User:Ascii/Definitions (by Meaning 1-600)

Metaconcepts

 * Definition:Mathematics
 * Definition:Natural Language


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


 * Definition:Formal Language
 * Definition:Well-Formed Formula
 * Definition:Formal Semantics


 * Definition:Algorithm

Logic

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


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


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


 * Definition:Logical Not
 * Definition:Conjunction
 * Definition:Disjunction
 * Definition:Conditional
 * 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:Contradiction
 * Definition:Language of Propositional Logic/Formal Grammar/WFF


 * Definition:Language of Predicate Logic
 * Definition:Language of Predicate Logic/Formal Grammar
 * Definition:Structure for Predicate Logic
 * Definition:Categorical Statement


 * Definition:By Hypothesis
 * Definition:Mutatis Mutandis
 * Definition:WLOG
 * Definition:Basis for the Induction
 * Definition:Induction Hypothesis
 * Definition:Induction Step

Set Theory

 * Definition:Set Theory


 * Definition:Set
 * Definition:Element
 * Definition:Subset
 * Definition:Proper Subset
 * Definition:Subset/Superset
 * Definition:Set Equality
 * Definition:Singleton
 * 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:Set Complement
 * Definition:Relative Complement
 * Definition:Successor Set


 * Definition:Finite
 * Definition:Finite Set
 * Definition:Countable Set
 * Definition: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/Indexed Set


 * Definition:Ordered Pair
 * Definition:Cartesian Product
 * Definition:Relation
 * Definition:Relational Structure
 * Definition:Domain (Relation Theory)/Relation
 * Definition:Inverse Relation
 * Definition:Endorelation
 * Definition:Reflexive Relation
 * Definition:Antireflexive Relation
 * Definition:Reflexivity
 * Definition:Symmetric Relation
 * Definition:Antisymmetric Relation
 * Definition:Transitive Relation
 * Definition:Connected Relation
 * Definition:Many-to-One Relation
 * Definition:Left-Total Relation
 * Definition:Left-Total Relation/Multifunction


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


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


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


 * Definition:Smallest/Ordered Set
 * Definition:Greatest/Ordered Set
 * Definition:Maximal Element
 * Definition:Minimal Element
 * 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:Lattice
 * Definition:Complete Lattice
 * Definition:Join Semilattice
 * Definition:Meet Semilattice


 * Definition:Ordered Tuple


 * Definition:Class (Class Theory)


 * Definition:Cardinal
 * Definition:Limit Ordinal

Mappings

 * Definition:Mapping
 * Definition:Graph of Mapping
 * Definition:Well-Defined/Mapping
 * Definition:Function
 * Definition:Domain (Relation Theory)/Mapping
 * Definition:Codomain (Relation 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: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: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:Order Isomorphism
 * Definition:Order Embedding
 * Definition:Increasing/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:Integer
 * Definition:Positive/Integer
 * Definition:Strictly Positive/Integer
 * Definition:Rational Number
 * Definition:Rational Number/Fraction/Numerator
 * Definition:Rational Number/Fraction/Denominator
 * Definition:Ratio


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


 * 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 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: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: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:Modulo Operation
 * Definition:Congruence (Number Theory)
 * Definition:Congruence Modulo Integer


 * Definition:Prime Number
 * Definition:Composite Number
 * Definition:Odd Prime
 * Definition:Prime Decomposition
 * Definition:Prime Decomposition/Multiplicity
 * Definition:Prime Factor
 * Definition:Coprime Integers
 * Definition:Perfect Number


 * Definition:Fibonacci Number
 * Definition:Golden Mean


 * Definition:Apotome


 * Definition:Divisor Sum Function
 * Definition:Divisor Counting Function
 * Definition:Euler Phi Function
 * Definition:Deficient Number


 * Definition:Triangular Number
 * Definition:Binomial (Euclidean)
 * Definition:Binomial Coefficient


 * Definition:Stirling Numbers of the Second Kind


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


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

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:Subset Product
 * 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:Order of Structure
 * Definition:Morphism Property
 * Definition:Homomorphism (Abstract Algebra)
 * Definition:Isomorphism (Abstract Algebra)


 * Definition:Magma
 * Definition:Semigroup
 * Definition:Subsemigroup
 * Definition:Naturally Ordered Semigroup
 * Definition:Commutative Semigroup
 * Definition:Monoid
 * Definition:Group
 * Definition:Cayley Table
 * Axiom:Group Axioms
 * Definition:Group Product
 * Definition:Finite Group
 * Definition:Order of Group Element
 * Definition:Abelian Group
 * Definition:Subgroup
 * Definition:Index of Subgroup
 * Definition:Normal Subgroup
 * Definition:Generated 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:Group Homomorphism
 * Definition:Kernel of Group Homomorphism
 * Definition:Isomorphism (Abstract Algebra)/Group Isomorphism
 * Definition:Coset/Left Coset
 * Definition:Coset/Right Coset
 * Definition:Quotient Group
 * Definition:Orbit (Group Theory)


 * Definition:Distributive Operation
 * Definition:Ring (Abstract Algebra)
 * Definition:Ring (Abstract Algebra)/Product
 * Definition:Kronecker Delta
 * Definition:Subring
 * Definition:Ring Zero
 * Definition:Commutative Ring
 * Definition:Unity (Abstract Algebra)/Ring
 * Definition:Ring with Unity
 * Definition:Divisor (Algebra)/Ring with Unity
 * Definition:Commutative and Unitary Ring
 * Definition:Unit of 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:Non-Archimedean/Norm (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:Integral Domain
 * 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:Field of Quotients
 * Definition:Valued Field
 * Definition:Field of Real Numbers


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


 * Definition:Summation


 * Definition:Module
 * Definition:Unitary Module
 * Definition:Linear Transformation
 * 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: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:Unit Matrix
 * Definition:Matrix Product (Conventional)
 * Definition:Determinant/Matrix

Topology

 * Definition:Topology
 * Definition:Topological Space
 * Definition:Open Set/Topology
 * Definition:Closed Set/Topology
 * Definition:Clopen Set
 * Definition:Discrete Topology
 * Definition:Indiscrete Topology
 * Definition:Particular Point Topology
 * Definition:Separation (Topology)
 * Definition:Topological Subspace


 * Definition:Interior (Topology)
 * Definition:Basis (Topology)
 * Definition:Basis (Topology)/Analytic Basis
 * Definition:Local Basis
 * Definition:Second-Countable Space


 * Definition:Neighborhood (Topology)/Point
 * Definition:Open Neighborhood
 * Definition:Limit Point/Topology/Set
 * Definition:Closure (Topology)
 * Definition:Everywhere Dense
 * Definition:Separable Space
 * Definition:Connected (Topology)/Topological Space
 * Definition:Connected Set (Topology)


 * Definition:Filter


 * Definition:Cover of Set
 * Definition:Subcover/Finite
 * Definition:Countably Compact Space
 * Definition:Open Cover
 * Definition:Compact Topological Space


 * Definition:Continuous Mapping (Topology)
 * Definition:Continuous Mapping (Topology)/Everywhere


 * Definition:Path (Topology)


 * Definition:Kolmogorov Space
 * Definition:Fréchet Space (Topology)
 * Definition:Hausdorff Space
 * Definition:T3 Space
 * Definition:T4 Space
 * Definition:T5 Space


 * Definition:Product Space (Topology)


 * Definition:Euclidean Space
 * Definition:Euclidean Space/Euclidean Topology/Real Number Line
 * Definition:Vector (Euclidean Space)


 * Definition:Metric Space
 * Axiom:Metric Space Axioms
 * Definition:Metric Space/Distance Function
 * Definition:Open Set/Metric Space
 * Definition:Closed Set/Metric Space
 * Definition:Open Ball
 * Definition:Neighborhood (Metric Space)
 * Definition:Isometry (Metric Spaces)
 * Definition:Continuous Mapping (Metric Spaces)
 * Definition:Convergent Sequence (Metric Space)
 * Definition:Bounded Metric Space
 * Definition:Complete Metric Space
 * Definition:Euclidean Metric/Real Number Line

Analysis

 * Definition:Extended Real Number Line


 * Definition:Real Function
 * Definition:Real-Valued Function
 * Definition:Strictly Increasing/Real Function
 * Definition:Bounded Mapping/Real-Valued


 * Definition:Convergent Sequence
 * Definition:Convergent Real Sequence
 * Definition:Limit of Sequence/Real Numbers
 * Definition:Series
 * Definition:Power Series
 * Definition:Generating Function
 * Definition:Convergent Series
 * Definition:Absolutely Convergent Series
 * Definition:Uniform Convergence


 * Definition:Cauchy Sequence


 * Definition:Continuous on Interval
 * Definition:Continuous Real Function
 * Definition:Continuous Complex Function


 * Definition:Exponential Function/Real
 * Definition:Natural Logarithm
 * Definition:Complex Natural Logarithm


 * Definition:Gamma Function


 * Definition:Differentiable Mapping/Real Function/Interval
 * Definition:Derivative
 * Definition:Differentiation
 * Definition:Primitive (Calculus)
 * Definition:Primitive (Calculus)/Arbitrary Constant
 * Definition:Definite Integral
 * Definition:Differential Equation
 * Definition:Differential Equation/Solution
 * Definition:Solution Set of Differential Equation
 * Definition:Initial Condition


 * Definition:First Order Ordinary Differential Equation
 * Definition:Second Order Ordinary Differential Equation
 * Definition:Constant Coefficient Homogeneous Linear Second Order ODE


 * Definition:Open Set/Complex Analysis
 * Definition:Functional/Real
 * Definition:Riemann Zeta Function


 * Definition:Laplace Transform


 * Definition:Hilbert Space

Geometry

 * Definition:Geometric Figure
 * Definition:Point
 * Definition:Line/Straight Line
 * Definition:Line/Segment
 * Definition:Line/Curve
 * Definition:Rational Line Segment
 * Definition:Bisection
 * Definition:Intersection (Geometry)


 * Definition:Linear Measure/Length
 * Definition:Linear Measure/Breadth
 * Definition:Commensurable in Length
 * Definition:Angle
 * Definition:Right Angle
 * Definition:Perpendicular
 * Definition:Parallel (Geometry)/Lines


 * Definition:Dimension (Geometry)


 * Definition:Locus


 * Definition:Polygon
 * Definition:Polygon/Side
 * Definition:Polygon/Vertex
 * Definition:Polygon/Regular
 * Definition:Triangle (Geometry)
 * Definition:Triangle (Geometry)/Right-Angled
 * Definition:Triangle (Geometry)/Equilateral
 * Definition:Quadrilateral/Square
 * Definition:Quadrilateral/Rectangle
 * Definition:Quadrilateral/Rectangle/Containment
 * Definition:Quadrilateral/Parallelogram
 * Definition:Circle
 * Definition:Circle/Center
 * Definition:Circle/Radius
 * Definition:Circle/Diameter
 * Definition:Circle/Circumference
 * Definition:Circle/Arc
 * Definition:Unit Circle
 * Definition:Ellipse
 * Definition:Plane Surface/The Plane
 * Definition:Plane Surface
 * Definition:Area
 * Definition:Rational Area
 * Definition:Medial Area


 * Definition:Polyhedron
 * Definition:Polyhedron/Face
 * Definition:Volume


 * Definition:Sine
 * Definition:Sine/Real Function
 * Definition:Cosine
 * Definition:Cosine/Real Function
 * Definition:Tangent to Curve/Circle
 * Definition:Tangent Function
 * Definition:Cotangent
 * Definition:Secant Function
 * Definition:Cosecant
 * Definition:Hyperbolic Sine
 * Definition:Hyperbolic Cosine
 * Definition:Hyperbolic Tangent

Graph Theory

 * Definition:Graph (Graph Theory)
 * Definition:Graph (Graph Theory)/Vertex
 * Definition:Graph (Graph Theory)/Edge


 * Definition:Directed Graph
 * Definition:Connected Graph
 * Definition:Tree (Graph Theory)
 * Definition:Tree (Graph Theory)/Node

Category Theory

 * Definition:Category
 * Definition:Object (Category Theory)
 * Definition:Morphism
 * Definition:Identity Morphism
 * Definition:Functor/Covariant
 * Definition:Commutative Diagram


 * Definition:Metacategory

Probability

 * Definition:Sigma-Algebra
 * Definition:Measure (Measure Theory)
 * Definition:Measurable Space
 * Definition:Measure Space
 * Definition:Probability Space
 * Definition:Experiment
 * Definition:Event
 * Definition:Random Variable
 * Definition:Random Variable/Discrete
 * Definition:Probability Density Function
 * Definition:Expectation
 * Definition:Game
 * Definition:Game/Player

Physics

 * Definition:Physics
 * Definition:Time
 * Definition:Body
 * Definition:Mass
 * Definition:Force
 * Definition:Velocity
 * Definition:Magnitude
 * Definition:Unit of Measurement
 * Definition:Imperial