User:Ascii/Definitions (by Meaning 1-600)
Jump to navigation
Jump to search
Metaconcepts
- Definition:Object
- Definition:Symbol
- Definition:Property
- Definition:Variable
- Definition:Constant
- Definition:Unique
- Definition:Distinct
- Definition:Distinct/Plural
- Definition:Operation
Logic
- Definition:Statement
- Definition:Proposition
- Definition:True
- Definition:False
- Definition:Truth Value
- Definition:Proof System
- Definition:Axiom
- 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
- 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:Universal Set
- 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 Section
- Definition:Lower Section
- Definition:Upper Closure/Element
- Definition:Lower Closure/Element
- Definition:Up-Complete
- Definition:Element is Way Below
- Definition:Smallest Element
- Definition:Greatest Element
- 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 (Order Theory)
- Definition:Complete Lattice
- Definition:Join Semilattice
- Definition:Meet Semilattice
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 (Relation Theory)/Mapping/Mapping
- Definition:Image (Relation Theory)/Mapping/Subset
- Definition:Image (Relation 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: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
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:Fraction/Numerator
- Definition:Fraction/Denominator
- Definition:Ratio
- Definition:Irrational Number
- Definition:Commensurable
- Definition:Incommensurable
- Definition:Commensurable in Square Only
- Definition:Real Number
- Axiom: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: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
Number Theory
- 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:Divisor Sum Function
- Definition:Divisor Count Function
- Definition:Euler Phi Function
- Definition:Deficient Number
- Definition:Real Sequence
- Definition:Complex Sequence
- Definition:Complex Roots of Unity
- Definition:Complex Function
Abstract Algebra
- Definition:Well-Defined/Operation
- Definition:Operation/Binary Operation
- Definition:Closure (Abstract Algebra)/Algebraic Structure
- Definition:Continued Product/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: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: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: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:Cover of Set
- Definition:Subcover/Finite
- Definition:Countably Compact Space
- Definition:Open Cover
- Definition:Compact Topological Space
- Definition:Kolmogorov Space
- Definition:Fréchet Space (Topology)
- Definition:Hausdorff Space
- Definition:T3 Space
- Definition:T4 Space
- Definition:T5 Space
- Definition:Euclidean Space
- Definition:Euclidean Space/Euclidean Topology/Real Number Line
- Definition:Vector/Real 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: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:Continuous on Interval
- Definition:Continuous Real Function
- Definition:Continuous Complex Function
- Definition:Exponential Function/Real
- Definition:Natural Logarithm
- Definition:Complex Natural Logarithm
- Definition:Differentiable Mapping/Real Function/Interval
- Definition:Derivative
- Definition:Differentiation
- Definition:Primitive (Calculus)
- Definition:Primitive (Calculus)/Constant of Integration
- 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
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: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:Sine
- Definition:Sine/Real Function
- Definition:Cosine
- Definition:Cosine/Real Function
- Definition:Tangent Line/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:Digraph
- 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
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