect targets
• Antisymmetric relation – Binary relation such that if A is related to B and is different from it then B is not related to A
• Transitivity (mathematics) – Type of binary relation
  • Transitive closure – Smallest transitive relation containing a given binary relation
  • Transitive property of equality – Relationship asserting that two quantities are the samePages displaying short descriptions of redirect targets
• Equivalence and identity
  • Equivalence relation – Mathematical concept for comparing objects
  • Equivalence class – Mathematical concept
  • Equality (mathematics) – Relationship asserting that two quantities are the same
    • Inequation – Mathematical statement that two values are not equal
    • Inequality (mathematics) – Mathematical relation expressed with < or ≤
  • Similarity (geometry) – Property of objects which are scaled or mirrored versions of each other
  • Congruence (geometry) – Relationship between two figures of the same shape and size, or mirroring each other
  • Equation – Mathematical formula expressing equality
  • Identity (mathematics) – Equation that is satisfied for all values of the variables
    • Identity element – Specific element of an algebraic structure
    • Identity function – In mathematics, a function that always returns the same value that was used as its argument
  • Substitution property of equality – Relationship asserting that two quantities are the samePages displaying short descriptions of redirect targets
  • Graphing equivalence – Mathematical concept for comparing objectsPages displaying short descriptions of redirect targets
  • Extensionality – Logic principle
  • Uniqueness quantification – Logical property of being the one and only object satisfying a condition

Mathematical phraseology

• If and only if – Logical connective
• Necessary and sufficient – Terms to describe a conditional relationship between two statementsPages displaying short descriptions of redirect targets
• Distinct – Relationship asserting that two quantities are the samePages displaying short descriptions of redirect targets
• Difference – One of the four basic arithmetic operations
• Absolute value – Distance from zero to a number
• Up to – Mathematical statement of uniqueness, except for an equivalent structure (equivalence relation)
• Modular arithmetic – Computation modulo a fixed integer
• Characterization (mathematics) – Term in mathematics
• Normal form – Standard representation of a mathematical objectPages displaying short descriptions of redirect targets
• Canonical form – Standard representation of a mathematical object
• Without loss of generality – Expression in mathematics
• Vacuous truth – Conditional statement which is true because the antecedent cannot be satisfied
• Contradiction – Logical incompatibility between two or more propositions, Reductio ad absurdum – Argument that leads to a logical absurdity
• Counterexample – Exception to a proposed general rule
• Sufficiently large – mathematical conceptPages displaying wikidata descriptions as a fallback
• Pons asinorum – Statement that the angles opposite the equal sides of an isosceles triangle are themselves equal
• Table of mathematical symbols – Meanings of symbols used in mathematicsPages displaying short descriptions of redirect targets
• Contrapositive – Mathematical logic conceptPages displaying short descriptions of redirect targets
• Mathematical induction – Form of mathematical proof

Combinatorics

Combinatorics – Branch of discrete mathematics

• Permutations and combinations – Selection of items from a set
• Permutation – Mathematical version of an order change
• Combination – Selection of items from a set
• Factorial – Product of numbers from 1 to n
  • Empty product – Result from multiplying no factors
• Pascal's triangle – Triangular array of the binomial coefficients in mathematics
• Combinatorial proof – proofs in enumerative combinatorics based on bijections or double countings of combinatorial objectsPages displaying wikidata descriptions as a fallback
  • Bijective proof – Technique for proving sets have equal size
  • Double counting (proof technique) – Type of proof technique

Probability

Probability – Branch of mathematics concerning chance and uncertainty

• Average – Number taken as representative of a list of numbers
• Expected value – Average value of a random variable
• Discrete random variable – Variable representing a random phenomenonPages displaying short descriptions of redirect targets
• Sample space – Set of all possible outcomes or results of a statistical trial or experiment
• Event – In statistics and probability theory, set of outcomes to which a probability is assigned
• Conditional Probability – Probability of an event occurring, given that another event has already occurredPages displaying short descriptions of redirect targets
• Independence – When the occurrence of one event does not affect the likelihood of another
• Random variables – Variable representing a random phenomenonPages displaying short descriptions of redirect targets

Propositional logic

• Logical operator – Symbol connecting sentential formulas in logicPages displaying short descriptions of redirect targets
• Truth table – Mathematical table used in logic
• De Morgan's laws – Pair of logical equivalences
• Open sentence – formula that contains at least one free variablePages displaying wikidata descriptions as a fallback
• List of topics in logic – Overview of and topical guide to logicPages displaying short descriptions of redirect targets