User:Ascii/Definitions (by Meaning 1-800)

Metaconcepts

 * Definition:Mathematics
 * Definition:Natural Language


 * Definition:Object
 * Definition:Symbol
 * Definition:Property
 * Definition:Constant
 * Definition:Variable
 * Definition:Unique
 * Definition:Distinct
 * Definition:Distinct/Singular
 * Definition:Distinct/Plural
 * Definition:Operation


 * Definition:Formal Language
 * Definition:Formal Language/Alphabet
 * Definition:String
 * Definition:Expression
 * Definition:Well-Formed Formula
 * Definition:Formal Semantics


 * Definition:Algorithm
 * Definition:Primitive Recursive/Function
 * Definition:Unlimited Register Machine

Logic

 * Definition:Logic
 * Definition:Symbolic Logic


 * Definition:Statement
 * Definition:Proposition
 * Definition:True
 * Definition:False
 * Definition:Truth Value
 * Definition:Proof System
 * Definition:Proof
 * Definition:Axiom
 * Definition:Assumption
 * Definition:Premise


 * Definition:Valid Argument
 * Definition:Sequent
 * Definition:Logical Language
 * Definition:Logical Formula
 * Definition:Parenthesis


 * Definition:Propositional Logic
 * Definition:Language of Propositional Logic


 * Definition:Logical Connective
 * Definition:Logical Not
 * Definition:Conjunction
 * Definition:Disjunction
 * Definition:Conditional
 * Definition:Conditional/Necessary Condition
 * Definition:Converse Statement
 * Definition:Biconditional
 * Definition:Logical Equivalence
 * Definition:Iff
 * Definition:Vacuous Truth
 * Definition:Main Connective/Propositional Logic
 * Definition:Propositional Function
 * Definition:Boolean Interpretation
 * Definition:Tautology
 * Definition:Contradiction
 * Definition:Language of Propositional Logic/Formal Grammar/WFF


 * Definition:Categorical Statement
 * Definition:Categorical Syllogism


 * Definition:Predicate Logic
 * Definition:Universal Quantifier
 * Definition:Existential Quantifier
 * Definition:Free Variable
 * Definition:Language of Predicate Logic
 * Definition:Language of Predicate Logic/Formal Grammar
 * Definition:Structure for Predicate Logic


 * Definition:By Hypothesis
 * Definition:Mutatis Mutandis
 * Definition:WLOG


 * Definition:Basis for the Induction
 * Definition:Induction Hypothesis
 * Definition:Induction Step


 * Definition:RHS

Set Theory

 * Definition:Set Theory


 * Definition:Set
 * Definition:Element
 * Definition:Subset
 * Definition:Proper Subset
 * Definition:Subset/Superset
 * Definition:Set Equality
 * Definition:Singleton
 * Definition:Doubleton
 * Definition:Empty Set
 * Definition:Non-Empty Set
 * Definition:Disjoint Sets
 * Definition:Pairwise Disjoint
 * Definition:Set of Sets
 * Definition:Power Set
 * Definition:Set Partition
 * Definition:Universe (Set Theory)


 * Definition:Set Union
 * Definition:Set Union/Set of Sets
 * Definition:Set Union/Countable Union
 * Definition:Set Union/Family of Sets
 * Definition:Set Intersection
 * Definition:Set Difference
 * Definition:Symmetric Difference
 * Definition:Set Complement
 * Definition:Relative Complement
 * Definition:Successor Set


 * Definition:Finite
 * Definition:Finite Set
 * Definition:Countable Set
 * Definition:Countable Set/Countably Infinite
 * Definition:Infinite
 * Definition:Infinite Set
 * Definition:Uncountable Set
 * Definition:Set Equivalence
 * Definition:Cardinality


 * Definition:Indexing Set
 * Definition:Indexing Set/Family
 * Definition:Indexing Set/Family of Sets
 * Definition:Indexing Set/Family of Subsets
 * Definition:Indexing Set/Indexed Set


 * Definition:Ordered Pair
 * Definition:Cartesian Product
 * Definition:Cartesian Product/Finite
 * Definition:Relation
 * Definition:Relational Structure
 * Definition:Domain (Set Theory)/Relation
 * Definition:Codomain (Set Theory)/Relation
 * Definition:Image (Set Theory)/Relation/Subset
 * Definition:Restriction/Relation
 * Definition:Inverse Relation
 * Definition:Endorelation
 * Definition:Reflexive Relation
 * Definition:Antireflexive Relation
 * Definition:Reflexivity
 * Definition:Symmetric Relation
 * Definition:Antisymmetric Relation
 * Definition:Asymmetric Relation
 * Definition:Transitive Relation
 * Definition:Connected Relation
 * Definition:One-to-Many Relation
 * Definition:Many-to-One Relation
 * Definition:Left-Total Relation
 * Definition:Left-Total Relation/Multifunction
 * Definition:Composition of Relations


 * Definition:Diagonal Relation
 * Definition:Equivalence Relation
 * Definition:Equivalence Class
 * Definition:Quotient Set


 * Definition:Ordering
 * Definition:Ordered Set
 * Definition:Ordered Subset
 * Definition:Interval/Ordered Set/Closed


 * Definition:Max Operation


 * Definition:Strictly Precede
 * Definition:Preordering/Preordered Set
 * Definition:Directed Subset
 * Definition:Upper Set
 * Definition:Lower Set
 * Definition:Upper Closure/Element
 * Definition:Lower Closure/Element
 * Definition:Up-Complete
 * Definition:Element is Way Below
 * Definition:Compact Element


 * Definition:Total Ordering
 * Definition:Totally Ordered Set
 * Definition:Chain (Set Theory)


 * Definition:Well-Ordering
 * Definition:Strict Well-Ordering
 * Definition:Well-Ordered Set


 * Definition:Smallest/Set
 * Definition:Smallest/Ordered Set
 * Definition:Greatest/Ordered Set
 * Definition:Maximal/Ordered Set
 * Definition:Minimal/Ordered Set
 * Definition:Upper Bound of Set
 * Definition:Lower Bound of Set
 * Definition:Bounded Above Set
 * Definition:Bounded Below Set
 * Definition:Supremum of Set
 * Definition:Supremum of Set/Real Numbers
 * Definition:Infimum of Set
 * Definition:Infimum of Set/Real Numbers


 * Definition:Continuous Ordered Set
 * Definition:Closure Operator


 * Definition:Ideal in Ordered Set
 * Definition:Ideal (Order Theory)


 * Definition:Lattice
 * Definition:Complete Lattice
 * Definition:Join Semilattice
 * Definition:Meet Semilattice


 * Definition:Ordered Tuple
 * Definition:Ordered Tuple as Ordered Set/Ordered Triple


 * Definition:Transitive Class
 * Definition:Minimal Infinite Successor Set


 * Definition:Class (Class Theory)
 * Definition:Small Class
 * Definition:Class/Proper Class


 * Definition:Cardinal
 * Definition:Ordinal Class
 * Definition:Limit Ordinal

Mappings

 * Definition:Mapping
 * Definition:Graph of Mapping
 * Definition:Well-Defined/Mapping
 * Definition:Function
 * Definition:Domain (Set Theory)/Mapping
 * Definition:Codomain (Set Theory)/Mapping
 * Definition:Image (Set Theory)/Mapping/Mapping
 * Definition:Image (Set Theory)/Mapping/Subset
 * Definition:Image (Set Theory)/Mapping/Element
 * Definition:Preimage/Mapping/Subset
 * Definition:Preimage/Mapping/Element
 * Definition:Fixed Point
 * Definition:Restriction/Mapping
 * Definition:Extension of Mapping
 * Definition:Inverse Mapping
 * Definition:Finite Sequence
 * Definition:Constant Mapping
 * Definition:Identity Mapping
 * Definition:Permutation
 * Definition:Surjection
 * Definition:Injection
 * Definition:Bijection


 * Definition:Projection (Mapping Theory)
 * Definition:Projection (Mapping Theory)/First Projection
 * Definition:Direct Image Mapping/Mapping


 * Definition:Set of All Mappings
 * Definition:Composition of Mappings


 * Definition:Characteristic Function (Set Theory)/Set
 * Definition:Inclusion Mapping


 * Definition:Sequence
 * Definition:Length of Sequence
 * Definition:Sequence/Infinite Sequence
 * Definition:Term of Sequence
 * Definition:Subsequence


 * Definition:Bounded Mapping
 * Definition:Bounded Sequence/Real
 * Definition:Bounded Below


 * Definition:Order Isomorphism
 * Definition:Order Embedding
 * Definition:Increasing/Mapping
 * Definition:Quotient Mapping


 * Definition:Ordinal

Number Systems

 * Definition:Number
 * Definition:Natural Numbers
 * Definition:Zero (Number)
 * Definition:Number Base
 * Definition:Decimal Notation
 * Definition:Digit
 * Definition:Decimal Expansion
 * Definition:Initial Segment
 * Definition:Initial Segment of Natural Numbers


 * Definition:Integer
 * Definition:Positive/Integer
 * Definition:Strictly Positive/Integer
 * Definition:Negative/Integer
 * Definition:Rational Number
 * Definition:Rational Number/Fraction
 * Definition:Rational Number/Fraction/Numerator
 * Definition:Rational Number/Fraction/Denominator
 * Definition:Rational Number/Canonical Form
 * Definition:Ratio


 * Definition:Medial
 * Definition:Irrational Number
 * Definition:Commensurable
 * Definition:Incommensurable
 * Definition:Commensurable in Square Only
 * Definition:Incommensurable in Square


 * Definition:Real Number
 * Definition:Real Number/Axioms
 * Definition:Positive/Real Number
 * Definition:Strictly Positive
 * Definition:Strictly Positive/Real Number
 * Definition:Negative/Real Number
 * Definition:Real Number/Real Number Line
 * Definition:Real Interval
 * Definition:Real Interval/Open
 * Definition:Real Interval/Closed
 * Definition:Real Interval/Half-Open
 * Definition:Coordinate System/Origin
 * Definition:Cartesian Coordinate System/Coordinate Plane
 * Definition:Axis/X-Axis
 * Definition:Axis/Y-Axis


 * Definition:Complex Number
 * Definition:Complex Number/Real Part
 * Definition:Complex Number/Imaginary Part
 * Definition:Complex Number/Imaginary Unit
 * Definition:Complex Number/Polar Form
 * Definition:Argument of Complex Number
 * Definition:Complex Conjugate
 * Definition:Complex Plane
 * Definition:Complex Arithmetic


 * Definition:Quaternion


 * Definition:Absolute Value
 * Definition:Addition
 * Definition:Addition/Natural Numbers
 * Definition:Addition/Integers
 * Definition:Addition/Real Numbers
 * Definition:Complex Addition
 * Definition:Multiplication
 * Definition:Multiplication/Natural Numbers
 * Definition:Multiplication/Integers
 * Definition:Multiplication/Real Numbers
 * Definition:Complex Multiplication
 * Definition:Power (Algebra)/Integer
 * Definition:Power (Algebra)/Real Number
 * Definition:Complex Modulus


 * Definition:Standard Number Field


 * Definition:Usual Ordering

Number Theory

 * Definition:Even Integer
 * Definition:Odd Integer
 * Definition:Reciprocal
 * Definition:Proportion


 * Definition:Floor Function
 * Definition:Ceiling Function


 * Definition:Square Number
 * Definition:Square/Function
 * Definition:Square Root
 * Definition:Quadratic Equation


 * Definition:Factorial
 * Definition:Falling Factorial
 * Definition:Integer Sequence
 * Definition:Divisor (Algebra)/Integer
 * Definition:Divisor (Algebra)/Integer/Aliquot Part
 * Definition:Common Divisor of Integers
 * Definition:Greatest Common Divisor/Integers
 * Definition:Lowest Common Multiple/Integers
 * Definition:Integers Modulo m
 * Definition:Modulo Operation
 * Definition:Congruence (Number Theory)
 * Definition:Congruence Modulo Integer
 * Definition:Quadratic Residue


 * Definition:Prime Number
 * Definition:Composite Number
 * Definition:Odd Prime
 * Definition:Semiprime Number
 * Definition:Prime Decomposition
 * Definition:Prime Decomposition/Multiplicity
 * Definition:Square-Free Integer
 * Definition:Prime Factor
 * Definition:Coprime Integers
 * Definition:Perfect Number


 * Definition:Fibonacci Number
 * Definition:Golden Mean


 * Definition:Apotome


 * Definition:Sigma Function
 * Definition:Tau Function
 * Definition:Euler Phi Function
 * Definition:Deficient Number


 * Definition:Triangular Number
 * Definition:Pascal's Triangle
 * Definition:Binomial (Euclidean)
 * Definition:Binomial Coefficient


 * Definition:Stirling Numbers of the First Kind/Unsigned
 * Definition:Stirling Numbers of the Second Kind


 * Definition:Geometric Progression
 * Definition:Geometric Progression/Integers


 * Definition:Real Sequence
 * Definition:Complex Sequence
 * Definition:Complex Roots of Unity
 * Definition:Complex Function


 * Definition:Algebraic Number
 * Definition:Harmonic Numbers
 * Definition:P-adic Norm
 * Definition:P-adic Number


 * Definition:Convergent of Continued Fraction

Abstract Algebra

 * Definition:Abstract Algebra


 * Definition:Well-Defined/Operation
 * Definition:Operation/Binary Operation
 * Definition:Closure (Abstract Algebra)/Algebraic Structure
 * Definition:Product Notation (Algebra)/Infinite
 * Definition:Restriction/Operation
 * Definition:Operation Induced on Set of Mappings


 * Definition:Subset Product
 * Definition:Idempotence/Element
 * Definition:Idempotence/Operation
 * Definition:Commute
 * Definition:Commutative Operation
 * Definition:Associative Operation
 * Definition:Cancellable Element
 * Definition:Identity (Abstract Algebra)/Two-Sided Identity
 * Definition:Invertible Element
 * Definition:Inverse (Abstract Algebra)/Inverse


 * Definition:Relation Compatible with Operation
 * Definition:Congruence Relation


 * Definition:Algebraic Structure
 * Definition:Underlying Set
 * Definition:Order of Structure
 * Definition:Morphism Property
 * Definition:Homomorphism (Abstract Algebra)
 * Definition:Epimorphism (Abstract Algebra)
 * Definition:Isomorphism (Abstract Algebra)
 * Definition:External Direct Product


 * Definition:Magma
 * Definition:Semigroup
 * Definition:Subsemigroup
 * Definition:Naturally Ordered Semigroup
 * Definition:Commutative Semigroup
 * Definition:Monoid
 * Definition:Commutative Monoid
 * Definition:Group
 * Definition:Trivial Group
 * Definition:Additive Group of Integers
 * Definition:Group Axioms
 * Definition:Group Product
 * Definition:Group Direct Product
 * Definition:Power of Element/Group
 * Definition:Finite Group
 * Definition:Cayley Table
 * Definition:Order of Group Element
 * Definition:Abelian Group
 * Definition:Subgroup
 * Definition:Index of Subgroup
 * Definition:Normal Subgroup
 * Definition:Generated Subgroup
 * Definition:Generator of Subgroup
 * Definition:Sylow p-Subgroup
 * Definition:Cyclic Group
 * Definition:Cyclic Group/Generator
 * Definition:Center (Abstract Algebra)/Group
 * Definition:Symmetric Group
 * Definition:Symmetric Group/n Letters
 * Definition:Normalizer


 * Definition:Group Homomorphism
 * Definition:Kernel of Group Homomorphism
 * Definition:Isomorphism (Abstract Algebra)/Group Isomorphism
 * Definition:Group Epimorphism
 * Definition:Coset/Left Coset
 * Definition:Coset/Right Coset
 * Definition:Quotient Group
 * Definition:Orbit (Group Theory)


 * Definition:Distributive Operation
 * Definition:Boolean Algebra


 * Definition:Ring (Abstract Algebra)
 * Definition:Ring (Abstract Algebra)/Ring Axioms
 * Definition:Ring (Abstract Algebra)/Ring Addition
 * Definition:Ring (Abstract Algebra)/Ring Product
 * Definition:Kronecker Delta
 * Definition:Subring
 * Definition:Ring Zero
 * Definition:Commutative Ring
 * Definition:Unity of Ring
 * Definition:Ring with Unity
 * Definition:Divisor (Algebra)/Ring with Unity
 * Definition:Commutative and Unitary Ring
 * Definition:Unit of Ring
 * Definition:Group of Units/Ring
 * Definition:Ideal of Ring
 * Definition:Principal Ideal of Ring
 * Definition:Maximal Ideal of Ring
 * Definition:Division Ring
 * Definition:Norm/Division Ring
 * Definition:Normed Division Ring
 * Definition:Metric Induced by Norm on Division Ring
 * Definition:Non-Archimedean/Norm (Division Ring)
 * Definition:Convergent Sequence/Normed Division Ring
 * Definition:Cauchy Sequence/Normed Division Ring
 * Definition:Quotient Ring
 * Definition:Ring Homomorphism
 * Definition:Isomorphism (Abstract Algebra)/Ring Isomorphism
 * Definition:Ring Monomorphism
 * Definition:Characteristic of Ring
 * Definition:Algebra over Ring


 * Definition:Integral Domain
 * Definition:Strict Positivity Property
 * Definition:Proper Zero Divisor
 * Definition:Ordered Basis
 * Definition:Ordered Integral Domain
 * Definition:Linearly Independent/Set


 * Definition:Field (Abstract Algebra)
 * Definition:Subfield
 * Definition:Field Extension
 * Definition:Quotient Field
 * Definition:Valued Field
 * Definition:Field of Real Numbers


 * Definition:Summation
 * Definition:Summation/Indexed


 * Definition:Polynomial
 * Definition:Polynomial over Ring
 * Definition:Polynomial Ring
 * Definition:Polynomial Ring/Indeterminate
 * Definition:Coefficient of Polynomial
 * Definition:Ring of Polynomial Forms


 * Definition:Module
 * Definition:Right Module
 * Definition:Unitary Module
 * Definition:Linear Transformation
 * Definition:Dimension (Linear Algebra)
 * Definition:Generator of Module


 * Definition:Vector Space
 * Definition:Vector (Linear Algebra)
 * Definition:Zero Vector
 * Definition:Vector Subspace
 * Definition:Real Vector Space
 * Definition:Dimension of Vector Space
 * Definition:Normed Vector Space
 * Definition:Norm/Vector Space
 * Definition:Basis of Vector Space
 * Definition:Vector-Valued Function
 * Definition:Linear Combination
 * Definition:Standard Ordered Basis/Vector Space


 * Definition:Coefficient
 * Definition:Degree of Polynomial
 * Definition:Root of Polynomial
 * Definition:Group Action


 * Definition:Matrix
 * Definition:Matrix/Element
 * Definition:Matrix/Row
 * Definition:Matrix/Column
 * Definition:Matrix/Square Matrix
 * Definition:Matrix/Square Matrix/Order
 * Definition:Matrix Space
 * Definition:Unit Matrix
 * Definition:Matrix Product (Conventional)
 * Definition:Determinant/Matrix