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# Nav/Definition

The following table lists all of the definitions in the wiki.

Page Link Defined words Title Clusters
Def/Abelian Abelian Abelian Clust/Basic group theory
Def/Algebraically closed Algebraically closed Algebraically closed Clust/Field theory
Def/Antisymmetric relation Antisymmetric Antisymmetric relation Clust/Relations
Def/Arithmetic progression Arithmetic progression
Linear progression
Slope
Step size
Arithmetic progression Clust/Sequences
Def/Associate Associate Associate Clust/Basic ring theory
Def/Associative Associative
Regroup
Associative Clust/Operations
Def/Associative bijection Associative bijection Associative bijection Clust/Basic set theory
Clust/Operations
Def/Basis (vector space) Basis Basis (vector space) Clust/Linear algebra
Def/Bijection Bijection Bijection Clust/Functions
Def/Binary predicate Binary predicate Binary Predicate Clust/Logic and foundations
Def/Binary operation Binary operation Binary operation Clust/Operations
Def/Binary relation Binary relation Binary relation Clust/Relations
Def/Boolean conjunction Boolean conjunction
AND
OR
XOR
IMPLIES
Hypothesis
Premise
Conclusion
Boolean conjunction Clust/Elementary logic
Def/Bound variable Bound variable Bound variable Clust/Logic and foundations
Def/Canonical decomposition into primes Canonical decomposition Canonical decomposition into primes Clust/Basic number theory
Def/Cardinality Cardinality
Equipotent
Cardinality Clust/Cardinals and ordinals
Clust/Basic set theory
Def/Cartesian product Cartesian product
Projection
Cartesian product Clust/Basic set theory
Def/Center (group) Center Center of a group Clust/Basic group theory
Def/Circuit Circuit Circuit
Def/Class Class
Proper class
Class Clust/Logic and foundations
Def/Commutative Commutative Commutative Clust/Operations
Def/Commute Commute Commute Clust/Operations
Def/Compact Compact Compact Clust/Topology
Def/Complement of a set Complement Complement of a set Clust/Basic set theory
Def/Complex number Complex number
Imaginary number
Complex conjugate
Norm
Absolute value
Complex number Clust/Field theory
Clust/Complex analysis
Clust/Number systems
Def/Composite number Composite number Composite number Clust/Basic number theory
Def/Composite function Compose Composition Clust/Functions
Def/Rooted ordered binary tree Binary composition tree
Rooted ordered binary tree
Leaf
Composition tree Clust/Graph theory
Clust/Operations
Def/Congruent Congruent
Mod
Congruent
Def/Conjugate Conjugate
Conjugacy
Conjugacy class
Conjugate
Def/Continuous function from R to R Continuous Continuous function (from R to R) Clust/Basic analysis
Def/Continuous function (in topology) Continuous Continuous function (in topology) Clust/Topology
Def/Coset Coset
Index
Coset Clust/Basic group theory
Def/Countable Countable
Denumerable
Aleph naught
Countable Clust/Basic set theory
Def/Cover Cover Cover Clust/Topology
Def/Cycle type Cycle Cycle type Clust/Permutations
Def/Cyclic Cyclic Cyclic (group) Clust/Basic group theory
Def/Cyclic permutation Cyclic permutation
Cycle
Cyclic permutation
Def/Dedekind complete Dedekind complete Dedekind complete Clust/Ordered ring theory
Def/Dedekind cut Dedekind cut Dedekind cut Clust/Ordered ring theory
Def/Descent of functions Descend
Well-defined
Descent of functions Clust/Functions
Def/Digraph Digraph
Directed graph
Vertex
Node
Edge
Source
Target
Digraph Clust/Graph theory
Def/Dimension Dimension Dimension Clust/Linear algebra
Def/Diophantine equation Diophantine equation Diophantine equation
Def/Discriminant of a binary quadratic form Discriminant
Definite
Indefinite
Degenerate
Def/Distributive Distributive Distributive Clust/Operations
Def/Divides Divides
Goes into
Multiple
Divides Clust/Basic number theory
Clust/Basic ring theory
Def/Division with remainder Remainder
Quotient
Division with remainder
Division of integers with remainder Clust/Basic number theory
Def/Domain topograph Domain topograph Domain Topograph Clust/Binary quadratic forms
Def/Element Element
Member
Element Clust/Basic set theory
Def/Empty set Empty set Empty set Clust/Basic set theory
Def/Equivalence class Equivalence class Equivalence class Clust/Relations
Def/Equivalence relation Equivalence relation Equivalence relation Clust/Relations
Def/Euclidean algorithm Euclidean algorithm Clust/Basic number theory
Clust/Factorization in rings
Def/Euclidean domain Euclidean domain Euclidean domain Clust/Factorization in rings
Def/Euclidean metric Euclidean metric Euclidean metric
Def/Euclidean valuation Euclidean valuation
Quotient
Remainder
Euclidean valuation Clust/Factorization in rings
Def/Even Even Even Clust/Basic number theory
State/Every lax basis is contained in exactly two lax superbases Every lax basis is contained in exactly two lax superbases Clust/Binary quadratic forms
Def/Extension of functions Extend Extension of a function Clust/Functions
Def/Factorial Factorial Factorial Clust/Properties of natural numbers
Clust/Basic counting
Def/Factorization into irreducibles Factorization into irreducibles Clust/Factorization in rings
Clust/Basic ring theory
Def/Field Field Field Clust/Basic ring theory
Clust/Field theory
Def/Finite (set) Finite
Pigeonhole principle
Finite Clust/Basic set theory
Def/Finite sequence Finite sequence
Length
Entry
Empty sequence
Reversion
Reverse sequence
Entrywise
Concatenate
Finite sequence Clust/Naive set theory
Clust/Sequences
Def/Fixed point Fixed
Fixed point
Fixed point
Def/Floor Floor
Integer part
Floor
Def/Function Function
Map
Domain (of a function)
Source (of a function)
Target (of a function)
Function Clust/Functions
Def/Gaussian integer Gaussian integer Gaussian integer Clust/Basic ring theory
Clust/Factorization in rings
Clust/Number systems
Def/Graph Graph
Point
Vertex
Edge
Endpoint
Graph
Def/Greatest common divisor Greatest common divisor Greatest common divisor Clust/Basic number theory
Clust/Factorization in rings
Def/Group Group Group Clust/Basic group theory
Clust/Abstract algebraic structures
Def/Generate (group) Generated
Word
Group generation Clust/Basic group theory
Def/Group homomorphism Homomorphism
Preserve
Group homomorphism Clust/Basic group theory
Def/Ideal Left ideal
Ideal
Right ideal
Two-sided ideal
Ideal Clust/Basic ring theory
Def/Ideal generation Generated Ideal generation Clust/Basic ring theory
Def/Identity function Identity function Identity function Clust/Functions
Def/Image Image
Corestriction
Image Clust/Functions
Def/Inclusion function Inclusion function Inclusion function Clust/Functions
Def/Inductive predicate Inductive predicate Inductive predicate Clust/Basic set theory
Def/Injective Injective
One-to-one
Injective Clust/Functions
Def/Integer Integer Integer Clust/Basic number theory
Clust/Number systems
Def/Integral domain Integral domain
Domain (in ring theory)
Integral domain Clust/Basic ring theory
Def/Interior Interior Interior Clust/Metric geometry
Clust/Topology
Def/Intersection Intersection Intersection Clust/Basic set theory
Def/Inverse function Left inverse
Right inverse
Two-sided inverse
Inverse function Clust/Functions
Def/Invertible residue Invertible residue Invertible residue Clust/Modular arithmetic
Def/Irreducible element Irreducible Irreducible Clust/Factorization in rings
Def/Kernel (group) Kernel Kernel of a group homomorphism Clust/Basic group theory
Def/Language of set theory Language of set theory
Well-formed formula
Wff
Language of Set Theory Clust/Logic and foundations
Def/Lax basis Lax basis Lax basis Clust/Binary quadratic forms
Def/Lax superbasis Lax superbasis Lax superbasis Clust/Binary quadratic forms
Def/Lax vector Lax vector
Primitive
Def/Least common multiple Least common multiple
LCM
Least common multiple Clust/Basic number theory
Clust/Factorization in rings
Def/Least upper bound Least upper bound
Supremum
Least upper bound Clust/Ordered sets
Def/Legendre symbol Legendre symbol Legendre Symbol Clust/Theory of quadratic residues
Def/Limit (sequence) Limit
Converge
Limit (sequence) Clust/Basic analysis
Clust/Metric geometry
Clust/Topology
Def/Linearly independent Linearly independent
Def/Maximal element Maximal element Maximal element Clust/Ordered sets
Def/Maximum Maximum Clust/Ordered sets
Def/Metric space Metric space
Metric
Triangle inequality
Distance
Open ball
Closed ball
Open
Metric topology
Metric space Clust/Metric geometry
Def/Minimal element Minimal element Minimal element Clust/Ordered sets
Def/Monoid Monoid Monoid Clust/Basic group theory
Clust/Abstract algebraic structures
Def/Multiplication of cardinal numbers Product Multiplication of cardinal numbers Clust/Cardinal arithmetic
Def/N to 1 function N to 1 N to 1 function
Def/Natural number Natural number
Successor
Natural Number Clust/Number systems
Clust/Logic and foundations
Def/Nilpotent Nilpotent Nilpotent Clust/Basic ring theory
Def/Normal subgroup Normal Normal subgroup
Def/Odd Def/Odd Odd Clust/Basic number theory
Def/Order (permutation) Order Order of a permutation. Clust/Permutations
Def/Ordered pair Ordered pair
Entry
Coordinate
Ordered Pair Clust/Basic set theory
Def/Ordered field Ordered field Ordered field Clust/Ordered ring theory
Def/Ordered ring Ordered ring
Positive
Negative
Ordered ring Clust/Ordered ring theory
Def/Ordered tuple Ordered triple
Tuple
Ordered tuple
Def/Ordinal number Ordinal
Ordinal number
Ordinal number Clust/Cardinals and ordinals
Def/PID Principal ideal domain
PID
PID Clust/Factorization in rings
Clust/Basic ring theory
Def/Partial order Partial order
Partially ordered set
Poset
Partial order Clust/Ordered sets
Clust/Relations
Def/Partition Partition Partition Clust/Basic set theory
Def/Permutation Permutation Permutation Clust/Permutations
Clust/Basic counting
Def/Polynomial Univariate
Coefficient
Degree
Evaluate
Polynomial Clust/The algebra of polynomials
Clust/Basic ring theory
Def/Power set Power set Power Set Clust/Basic set theory
Def/Preimage Preimage Preimage Clust/Functions
Def/Prime number Prime number Prime Number Clust/Basic number theory
Def/Prime counting function Prime counting function Prime counting function
Def/Prime element Prime element Prime element Clust/Factorization in rings
Def/Prime factorization Prime factorization Prime factorization
Def/Principal ideal Principal
Generated
Principal Clust/Basic ring theory
Clust/Modular arithmetic
Acceleration
Def/Quotient ring Congruent
Quotient ring
Quotient ring Clust/Basic ring theory
Def/Range topograph Range topograph
Lake
River
Neutral edge
Climb
Well
Double-well
Def/Rational number Rational number
Fraction
Rational number Clust/Number systems
Def/Real number Real number Real number Clust/Number systems
Clust/Ordered ring theory
Clust/Field theory
Clust/Basic analysis
Def/Recursion Recursive Recursion Clust/Properties of natural numbers
Clust/Logic and foundations
Def/Reduce mod n Reduce Reduce mod n Clust/Modular arithmetic
Def/Reflexive relation Reflexive Reflexive relation Clust/Relations
Def/Relatively prime Relatively prime
Coprime
Relatively prime Clust/Basic number theory
Clust/Basic ring theory
Def/Residue Residue
Modular arithmetic
Residue Clust/Modular arithmetic
Def/Restriction of functions Restriction Restriction of functions Clust/Functions
Def/Ring Ring Ring Clust/Basic ring theory
Def/Ring automorphism Automorphism Ring automorphism Clust/Basic ring theory
Def/Ring homomorphism Homomorphism Ring homomorphism Clust/Basic ring theory
Def/Root of a polynomial Root Roots of a polynomial Clust/The algebra of polynomials
Def/Russell predicate Russell predicate Russell predicate Clust/Logic and foundations
Def/Sequence Sequence Sequence Clust/Sequences
Def/Sequence of differences Difference sequence Sequence of differences
Def/Sequence of primes Sequence of primes Sequence of primes Clust/Basic number theory
Def/Set Set Set Clust/Basic set theory
Clust/Logic and foundations
Def/Sign of a permutation Sign
Derangement
Inversion
Sign of a permutation Clust/Permutations
Def/Span Span Span Clust/Linear algebra
Def/Square root Square root Square root Clust/Basic ring theory
Def/Subfield Subfield
Field extension
Characteristic subfield
Degree
Subfield Clust/Field theory
Def/Subgroup Subgroup
Trivial subgroup
Subgroup Clust/Basic group theory
Def/Subset Subset
Proper subset
Subset Clust/Basic set theory
Def/Subspace Subspace Subspace
Def/Successor Successor Successor Clust/Basic set theory
Clust/Cardinals and ordinals
Def/Surjective Surjective
Onto
Surjective Clust/Functions
Def/Sylow subgroup Sylow subgroup Sylow subgroup Clust/Structure theory of finite groups
Def/Symmetric relation Symmetric Symmetric relation Clust/Relations
Def/Topological space Topological space
Topology
Open
Basis
Topological space Clust/Topology
Def/Total order Total order Totally ordered Clust/Ordered sets
Clust/Relations
Def/Totient Totient Totient Clust/Modular arithmetic
Def/Transitive relation Transitive Transitive relation Clust/Relations
Def/Transposition Transposition
Transpose
Switch
Exchange
Transposition
Def/Two to one Two to one Two to one Clust/Functions
Clust/Basic counting
Def/UFD Unique factorization domain
UFD
UFD Clust/Factorization in rings
Def/Unary predicate Unary predicate Unary predicate Clust/Logic and foundations
Def/Union Union Union Clust/Basic set theory
Def/Unit Multiplicative inverse
Unit
Unit Clust/Basic ring theory
Def/Unital Unital
Multiplicative identity element
Unital Clust/Basic ring theory
Def/Unordered pair Unordered pair Unordered Pair Clust/Basic set theory
Def/Upper bound Upper bound
Bounded above
Upper bound Clust/Ordered sets
Def/Vector space Vector space
Vector
Scaling
Scalar multiplication
Vector space Clust/Linear algebra
Clust/Abstract algebraic structures
Def/Well ordered Well-ordered Well ordered
Def/Zero divisor Zero divisor Zero divisor Clust/Basic ring theory
Def/Nonempty Nonempty nonempty Clust/Basic set theory
Def/Order of a group element Infinite order
Order
order of a group element Clust/Basic group theory
Def/P-group P-group p-group Clust/Structure theory of finite groups
Def/Unique factorization Unique factorization unique factorization Clust/Factorization in rings