User:StarTower/Structure Notes/Definition Pages/Heading Two Statistics/Plan of Use/Sourceless Pages

About
This is a list (nearly complete) of all definition pages, in alphabetical order, without a Sources or Source subsection in them.


 * Update: Work is in progress removing disambiguation pages and parent pages, all of whose content is on subpages.

Page List

 * 1) Definition:Abnormal Subgroup
 * 2) Definition:Absolute Convergence of Product
 * 3) Definition:Absolutely Convergent Series/Complex Numbers
 * 4) Definition:Absolutely Convergent Series/General
 * 5) Definition:Absolute Value of Mapping/Extended Real-Valued Function
 * 6) Definition:Absolute Value of Mapping/Real-Valued Function
 * 7) Definition:Absolute Value of Mapping
 * 8) Definition:Absurd
 * 9) Definition:Abundance
 * 10) Definition:Abuse of Notation
 * 11) Definition:Addition/Multiindices
 * 12) Definition:Addition/Naturally Ordered Semigroup
 * 13) Definition:Additive Arithmetic Function
 * 14) Definition:Additive Group of Complex Numbers
 * 15) Definition:Additive Group of Integer Multiples
 * 16) Definition:Additive Group of Rational Numbers
 * 17) Definition:Additive Monoid of Natural Numbers
 * 18) Definition:Adjacent (Graph Theory)/Edges/Digraph
 * 19) Definition:Adjacent (Graph Theory)/Faces
 * 20) Definition:Adjacent (Graph Theory)/Vertices/Digraph
 * 21) Definition:Adjacent (Graph Theory)
 * 22) Definition:Affine Frame
 * 23) Definition:Agreement/Relations
 * 24) Axiom:Aleph Hypothesis
 * 25) Definition:Algebraic (Model Theory)
 * 26) Definition:Algebraic Integer/Quadratic
 * 27) Definition:Algebraic Substructure
 * 28) Definition:Algebraic Element of Field Extension
 * 29) Definition:Algebraically Closed Field
 * 30) Definition:Algorithmic Computability
 * 31) Definition:All-Harshad Number
 * 32) Definition:Alternate Ratio
 * 33) Definition:Analytic Geometry/Plane
 * 34) Definition:Analytic Geometry/Solid
 * 35) Definition:Angle/Adjacent
 * 36) Definition:Angle/Rectilineal
 * 37) Definition:Annihilator
 * 38) Definition:Antiassociative Operation
 * 39) Definition:Antiassociative Structure
 * 40) Definition:Antihomomorphism
 * 41) Definition:Antisymmetric Quotient
 * 42) Definition:Arbitrarily Large
 * 43) Definition:Arc-Connected/Subset
 * 44) Definition:Archimedean Property/Norm
 * 45) Definition:Archimedean Property/Ordering
 * 46) Definition:Argumentum ad Passiones
 * 47) Definition:Argumentum ad Verecundiam
 * 48) Definition:Operation/Arity/Finitary
 * 49) Definition:Operation/Arity/Multiary
 * 50) Definition:Operation/Arity/Ternary
 * 51) Definition:Operation/Arity/Zero
 * 52) Definition:Artinian Ring
 * 53) Definition:Ascending Chain Condition
 * 54) Definition:Atomic Domain
 * 55) Definition:Axiom/Formal Systems
 * 56) Definition:Backus-Naur Form/Alphabet
 * 57) Definition:Backus-Naur Form/Rules of Formation
 * 58) Definition:Backus-Naur Form/Specification
 * 59) Definition:Baire Space (Set Theory)
 * 60) Definition:Baire Space (Topology)
 * 61) Definition:Balanced Incomplete Block Design
 * 62) Definition:Balanced Signed Graph
 * 63) Definition:Barycenter
 * 64) Definition:Basic Null Sequence
 * 65) Definition:Basic Open Set
 * 66) Definition:Basic Primitive Recursive Function/Identity Function
 * 67) Definition:Basic Primitive Recursive Function/Projection Function
 * 68) Definition:Basic Primitive Recursive Function/Successor Function
 * 69) Definition:Basic Primitive Recursive Function/URM Computability
 * 70) Definition:Basic Primitive Recursive Function/Zero Function
 * 71) Definition:Basic Primitive Recursive Function
 * 72) Definition:Basis Element
 * 73) Definition:Bernoulli Process
 * 74) Definition:Big Model
 * 75) Definition:Bilinear Mapping
 * 76) Definition:Binomial Coefficient/Multiindices
 * 77) Definition:Block Incidence Matrix of a Design
 * 78) Definition:Boolean Interpretation/Formal Semantics/Invalid
 * 79) Definition:Boolean Interpretation/Formal Semantics
 * 80) Definition:Boolean Lattice/Definition 1
 * 81) Definition:Boolean Lattice/Definition 2
 * 82) Definition:Borel Algebra
 * 83) Definition:Bottom of Lattice/Definition 1
 * 84) Definition:Bottom of Lattice/Definition 2
 * 85) Definition:Bottom-Up Form of Top-Down Grammar
 * 86) Definition:Boubaker Polynomials
 * 87) Definition:Boundary (Geometry)/Containment
 * 88) Definition:Boundary (Geometry)
 * 89) Definition:Boundary (Graph Theory)
 * 90) Definition:Bounded Lattice/Definition 1
 * 91) Definition:Bounded Lattice/Definition 2
 * 92) Definition:Bounded Lattice/Definition 3
 * 93) Definition:Bounded Minimization
 * 94) Definition:Bounded Ordered Set
 * 95) Definition:Bounded Mapping/Complex-Valued
 * 96) Definition:Bounded Mapping
 * 97) Definition:Bounded Metric Space/Unbounded
 * 98) Definition:Box Topology
 * 99) Definition:Bozo Bit
 * 100) Definition:Braid Group
 * 101) Definition:By Hypothesis
 * 102) Definition:Bézout Domain
 * 103) Definition:Bézout Numbers
 * 104) Definition:Can't Happen
 * 105) Definition:Cancellable Operation
 * 106) Definition:Cancellable Semiring
 * 107) Definition:Cantor Normal Form
 * 108) Definition:Cantor Set/Limit of Decreasing Sequence
 * 109) Definition:Cantor Space
 * 110) Definition:Cartesian Product of Relations
 * 111) Definition:Cartesian Product/Uncountable
 * 112) Definition:Categorical (Model Theory)
 * 113) Definition:Categorical Statement/Abbreviation
 * 114) Definition:Category of Cocones
 * 115) Definition:Category of Groups
 * 116) Definition:Category of Vector Spaces
 * 117) Definition:Category with Exponentials
 * 118) Definition:Category with Products/Finite
 * 119) Definition:Category with Products
 * 120) Definition:Cauchy Sequence/Rational Numbers
 * 121) Definition:Center of Tree
 * 122) Definition:Central Subgroup
 * 123) Definition:Chain (Physics)
 * 124) Definition:Character (Number Theory)
 * 125) Definition:Character (Representation Theory)
 * 126) Definition:Characteristic Function of Random Variable
 * 127) Definition:Characteristic Function of Relation
 * 128) Definition:Characteristic Function (Set Theory)
 * 129) Definition:Chebyshev Function
 * 130) Definition:Circle/Equality
 * 131) Definition:Circle/Equidistant
 * 132) Definition:Circumcircle of Triangle/Circumradius
 * 133) Definition:Circumference (Graph Theory)
 * 134) Definition:Circumradius/Polygon
 * 135) Definition:Circumradius/Polyhedron
 * 136) Definition:Class (Class Theory)/Zermelo-Fraenkel
 * 137) Definition:Claw
 * 138) Definition:Clearly
 * 139) Definition:Closed Ball/Metric Space/Radius
 * 140) Definition:Closed Element/Definition 1
 * 141) Definition:Closed Element/Definition 2
 * 142) Definition:Closed Element
 * 143) Definition:Closed Linear Subspace
 * 144) Definition:Closed Path (Topology)
 * 145) Definition:Closed Set/Closed Point
 * 146) Definition:Closed Set/Closure Operator
 * 147) Definition:Closed Subset
 * 148) Definition:Closed Unit Ball
 * 149) Definition:Closed-Form Expression
 * 150) Definition:Closed-Form Solution
 * 151) Definition:Closure (Topology)/Definition 3
 * 152) Definition:Closure (Topology)/Definition 4
 * 153) Definition:Closure (Topology)/Definition 5
 * 154) Definition:Closure Operator/Ordering/Definition 1
 * 155) Definition:Closure Operator/Ordering/Definition 2
 * 156) Definition:Closure Operator/Ordering
 * 157) Definition:Closure Operator
 * 158) Definition:Cluster Point
 * 159) Definition:Co-Countable Set
 * 160) Definition:Cobordism
 * 161) Definition:Codimension
 * 162) Definition:Codomain (Category Theory)
 * 163) Definition:Cohomology Groups
 * 164) Definition:Colimit/Finite Colimit
 * 165) Definition:Collation/Collation System
 * 166) Definition:Collation/Unique Readability
 * 167) Definition:Collation
 * 168) Definition:Coloring
 * 169) Definition:Combinable/Relations
 * 170) Definition:Combinable
 * 171) Definition:Commensurable in Square
 * 172) Definition:Compact Subspace
 * 173) Definition:Compact Space/Metric Space
 * 174) Definition:Compact Space/Topology/Subspace/Definition 1
 * 175) Definition:Compact Space/Topology/Subspace
 * 176) Definition:Compatible Atlases
 * 177) Definition:Complement (Graph Theory)
 * 178) Definition:Complement (Lattice Theory)
 * 179) Definition:Complement of Truth Function
 * 180) Definition:Complementary Idempotent
 * 181) Definition:Complemented Lattice
 * 182) Definition:Complements of Parallelograms
 * 183) Definition:Completed Dirichlet L-Function
 * 184) Definition:Completed Riemann Zeta Function
 * 185) Definition:Completely Additive Function
 * 186) Definition:Completion (Measure Space)
 * 187) Definition:Complex Analytic Differentiable Structure
 * 188) Definition:Complex Conjugate/Complex Conjugation
 * 189) Definition:Complex Locally Euclidean Space
 * 190) Definition:Complex Sequence
 * 191) Definition:Complex-Valued Function
 * 192) Definition:Component (Topology)/Definition 2
 * 193) Definition:Component (Topology)
 * 194) Definition:Composable Morphisms
 * 195) Definition:Composant/Point
 * 196) Definition:Composant
 * 197) Definition:Composite Number/Negative Composite
 * 198) Definition:Composition (Combinatorics)
 * 199) Definition:Composition Functor
 * 200) Definition:Composition of Morphisms
 * 201) Definition:Composition of Ratio
 * 202) Definition:Compound Ratio
 * 203) Definition:Compound Statement/Ill-Formed
 * 204) Definition:Computer Program
 * 205) Definition:Concatenation (Topology)
 * 206) Definition:Concatenation of URM Programs
 * 207) Definition:Concatenation
 * 208) Definition:Conflation
 * 209) Definition:Congruence (Metric Spaces)
 * 210) Definition:Congruence (Number Theory)/Integers/Modulo Operation
 * 211) Definition:Connected (Graph Theory)
 * 212) Definition:Connected (Topology)/Set/Definition 2
 * 213) Definition:Connected (Topology)/Topological Space/Definition 2
 * 214) Definition:Connected (Topology)/Topological Space
 * 215) Definition:Connected (Topology)
 * 216) Definition:Connected Sum
 * 217) Definition:Connectivity
 * 218) Definition:Continuation
 * 219) Definition:Convergent of Continued Fraction/Even
 * 220) Definition:Convergent of Continued Fraction/Odd
 * 221) Definition:Continued Fraction/Finite
 * 222) Definition:Continued Fraction/Infinite
 * 223) Definition:Numerators and Denominators of Continued Fraction
 * 224) Definition:Value of Continued Fraction
 * 225) Definition:Continuous Complex Function
 * 226) Definition:Continuous Mapping (Metric Space)/Point/Definition 2
 * 227) Definition:Continuous Mapping (Metric Space)/Point
 * 228) Definition:Continuous Mapping (Metric Space)/Space
 * 229) Definition:Continuous Mapping (Metric Space)
 * 230) Definition:Continuous Real Function/Subset
 * 231) Definition:Continuous Real-Valued Vector Function
 * 232) Definition:Continuous Mapping (Topology)/Set
 * 233) Definition:Continuous Mapping (Topology)
 * 234) Definition:Continuous Extension
 * 235) Definition:Continuous Mapping
 * 236) Definition:Continuously Embedded
 * 237) Definition:Contradictory
 * 238) Definition:Contranormal Subgroup
 * 239) Definition:Convergence Almost Everywhere
 * 240) Definition:Convergent Function
 * 241) Definition:Convergent Sequence/Topology
 * 242) Definition:Convergent Sequence
 * 243) Definition:Convergent Series/Normed Vector Space
 * 244) Definition:Convergent Series
 * 245) Definition:Conversion of Ratio
 * 246) Definition:Coordinate System/Coordinate Function
 * 247) Definition:Coordinate System/Coordinates on Affine Space
 * 248) Definition:Coprime/GCD Domain
 * 249) Definition:Coprime/Integers/Relatively Composite
 * 250) Definition:Cord (Physics)
 * 251) Definition:Coreflexive Relation/Definition 1
 * 252) Definition:Coreflexive Relation/Definition 2
 * 253) Definition:Coreflexive Relation
 * 254) Definition:Corresponding Conditional
 * 255) Definition:Corresponding Magnitudes
 * 256) Definition:Cosecant/Complex Function
 * 257) Definition:Cosecant/Real Function
 * 258) Definition:Cotangent/Complex Function
 * 259) Definition:Cotangent/Real Function
 * 260) Definition:Countability Axioms
 * 261) Definition:Countable Basis
 * 262) Definition:Countable Complement Topology/Countable
 * 263) Definition:Countably Subadditive Function
 * 264) Definition:Countable Cover
 * 265) Definition:Crackpot
 * 266) Definition:Critical Point (Topology)
 * 267) Definition:Cross Cancellation Property
 * 268) Definition:Cross Product
 * 269) Definition:Cross-Relation
 * 270) Definition:Cube Number
 * 271) Definition:Cubic Graph
 * 272) Definition:Cycle (Graph Theory)/Even
 * 273) Definition:Cycle (Graph Theory)/Odd
 * 274) Definition:Cycle (Periodic Solution)
 * 275) Definition:Cycle Decomposition
 * 276) Definition:Cycle Graph
 * 277) Definition:Cylinder/Similar Cylinders
 * 278) Definition:Decision Procedure
 * 279) Definition:Decomposable Set
 * 280) Definition:Decomposition (Topology)
 * 281) Definition:Dedekind Complete
 * 282) Definition:Dedekind Completion
 * 283) Definition:Dedekind-Infinite
 * 284) Definition:Dedekind-MacNeille Completion
 * 285) Definition:Deductive Apparatus
 * 286) Definition:Definitional Abbreviation
 * 287) Definition:Degenerate Connected Set/Non-Degenerate
 * 288) Definition:Degenerate Continuum
 * 289) Definition:Degenerate Distribution
 * 290) Definition:Degree of Polynomial/Polynomial Form
 * 291) Definition:Degree of Polynomial/Sequence/Ring
 * 292) Definition:Degree of Polynomial/Sequence
 * 293) Definition:Degree Sequence
 * 294) Definition:Deleted Neighborhood/Complex Analysis
 * 295) Definition:Deleted Neighborhood/Metric Space
 * 296) Definition:Deleted Neighborhood/Real Analysis
 * 297) Definition:Deleted Neighborhood/Topology
 * 298) Definition:Delta-Algebra
 * 299) Definition:Delta-Ring
 * 300) Definition:Densely Ordered/Subset
 * 301) Definition:Depressed Polynomial
 * 302) Definition:Derivative/Complex Function
 * 303) Definition:Derivative/Higher Derivatives/Order of Derivative
 * 304) Definition:Derivative/Real Function/Derivative on Interval
 * 305) Definition:Descending Chain Condition
 * 306) Definition:Determinant/Linear Operator
 * 307) Definition:Diagonal Mapping
 * 308) Definition:Dialetheia
 * 309) Definition:Diameter of Parallelogram
 * 310) Definition:Diameter of Quadrilateral
 * 311) Definition:Dicyclic Group
 * 312) Definition:Differentiable Structure
 * 313) Definition:Differentiable Mapping/Complex Function
 * 314) Definition:Differentiable Mapping/Real Function/Real Number Line
 * 315) Definition:Differentiable Mapping/Real-Valued Function/Open Set
 * 316) Definition:Differentiable Mapping/Real-Valued Function
 * 317) Definition:Differentiable Mapping
 * 318) Definition:Differential Complex
 * 319) Definition:Differential Form
 * 320) Definition:Differential Module
 * 321) Definition:Differential of Mapping/Vector-Valued Function
 * 322) Definition:Dimension (Measurement)/Units
 * 323) Definition:Dimension (Representation Theory)
 * 324) Definition:Direct Limit of Sequence of Groups
 * 325) Definition:Directed Graph/Arc/Endvertex
 * 326) Definition:Directed Set
 * 327) Definition:Dirichlet Character
 * 328) Definition:Dirichlet Convolution
 * 329) Definition:Dirichlet Density
 * 330) Definition:Dirichlet L-function
 * 331) Definition:Discontinuous
 * 332) Definition:Discrete Measure
 * 333) Definition:Discriminant of Polynomial
 * 334) Definition:Disjoint Union
 * 335) Definition:Disjunction/Truth Function
 * 336) Definition:Distance-Preserving Mapping
 * 337) Definition:Distance/Points
 * 338) Definition:Distance/Sets
 * 339) Definition:Distributive Lattice
 * 340) Definition:Distributor
 * 341) Definition:Divide (Model Theory)
 * 342) Definition:Domain (Category Theory)
 * 343) Definition:Domain (Relation Theory)/Binary Operation
 * 344) Definition:Dominate (Analysis)
 * 345) Definition:Dual Order Embedding
 * 346) Definition:Dual Relation/Complement of Inverse
 * 347) Definition:Dual Statement (Order Theory)
 * 348) Definition:Duplicate Ratio
 * 349) Definition:Dyadic Rational
 * 350) Definition:Edge Contraction
 * 351) Definition:Edge-Disjoint Trails
 * 352) Definition:Eisenstein Integer
 * 353) Definition:Eisenstein Prime
 * 354) Definition:Eleatic School
 * 355) Definition:Elementary Embedding
 * 356) Definition:Elementary Equivalence
 * 357) Definition:Ellipse/Covertex
 * 358) Definition:Embedded
 * 359) Definition:Embedding (Galois Theory)
 * 360) Definition:Embedding (Model Theory)
 * 361) Definition:Embedding
 * 362) Definition:Empty Infimum
 * 363) Definition:Empty Supremum
 * 364) Definition:Enumeration/Finite
 * 365) Definition:Equimultiples
 * 366) Definition:Equiprobability Space
 * 367) Definition:Equivalence of Categories/Equivalent Categories
 * 368) Definition:Equivalent Metrics
 * 369) Definition:Equivalent Linear Representations
 * 370) Definition:Euclidean Relation
 * 371) Definition:Euclidean Space/Rational
 * 372) Definition:Exact Sequence of Modules
 * 373) Definition:Excluded Point Topology/Infinite
 * 374) Definition:Exclusive Or/Boolean Interpretation
 * 375) Definition:Exclusive Or/Truth Function
 * 376) Definition:Exponential (Category Theory)/Evaluation
 * 377) Definition:Exponential (Category Theory)/Transpose
 * 378) Definition:Exponential Function/Complex/Limit of Sequence
 * 379) Definition:Exponential Function/Complex/Differential Equation
 * 380) Definition:Exponentiation Functor
 * 381) Definition:Extended Absolute Value
 * 382) Definition:Extended Real Addition
 * 383) Definition:Extended Real Multiplication
 * 384) Definition:Extended Real Subtraction
 * 385) Definition:Extension of Branch of Propositional Tableau
 * 386) Definition:Extension of Branch of Rooted Tree
 * 387) Definition:Extension of Propositional Tableau/Definition 2
 * 388) Definition:Extension of Propositional Tableau
 * 389) Definition:Extension of Rooted Tree
 * 390) Definition:Extension of Operation
 * 391) Definition:Extension of Relation
 * 392) Definition:Exterior Derivative
 * 393) Definition:F-Homomorphism
 * 394) Definition:Faithful (Module Theory)
 * 395) Definition:Faithful Functor
 * 396) Definition:Faithful Representation
 * 397) Definition:Faithful
 * 398) Definition:Falsidical Paradox
 * 399) Definition:Falsifiable/Formula
 * 400) Definition:Falsifiable/Set of Formulas
 * 401) Definition:Falsifiable
 * 402) Definition:Fiber
 * 403) Definition:Field Automorphism
 * 404) Definition:Field Endomorphism
 * 405) Definition:Field Epimorphism
 * 406) Definition:Field Monomorphism
 * 407) Definition:Filter
 * 408) Definition:Filtered Algebra
 * 409) Definition:Final Topology
 * 410) Definition:Finished
 * 411) Definition:Finitary
 * 412) Definition:Finite Category
 * 413) Definition:Finite Dimensional Vector Space
 * 414) Definition:Finite Extended Real Number
 * 415) Definition:Finite Graph
 * 416) Definition:Finite Integral Domain
 * 417) Definition:Finite Join Property
 * 418) Definition:Finite Monoid
 * 419) Definition:Finite Path
 * 420) Definition:Finite Probability Space
 * 421) Definition:Finite Ring Homomorphism
 * 422) Definition:Finite Ring
 * 423) Definition:Finite State Machine
 * 424) Definition:Finitely Branching
 * 425) Definition:Finitely Generated Extension
 * 426) Definition:First Chebyshev Function
 * 427) Definition:Fixed Element of Permutation/Set of Fixed Elements
 * 428) Definition:Fixed Element
 * 429) Definition:Fixed Set of Sets
 * 430) Definition:Fork
 * 431) Definition:Forking Extension
 * 432) Definition:Formal Derivative
 * 433) Definition:Formal Grammar/Bottom-Up
 * 434) Definition:Formal Grammar/Top-Down
 * 435) Definition:Formal Language/Alphabet/Letter
 * 436) Definition:Formal Semantics/Structure
 * 437) Definition:Formal Semantics/Valid
 * 438) Definition:Formal Semantics
 * 439) Definition:Free Idempotent Monoid
 * 440) Definition:Free Semigroup
 * 441) Definition:Free Set of Sets
 * 442) Definition:Friedman Number
 * 443) Definition:Fréchet Space (Topology)
 * 444) Definition:Full Functor
 * 445) Definition:Full Subcategory
 * 446) Definition:Function Symbol
 * 447) Definition:Functor
 * 448) Definition:G-Module Homomorphism
 * 449) Definition:G-Module
 * 450) Definition:G-Submodule
 * 451) Definition:Galois Extension
 * 452) Definition:Galois Group of Field Extension
 * 453) Definition:Gaussian Rational
 * 454) Definition:GCD Domain
 * 455) Definition:Generalized Inverse Gaussian Distribution
 * 456) Definition:Generalized Momentum
 * 457) Definition:Generalized Ordered Space/Definition 1
 * 458) Definition:Generalized Ordered Space/Definition 2
 * 459) Definition:Generalized Ordered Space/Definition 3
 * 460) Definition:Generalized Ordered Space
 * 461) Definition:Generator of Algebra
 * 462) Definition:Generated Algebraic Substructure
 * 463) Definition:Geometric Figure/Plane Figure
 * 464) Definition:Geometric Sequence/Scale Factor
 * 465) Definition:Girth
 * 466) Definition:Gradation
 * 467) Definition:Graded Algebra
 * 468) Definition:Graded Module
 * 469) Definition:Graded Ring
 * 470) Definition:Graph (Category Theory)
 * 471) Definition:Graph (Graph Theory)/Edge/Endvertex
 * 472) Definition:Group Algebra
 * 473) Definition:Group of Units of Ring
 * 474) Definition:Gödel-Bernays Axioms
 * 475) Definition:Half-Integer
 * 476) Definition:Hall Divisor
 * 477) Definition:Hartogs Number
 * 478) Definition:Hereditary Ring
 * 479) Definition:Higher-Aleph Complement Topology
 * 480) Definition:Homeomorphism/Topological Spaces/Definition 4
 * 481) Definition:Homogeneous (Model Theory)
 * 482) Definition:Homogeneous (Physics)
 * 483) Definition:Homology Group
 * 484) Definition:Homomorphism (Graph Theory)
 * 485) Definition:Homomorphism of Complexes
 * 486) Definition:Homotopy Class
 * 487) Definition:Homotopy Group
 * 488) Definition:Homotopy/Free
 * 489) Definition:Homotopy/Relative
 * 490) Definition:Hurwitz Quaternion
 * 491) Definition:Ideal (Physics)
 * 492) Definition:Identity Arithmetic Function
 * 493) Definition:Identity Morphism
 * 494) Definition:If
 * 495) Definition:Image Filter
 * 496) Definition:Image Set
 * 497) Definition:Image (Relation Theory)/Relation
 * 498) Definition:Immersion
 * 499) Definition:In-Degree
 * 500) Definition:In-Order Traversal of Labeled Tree
 * 501) Definition:Incident (Graph Theory)/Digraph/Incident From
 * 502) Definition:Incident (Graph Theory)/Digraph/Incident To
 * 503) Definition:Incident (Graph Theory)/Digraph
 * 504) Definition:Incident (Graph Theory)/Planar Graph
 * 505) Definition:Incident (Graph Theory)
 * 506) Definition:Inclusion Relation on Subobject Classes
 * 507) Definition:Inclusion-Reversing
 * 508) Definition:Inconsistent (Logic)
 * 509) Definition:Increasing Sequence of Extended Real-Valued Functions
 * 510) Definition:Increasing Sequence of Mappings
 * 511) Definition:Increasing Sequence of Real-Valued Functions
 * 512) Definition:Independent Events/Dependent
 * 513) Definition:Indeterminate Variable
 * 514) Definition:Indeterminate
 * 515) Definition:Indicator Function
 * 516) Definition:Indicator of Group Element
 * 517) Definition:Indiscernible
 * 518) Definition:Induced Outer Measure
 * 519) Definition:Induced Representation
 * 520) Definition:Induced Subgraph
 * 521) Definition:Inductive Ordered Set
 * 522) Definition:Infimum of Set/Finite Infimum
 * 523) Definition:Infinite Matrix
 * 524) Definition:Injective on Morphisms
 * 525) Definition:Injective on Objects
 * 526) Definition:Injective Restriction
 * 527) Definition:Inner Limit
 * 528) Definition:Inner Product Space
 * 529) Definition:Integer Division
 * 530) Definition:Integer-Valued Function
 * 531) Definition:Integral Closure
 * 532) Definition:Integral Dependence
 * 533) Definition:Integral Domain/Definition 2
 * 534) Definition:Integrally Closed
 * 535) Definition:Interior Point (Topology)
 * 536) Definition:Intermediate Field
 * 537) Definition:Intersection of Relations/General Definition
 * 538) Definition:Intersection of Relations
 * 539) Definition:Intuitionist School
 * 540) Definition:Inverse Morphism
 * 541) Definition:Inverse Semigroup
 * 542) Definition:Inversion Mapping/Topology
 * 543) Definition:Irreducible (Representation Theory)/G-Module
 * 544) Definition:Irreducible (Representation Theory)/Linear Representation
 * 545) Definition:Irreducible (Representation Theory)
 * 546) Definition:Irreducible Polynomial
 * 547) Definition:Irreducible Representation
 * 548) Definition:Isolated Point (Complex Analysis)
 * 549) Definition:Isolated Point (Metric Space)/Space
 * 550) Definition:Isolated Point (Metric Space)/Subset
 * 551) Definition:Isolated Point (Metric Space)
 * 552) Definition:Isolated Point (Real Analysis)
 * 553) Definition:Isolated Type
 * 554) Definition:Isolated Vertex
 * 555) Definition:Isomorphism (Abstract Algebra)/F-Isomorphism
 * 556) Definition:Isomorphism (Abstract Algebra)/Ordered Structure Isomorphism
 * 557) Definition:Isomorphism (Abstract Algebra)/R-Algebraic Structure Isomorphism/Module Isomorphism
 * 558) Definition:Isomorphism (Abstract Algebra)/R-Algebraic Structure Isomorphism/Vector Space Isomorphism
 * 559) Definition:Isomorphism of Categories/Isomorphic Categories
 * 560) Definition:Jacobi Symbol
 * 561) Definition:Jacobson Ring
 * 562) Definition:Johansson's Minimal Logic/Axioms
 * 563) Definition:Join (Order Theory)
 * 564) Definition:Join
 * 565) Definition:Jordan Curve/Exterior
 * 566) Definition:Jordan Curve/Interior
 * 567) Definition:K-Algebra
 * 568) Definition:K-Connected
 * 569) Definition:Kernel of Homomorphism of Differential Complexes
 * 570) Definition:Kernel of Magma Homomorphism
 * 571) Definition:Kronecker Product
 * 572) Definition:Kronecker Sum
 * 573) Definition:Kuratowski Closure Operator/Definition 1
 * 574) Definition:Kuratowski Closure Operator/Definition 2
 * 575) Definition:Kuratowski Closure Operator
 * 576) Definition:Labeled Graph
 * 577) Definition:Labeled Tree
 * 578) Definition:Lagrange Basis Polynomial
 * 579) Definition:Language of Arithmetic
 * 580) Definition:Language of Category Theory
 * 581) Definition:Latin Square Property
 * 582) Definition:Lattice (Group Theory)
 * 583) Definition:Lattice/Definition 1
 * 584) Definition:Lattice/Definition 2
 * 585) Definition:Lattice/Definition 3
 * 586) Definition:Laurent Series
 * 587) Definition:Leading Coefficient (Matrix)
 * 588) Definition:Least Absolute Residue
 * 589) Definition:Lebesgue Sigma-Algebra
 * 590) Definition:Left Difference Quotient
 * 591) Definition:Left-Hand Derivative
 * 592) Definition:Length of Integer
 * 593) Definition:Limit (Category Theory)/Finite Limit
 * 594) Definition:Limit Inferior of Sequence of Sets
 * 595) Definition:Limit of Complex Function
 * 596) Definition:Limit of Mapping between Metric Spaces/Epsilon-Ball Condition
 * 597) Definition:Limit of Mapping between Metric Spaces/Epsilon-Delta Condition
 * 598) Definition:Limit of Mapping between Metric Spaces
 * 599) Definition:Limit of Sequence of Events
 * 600) Definition:Limit Point/Topology/Point
 * 601) Definition:Limit Point/Topology/Set/Definition 2
 * 602) Definition:Limit Point/Topology/Set/Definition 3
 * 603) Definition:Limit Point/Topology/Set/Definition 4
 * 604) Definition:Limit Point/Topology
 * 605) Definition:Limit Superior of Sequence of Sets
 * 606) Definition:Line/Endpoint
 * 607) Definition:Line Segment/Equality
 * 608) Definition:Line/Infinite Straight Line
 * 609) Definition:Line/Infinite
 * 610) Definition:Line/Segment
 * 611) Definition:Linear Congruence
 * 612) Definition:Linear Continuum
 * 613) Definition:Linear Functional
 * 614) Definition:Linear Group Action
 * 615) Definition:Linear Measure/Breadth
 * 616) Definition:Linear Measure/Depth
 * 617) Definition:Linear Measure/Height
 * 618) Definition:Linear Measure
 * 619) Definition:Linear Recurrence Relation
 * 620) Definition:Linear Span
 * 621) Definition:Linear Subspace
 * 622) Definition:Linearly Dependent/Sequence/Real Vector Space
 * 623) Definition:Linearly Dependent/Set/Real Vector Space
 * 624) Definition:Linearly Independent/Sequence/Real Vector Space
 * 625) Definition:Linearly Independent
 * 626) Definition:Linearly Ordered Space
 * 627) Definition:Link (Graph Theory)
 * 628) Definition:Lipschitz Continuity/Lipschitz Constant
 * 629) Definition:Lipschitz Continuity
 * 630) Definition:Lipschitz Equivalence
 * 631) Definition:Lipschitz Quaternion
 * 632) Definition:Local Ring
 * 633) Definition:Local Sub-Basis
 * 634) Definition:Localization of Ring
 * 635) Definition:Locally Euclidean Space
 * 636) Definition:Locally Finite Graph
 * 637) Definition:Locally Finite
 * 638) Definition:Locally Uniform Convergence
 * 639) Definition:Logarithmic Integral
 * 640) Definition:Logical Argument/Finitary
 * 641) Definition:Logical Complement/Complementary Pair
 * 642) Definition:Logical Complement
 * 643) Definition:Logical Form
 * 644) Definition:Logical Formula
 * 645) Definition:Logical Language
 * 646) Definition:Logical Matrix
 * 647) Definition:Logical NAND/Boolean Interpretation
 * 648) Definition:Logical NAND/Notational Variants
 * 649) Definition:Logical NAND/Truth Function
 * 650) Definition:Logical NAND/Truth Table
 * 651) Definition:Logical NOR/Boolean Interpretation
 * 652) Definition:Logical NOR/Notational Variants
 * 653) Definition:Logical NOR/Truth Function
 * 654) Definition:Logical NOR/Truth Table
 * 655) Definition:Lower Closure of Element
 * 656) Definition:Lower Closure
 * 657) Definition:Lower Level Set
 * 658) Definition:Lower Limit (Topological Space)
 * 659) Definition:Lower Semicontinuous
 * 660) Definition:Lower Section
 * 661) Definition:Lowest Common Multiple/Integral Domain
 * 662) Definition:Lyapunov Function
 * 663) Definition:Lyndon Word
 * 664) Definition:Magma of Sets Generated by Collection of Subsets
 * 665) Definition:Magma of Sets
 * 666) Definition:Main Connective/Propositional Logic
 * 667) Definition:Many-to-Many Relation
 * 668) Definition:Matrix Exponential
 * 669) Definition:Matrix/Underlying Structure
 * 670) Definition:Maximal Algebraic Extension
 * 671) Definition:Maximal Chain
 * 672) Definition:Maximal Condition
 * 673) Definition:Maximal Spectrum of Ring
 * 674) Definition:Strictly Maximal Relation
 * 675) Definition:Maximum Spanning Tree
 * 676) Definition:Measure (Geometry)
 * 677) Definition:Measure of Finite Stieltjes Function
 * 678) Definition:Mediant
 * 679) Definition:Meet (Order Theory)
 * 680) Definition:Metagraph
 * 681) Definition:Metalanguage/Formal Systems
 * 682) Definition:Metalanguage/Metasyntax
 * 683) Definition:Metamodel
 * 684) Definition:Metatheorem
 * 685) Definition:Metric Space/Point
 * 686) Definition:Metrizable
 * 687) Definition:Middle Cancellation Property
 * 688) Definition:Minimal (Model Theory)
 * 689) Definition:Minimal Arithmetic
 * 690) Definition:Minimal Condition
 * 691) Definition:Minimal Topology
 * 692) Definition:Strictly Minimal Relation
 * 693) Definition:Minimization/Function
 * 694) Definition:Minimization/Partial Function
 * 695) Definition:Minimization/Relation
 * 696) Definition:Minimization
 * 697) Definition:Minimum Degree
 * 698) Definition:Minkowski Sum
 * 699) Definition:Mistake/Homophone Horror
 * 700) Definition:Mistake/Spello
 * 701) Definition:Mistake/Typo
 * 702) Definition:Mistake
 * 703) Definition:Model (Logic)/Logical Formula
 * 704) Definition:Model (Logic)/Set of Logical Formulas
 * 705) Definition:Module Automorphism
 * 706) Definition:Module Direct Sum
 * 707) Definition:Modulus (Geometric Function Theory)
 * 708) Definition:Modulus of Complex-Valued Function
 * 709) Definition:Modulus
 * 710) Definition:Monic Polynomial/Polynomial Form
 * 711) Definition:Monochromatic Graph
 * 712) Definition:Monomorphism
 * 713) Definition:Monomial of Free Commutative Monoid/Degree
 * 714) Definition:Monotone (Measure Theory)
 * 715) Definition:Monotone (Order Theory)
 * 716) Definition:Monotone
 * 717) Definition:Monotonicity
 * 718) Definition:Monster Model
 * 719) Definition:Morphisms-Only Metacategory
 * 720) Definition:Multigraph/Multiplicity
 * 721) Definition:Multigraph/Simple Edge
 * 722) Definition:Multiindex/Modulus
 * 723) Definition:Multiindex
 * 724) Definition:Multilinear Mapping
 * 725) Definition:Multiple Pointed Topology
 * 726) Definition:Multiplication of Polynomials/Polynomial Forms
 * 727) Definition:Multiplication/Rational Numbers
 * 728) Definition:Multiplicative Group of Positive Rational Numbers
 * 729) Definition:Multiplicative Group of Positive Real Numbers
 * 730) Definition:Multiplicative Group of Rational Numbers
 * 731) Definition:Multiplicative Group of Real Numbers
 * 732) Definition:Multiplicative Monoid of Integers Modulo m
 * 733) Definition:Multiplicatively Closed Subset of Ring
 * 734) Definition:Multiplicity (Complex Analysis)
 * 735) Definition:Multiset
 * 736) Definition:Nagata Criterion
 * 737) Definition:Name
 * 738) Definition:Quotient Epimorphism
 * 739) Definition:Negative Binomial Distribution/First Form
 * 740) Definition:Negative Categorical Statement
 * 741) Definition:Negative/Integer
 * 742) Definition:Negative/Number
 * 743) Definition:Negative/Rational Number
 * 744) Definition:Negatively Transitive Relation
 * 745) Definition:Neighborhood (Complex Analysis)
 * 746) Definition:Neighborhood (Real Analysis)
 * 747) Definition:Neighborhood (Analysis)
 * 748) Definition:Neighborhood (Graph Theory)
 * 749) Definition:Closed Neighborhood
 * 750) Definition:Neighborhood (Topology)
 * 751) Definition:Neighborhood Basis
 * 752) Definition:Neighborhood Sub-Basis
 * 753) Definition:Neighborhood
 * 754) Definition:Neo-Pythagoreanism
 * 755) Definition:Net (Preordered Set)
 * 756) Definition:Net (Set Theory)
 * 757) Definition:Network/Weight Function
 * 758) Definition:Network/Weight
 * 759) Definition:Nilradical
 * 760) Definition:Niven Number
 * 761) Definition:Noetherian Ring
 * 762) Definition:Non-Archimedean/Metric/Archimedean
 * 763) Definition:Non-Archimedean/Metric
 * 764) Definition:Non-Archimedean
 * 765) Definition:Nondeterministic Turing Machine
 * 766) Definition:Nonvanishing
 * 767) Definition:Normal Extension
 * 768) Definition:Normal Series/Length
 * 769) Definition:Normal Subgroup/Definition 2
 * 770) Definition:Normal Subgroup/Definition 4
 * 771) Definition:Normal Subgroup/Definition 7
 * 772) Definition:Normal Subset/Definition 1
 * 773) Definition:Normal Subset/Definition 2
 * 774) Definition:Normal Subset/Definition 3
 * 775) Definition:Normal Subset/Definition 4
 * 776) Definition:Normal Subset/Definition 5
 * 777) Definition:Normal Subset
 * 778) Definition:Normalized Weight Function
 * 779) Definition:Nowhere Dense
 * 780) Definition:NP-Complete
 * 781) Definition:NP Complexity Class
 * 782) Definition:Null Module
 * 783) Definition:Null Polynomial/Polynomial Form
 * 784) Definition:Null Polynomial/Ring
 * 785) Definition:Null Polynomial/Sequence
 * 786) Definition:Null Polynomial
 * 787) Definition:Null Sequence (Analysis)
 * 788) Definition:Null Sequence (Homological Algebra)
 * 789) Definition:Occurrence
 * 790) Definition:One (Ordinal)
 * 791) Definition:One-Sided Derivative
 * 792) Definition:Ones Matrix
 * 793) Definition:Open Point
 * 794) Definition:Open Refinement
 * 795) Definition:Open Set/Complex Analysis
 * 796) Definition:Open Set/Pseudometric Space
 * 797) Definition:Open Set/Real Analysis
 * 798) Definition:Operation Induced by Injection
 * 799) Definition:Operator Domain
 * 800) Definition:Orbit (Group Theory)/Length
 * 801) Definition:Order Category/Definition 2
 * 802) Definition:Order Category
 * 803) Definition:Order Completion
 * 804) Definition:Order Embedding
 * 805) Definition:Order Indiscernible
 * 806) Definition:Order Isomorphism/Definition 1
 * 807) Definition:Order of Entire Function
 * 808) Definition:Order of Pole
 * 809) Definition:Order of Zero/Simple Zero
 * 810) Definition:Order of Zero
 * 811) Definition:Order Topology/Definition 1
 * 812) Definition:Order Topology/Definition 2
 * 813) Definition:Order Topology
 * 814) Definition:Ordered Commutative Semigroup
 * 815) Definition:Ordered Group Automorphism
 * 816) Definition:Ordered Group Isomorphism
 * 817) Definition:Ordered Group Monomorphism
 * 818) Definition:Ordered Monoid
 * 819) Definition:Ordered Square
 * 820) Definition:Ordered Statistic
 * 821) Definition:Ordered Structure Automorphism
 * 822) Definition:Ordered Structure Monomorphism
 * 823) Definition:Ordered Structure
 * 824) Definition:Ordered Subgroup
 * 825) Definition:Ordered Tree
 * 826) Definition:Ordered Tuple as Ordered Set
 * 827) Definition:Ordering Induced by Injection
 * 828) Definition:Ordering on Extended Real Numbers
 * 829) Definition:Ordering on Multiindices
 * 830) Definition:Ordinal Sum
 * 831) Definition:Ordinal
 * 832) Definition:Oscillation (Analysis)
 * 833) Definition:Out-Degree
 * 834) Definition:Outer Limit
 * 835) Definition:P-adic Metric
 * 836) Definition:P-Integrable Function
 * 837) Definition:P-Subgroup
 * 838) Definition:Painlevé-Kuratowski Convergence
 * 839) Definition:Pairwise Coprime/Euclidean Domain
 * 840) Definition:Pairwise Coprime/GCD Domain
 * 841) Definition:Parametric Operator
 * 842) Definition:Paranormal Subgroup
 * 843) Definition:Parity of Integer
 * 844) Definition:Partial Differential Operator
 * 845) Definition:Partial Function Equality
 * 846) Definition:Partial Function
 * 847) Definition:Partial Preordering
 * 848) Definition:Particular Categorical Statement
 * 849) Definition:Particular Point Topology/Infinite
 * 850) Definition:Set Partition/Component
 * 851) Definition:Set Partition/Finite Expansion
 * 852) Definition:Path (Category Theory)
 * 853) Definition:Path (Graph Theory)/Open
 * 854) Definition:Path Graph
 * 855) Definition:Path-Connected/Topology/Set
 * 856) Definition:Peano Structure
 * 857) Definition:Periodic Continued Fraction
 * 858) Definition:Periodic Process
 * 859) Definition:Permutation Symbol
 * 860) Definition:Perturbed Proportion
 * 861) Definition:Petersen Graph
 * 862) Definition:Philosophical Position
 * 863) Definition:Physical Law
 * 864) Definition:Physical Universe
 * 865) Definition:Plane Number
 * 866) Definition:Platonic Graph/Cube
 * 867) Definition:Platonic Graph/Dodecahedron
 * 868) Definition:Platonic Graph/Icosahedron
 * 869) Definition:Platonic Graph/Octahedron
 * 870) Definition:Platonic Graph/Tetrahedron
 * 871) Definition:Platonic Graph
 * 872) Definition:Point-to-Set Distance
 * 873) Definition:Pointwise Addition of Complex-Valued Functions
 * 874) Definition:Pointwise Addition of Integer-Valued Functions
 * 875) Definition:Pointwise Addition of Mappings
 * 876) Definition:Pointwise Addition of Rational-Valued Functions
 * 877) Definition:Pointwise Addition
 * 878) Definition:Pointwise Inequality of Extended Real-Valued Functions
 * 879) Definition:Pointwise Inequality of Real-Valued Functions
 * 880) Definition:Pointwise Inequality
 * 881) Definition:Pointwise Limit
 * 882) Definition:Pointwise Maximum of Mappings/Extended Real-Valued Functions
 * 883) Definition:Pointwise Maximum of Mappings/Real-Valued Functions
 * 884) Definition:Pointwise Maximum of Mappings
 * 885) Definition:Pointwise Minimum of Mappings/Extended Real-Valued Functions
 * 886) Definition:Pointwise Minimum of Mappings/Real-Valued Functions
 * 887) Definition:Pointwise Minimum of Mappings
 * 888) Definition:Pointwise Multiplication of Complex-Valued Functions
 * 889) Definition:Pointwise Multiplication of Integer-Valued Functions
 * 890) Definition:Pointwise Multiplication of Rational-Valued Functions
 * 891) Definition:Pointwise Multiplication
 * 892) Definition:Pointwise Operation on Complex-Valued Functions
 * 893) Definition:Pointwise Operation on Integer-Valued Functions
 * 894) Definition:Pointwise Operation on Number-Valued Functions
 * 895) Definition:Pointwise Operation on Rational-Valued Functions
 * 896) Definition:Pointwise Scalar Multiplication of Complex-Valued Function
 * 897) Definition:Pointwise Scalar Multiplication of Extended Real-Valued Functions
 * 898) Definition:Pointwise Scalar Multiplication of Integer-Valued Function
 * 899) Definition:Pointwise Scalar Multiplication of Mappings/Real-Valued Functions
 * 900) Definition:Pointwise Scalar Multiplication of Mappings
 * 901) Definition:Pointwise Scalar Multiplication of Number-Valued Function
 * 902) Definition:Pointwise Scalar Multiplication of Rational-Valued Function
 * 903) Definition:Pointwise Scalar Multiplication of Real-Valued Function
 * 904) Definition:Pointwise Supremum of Extended Real-Valued Functions
 * 905) Definition:Pointwise Supremum of Real-Valued Functions
 * 906) Definition:Pointwise Supremum
 * 907) Definition:Polar Coordinates/Polar Plane
 * 908) Definition:Pole
 * 909) Definition:Polygon/Base
 * 910) Definition:Polygon/Height
 * 911) Definition:Polygon/Multi-lateral
 * 912) Definition:Polygon/Opposite
 * 913) Definition:Polygonal Number
 * 914) Definition:Polynomial Addition/Polynomial Forms
 * 915) Definition:Polynomial over Ring as Sequence
 * 916) Definition:Polynomial/Complex Numbers
 * 917) Definition:Polynomial Function/Complex
 * 918) Definition:Coefficient of Polynomial/Polynomial Form
 * 919) Definition:Coefficient of Polynomial
 * 920) Definition:Polynomial Congruence/Number of Solutions
 * 921) Definition:Polynomial Congruence/Solution
 * 922) Definition:Polynomial Congruence
 * 923) Definition:Polynormal Subgroup
 * 924) Definition:Positive/Number
 * 925) Definition:Positive/Rational Number
 * 926) Definition:Power (Algebra)/Even Power
 * 927) Definition:Power (Algebra)/Multiindices
 * 928) Definition:Power (Algebra)/Odd Power
 * 929) Definition:Power of Element/Monoid/Invertible Element
 * 930) Definition:Power of Element
 * 931) Definition:Pre-Image Sigma-Algebra
 * 932) Definition:Pre-Socratic
 * 933) Definition:Precise Refinement of Cover
 * 934) Definition:Preimage Set
 * 935) Definition:Preimage/Relation/Element
 * 936) Definition:Preimage/Relation
 * 937) Definition:Preorder Category/Definition 2
 * 938) Definition:Preordering/Definition 2
 * 939) Definition:Primal
 * 940) Definition:Prime Element
 * 941) Definition:Prime Enumeration Function
 * 942) Definition:Prime Exponent Function
 * 943) Definition:Prime Factor
 * 944) Definition:Prime Group
 * 945) Definition:Prime Ideal (Order Theory)
 * 946) Definition:Prime Number/Definition 3
 * 947) Definition:Prime Number/Negative Prime
 * 948) Definition:Prime Power
 * 949) Definition:Primitive Recursion/One Variable
 * 950) Definition:Primitive Recursion/Partial Function
 * 951) Definition:Primitive Recursion/Several Variables
 * 952) Definition:Primitive Recursion
 * 953) Definition:Primitive Recursive/Function
 * 954) Definition:Primitive Recursive/Relation
 * 955) Definition:Primitive Recursive/Set
 * 956) Definition:Primitive Recursive
 * 957) Definition:Primorial
 * 958) Definition:Probability Function
 * 959) Definition:Probability Mass Function/General Definition
 * 960) Definition:Probability Space/Continuous
 * 961) Definition:Probability Space/Discrete
 * 962) Definition:Product (Category Theory)/General Definition/Finite Product
 * 963) Definition:Product (Category Theory)/General Definition
 * 964) Definition:Product (Category Theory)
 * 965) Definition:Product Inverse
 * 966) Definition:Product Notation (Algebra)/Multiplicand
 * 967) Definition:Product of Affine Spaces
 * 968) Definition:Product of Ideals of Ring
 * 969) Definition:Product Space
 * 970) Definition:Product Topology
 * 971) Definition:Projective Module
 * 972) Definition:Projective Space/Over a Field
 * 973) Definition:Projective Space/Real Projective Space
 * 974) Definition:Projective Space
 * 975) Definition:Pronormal Subgroup
 * 976) Definition:Proof System/Formal Proof
 * 977) Definition:Proof System
 * 978) Definition:Proper Coloring
 * 979) Definition:Proper Element of Ring
 * 980) Definition:Proper G-Submodule
 * 981) Definition:Properties of Algebraic Structures of One Operation
 * 982) Definition:Properties of Algebraic Structures of Two Operations
 * 983) Definition:Propositional Expansion/Existential Quantifier
 * 984) Definition:Propositional Expansion/Universal Quantifier
 * 985) Definition:Propositional Expansion
 * 986) Definition:Propositional Function/Examples
 * 987) Definition:Provable Consequence
 * 988) Definition:Prüfer Domain
 * 989) Definition:Prüfer Sequence
 * 990) Definition:Pseudometrizable Topology
 * 991) Definition:Pseudometrizable
 * 992) Definition:Pure Set Theory
 * 993) Definition:Pure Transcendental Extension
 * 994) Definition:Pyramidal Number
 * 995) Definition:Pythagorean Equation
 * 996) Definition:Quadratic Algebra
 * 997) Definition:Quadratic Real Algebra
 * 998) Definition:Quadrilateral/Parallelogram/Altitude
 * 999) Definition:Quadrilateral/Parallelogram/Base
 * 1000) Definition:Quadrilateral/Rectangle/Containment
 * 1001) Definition:Quadrilateral/Trapezoid/Height
 * 1002) Definition:Quantified Statement
 * 1003) Definition:Quasigroup/Left Quasigroup
 * 1004) Definition:Quasigroup/Right Quasigroup
 * 1005) Definition:Quasimetric/Quasimetric Space
 * 1006) Definition:Quaternion/Algebra over Field
 * 1007) Definition:Quaternion/Construction from Complex Pairs
 * 1008) Definition:Radical Extension
 * 1009) Definition:Radical Ideal of Ring
 * 1010) Definition:Radical of Integer
 * 1011) Definition:Radical of Ideal of Ring
 * 1012) Definition:Ramanujan Sum
 * 1013) Definition:Ramsey Number
 * 1014) Definition:Rank (Linear Algebra)
 * 1015) Definition:Rate
 * 1016) Definition:Rational Sequence
 * 1017) Definition:Rational-Valued Function
 * 1018) Definition:Ray (Order Theory)
 * 1019) Definition:Ray (Topology)
 * 1020) Definition:Reachability Relation
 * 1021) Definition:Reachable
 * 1022) Definition:Real Algebra
 * 1023) Definition:Real Element in Star-Algebra
 * 1024) Definition:Real Interval/Empty
 * 1025) Definition:Real Interval/Midpoint
 * 1026) Definition:Real Interval/Notation/Conventional
 * 1027) Definition:Real Interval/Notation/Reverse-Bracket
 * 1028) Definition:Real Interval/Notation/Unbounded Intervals
 * 1029) Definition:Real Interval/Notation
 * 1030) Definition:Real Matrix
 * 1031) Definition:Reciprocal Proportion
 * 1032) Definition:Recursive/Function
 * 1033) Definition:Recursive/Relation
 * 1034) Definition:Recursive/Set
 * 1035) Definition:Recursive
 * 1036) Definition:Reduced Ring
 * 1037) Definition:Reducible G-Module
 * 1038) Definition:Reducible Linear Representation
 * 1039) Definition:Refinement
 * 1040) Definition:Reflexive Closure/Intersection of Reflexive Supersets
 * 1041) Definition:Reflexive Closure/Smallest Reflexive Superset
 * 1042) Definition:Reflexive Closure
 * 1043) Definition:Reflexive Reduction
 * 1044) Definition:Reflexive Transitive Closure/Transitive Closure of Reflexive Closure
 * 1045) Definition:Reflexivity
 * 1046) Definition:Region/Metric Space
 * 1047) Definition:Regular Expression
 * 1048) Definition:Regular Value
 * 1049) Definition:Reidemeister Move
 * 1050) Definition:Relation Conversely Compatible with Operation
 * 1051) Definition:Relation Strongly Compatible with Operation
 * 1052) Definition:Relational Closure
 * 1053) Definition:Relational Loop
 * 1054) Definition:Relatively Closed
 * 1055) Definition:Residue (Complex Analysis)
 * 1056) Definition:Residue
 * 1057) Definition:Rest Mass
 * 1058) Definition:Restricted Existential Quantifier
 * 1059) Definition:Restricted Universal Quantifier
 * 1060) Definition:Restriction of Ordering
 * 1061) Definition:Rig
 * 1062) Definition:Right Angle/Perpendicular/Foot
 * 1063) Definition:Right Cancellable Operation
 * 1064) Definition:Right Cancellable
 * 1065) Definition:Right Circular Cone/Acute-Angled
 * 1066) Definition:Right Circular Cone/Base
 * 1067) Definition:Right Circular Cone/Directrix
 * 1068) Definition:Right Circular Cone/Generatrix
 * 1069) Definition:Right Circular Cone/Obtuse-Angled
 * 1070) Definition:Right Circular Cone/Opening Angle
 * 1071) Definition:Right Circular Cone/Right-Angled
 * 1072) Definition:Right Circular Cone/Similar Cones
 * 1073) Definition:Right Difference Quotient
 * 1074) Definition:Right Inverse
 * 1075) Definition:Right-Hand Derivative
 * 1076) Definition:Right-Total Relation
 * 1077) Definition:Ring (Abstract Algebra)/Binding Priority
 * 1078) Definition:Ring Extension
 * 1079) Definition:Ring of Sets/Definition 1
 * 1080) Definition:Ring of Sets
 * 1081) Definition:Root of Propositional Tableau
 * 1082) Definition:Root of Unity Modulo m
 * 1083) Definition:Rooted Subtree
 * 1084) Definition:Rooted Tree/Child Node/Grandchild Node
 * 1085) Definition:Rooted Tree/Proper Descendant
 * 1086) Definition:Rooted Tree/Sibling
 * 1087) Definition:Satisfiable/Formula
 * 1088) Definition:Satisfiable/Set of Formulas
 * 1089) Definition:Saturated Model
 * 1090) Definition:Schreier Domain
 * 1091) Definition:Schwarz Function
 * 1092) Definition:Scope
 * 1093) Definition:Secant Function/Complex
 * 1094) Definition:Secant Function/Real
 * 1095) Definition:Second Chebyshev Function
 * 1096) Definition:Second Order Ordinary Differential Equation
 * 1097) Definition:Second Order Partial Differential Equation
 * 1098) Definition:Section of Line by Line
 * 1099) Definition:Segment of Circle/Angle in Segment
 * 1100) Definition:Segment of Circle/Angle of Segment
 * 1101) Definition:Segment of Circle/Base
 * 1102) Definition:Segment of Circle/Similar
 * 1103) Definition:Seifert Matrix
 * 1104) Definition:Self Distributive
 * 1105) Definition:Self-Inverse Element
 * 1106) Definition:Self-Map
 * 1107) Definition:Self-Normalizing Subgroup
 * 1108) Definition:Semihereditary Ring
 * 1109) Definition:Seminorm
 * 1110) Definition:Semiring (Abstract Algebra)
 * 1111) Definition:Semiring
 * 1112) Definition:Separated by Closed Neighborhoods
 * 1113) Definition:Separated by Function
 * 1114) Definition:Separated by Neighborhoods
 * 1115) Definition:Separation of Ratio
 * 1116) Definition:Sequence Coding
 * 1117) Definition:Sequence/Empty Sequence
 * 1118) Definition:Sequential Continuity
 * 1119) Definition:Series/General/Sequence of Partial Products
 * 1120) Definition:Series/General
 * 1121) Definition:Set of Truth Values
 * 1122) Definition:Set Variable
 * 1123) Definition:Set/Implicit Set Definition/Multipart Infinite Set
 * 1124) Definition:Sheffer Operator
 * 1125) Definition:Short Exact Sequence of Modules
 * 1126) Definition:Sierpiński Number
 * 1127) Definition:Sigma-Algebra/Definition 4
 * 1128) Definition:Sigma-Algebra
 * 1129) Definition:Sigma-Ring/Definition 1
 * 1130) Definition:Sigma-Ring
 * 1131) Definition:Sign of Permutation
 * 1132) Definition:Signature (Logic)
 * 1133) Definition:Signum Function/Natural Numbers
 * 1134) Definition:Signum Function/Signum Complement
 * 1135) Definition:Similar Figures
 * 1136) Definition:Similar Inclination
 * 1137) Definition:Similar Triangles
 * 1138) Definition:Simply Connected
 * 1139) Definition:Simultaneous Congruences
 * 1140) Definition:Singleton Relation
 * 1141) Definition:Skolem Sequence
 * 1142) Definition:Smallest
 * 1143) Definition:Smooth Differentiable Structure
 * 1144) Definition:Smooth Homotopy
 * 1145) Definition:Solid Number
 * 1146) Definition:Sound Proof System
 * 1147) Definition:Spacetime
 * 1148) Definition:Spanning Subgraph
 * 1149) Definition:Spanning Tree/Cutting-Down Method
 * 1150) Definition:Spectrum of Ring
 * 1151) Definition:Sphere/Geometry/Axis
 * 1152) Definition:Sphere/Geometry/Center
 * 1153) Definition:Sphere/Geometry/Diameter
 * 1154) Definition:Sphere/Geometry/Radius
 * 1155) Definition:Sphere/Topology/Center
 * 1156) Definition:Sphere/Topology/Radius
 * 1157) Definition:Splitting Field
 * 1158) Definition:Stability (Differential Equations)
 * 1159) Definition:Stability (Model Theory)
 * 1160) Definition:Stable under Intersection
 * 1161) Definition:Standard Affine Space
 * 1162) Definition:Standard Affine Structure on Vector Space
 * 1163) Definition:Standard Number Field
 * 1164) Definition:Star Shaped Set
 * 1165) Definition:Statement Form/Substatement
 * 1166) Definition:Steiner Inellipse
 * 1167) Definition:Steiner Triple System
 * 1168) Definition:Stirling Numbers
 * 1169) Definition:Stirling's Triangle of the First Kind (Signed)
 * 1170) Definition:Stirling's Triangles
 * 1171) Definition:Stratified Random Sample/Strata
 * 1172) Definition:Stratified Random Sample
 * 1173) Definition:Strict Ordering/Antireflexive and Transitive
 * 1174) Definition:Strict Partial Ordering
 * 1175) Definition:Strict Upper Closure
 * 1176) Definition:Strict Weak Ordering
 * 1177) Definition:Strict Well-Ordering
 * 1178) Definition:Strictly Decreasing
 * 1179) Definition:Strictly Increasing
 * 1180) Definition:Strictly Monotone/Sequence/Real Sequence
 * 1181) Definition:Strictly Monotone
 * 1182) Definition:Strictly Negative/Integer
 * 1183) Definition:Strictly Negative/Number
 * 1184) Definition:Strictly Negative/Rational Number
 * 1185) Definition:Strictly Negative
 * 1186) Definition:Strictly Positive/Number
 * 1187) Definition:Strictly Positive/Rational Number
 * 1188) Definition:Strictly Precede/Definition 1
 * 1189) Definition:Strictly Precede
 * 1190) Definition:Strictly Succeed
 * 1191) Definition:Strictly Totally Ordered Set
 * 1192) Definition:Strictly Well-Ordered Set
 * 1193) Definition:Strongly Additive Function
 * 1194) Definition:Structure
 * 1195) Definition:Sub-Basis
 * 1196) Definition:Sub-Sigma-Algebra
 * 1197) Definition:Subadditive Function (Measure Theory)
 * 1198) Definition:Subadditive Function
 * 1199) Definition:Subalgebra
 * 1200) Definition:Subcategory
 * 1201) Definition:Subcontinuum
 * 1202) Definition:Subcover/Countable
 * 1203) Definition:Subcover/Finite
 * 1204) Definition:Subdivision (Real Analysis)/Normal Subdivision
 * 1205) Definition:Subgraph/Embedding
 * 1206) Definition:Sublattice
 * 1207) Definition:Submanifold
 * 1208) Definition:Submersion
 * 1209) Definition:Subnormal Subgroup
 * 1210) Definition:Subobject Class/Morphism Class
 * 1211) Definition:Subsemiring
 * 1212) Definition:Substatement
 * 1213) Definition:Substitution (Mathematical Logic)
 * 1214) Definition:Substring
 * 1215) Definition:Subtraction/Natural Numbers
 * 1216) Definition:Subtree (Graph Theory)
 * 1217) Definition:Subtree
 * 1218) Definition:Succeed
 * 1219) Definition:Successor
 * 1220) Definition:Sufficiently Large
 * 1221) Definition:Sum Over Divisors
 * 1222) Definition:Summation/Summand
 * 1223) Definition:Support of Continuous Mapping
 * 1224) Definition:Support of Distribution
 * 1225) Definition:Support of Continuous Real-Valued Function
 * 1226) Definition:Support of Real-Valued Function
 * 1227) Definition:Support
 * 1228) Definition:Supremum of Mapping
 * 1229) Definition:Supremum of Set/Finite Supremum
 * 1230) Definition:Surjective on Morphisms
 * 1231) Definition:Surjective on Objects
 * 1232) Definition:Symmetric Closure
 * 1233) Definition:Symmetric Polynomial
 * 1234) Definition:Symmetric Set
 * 1235) Definition:Symmetry (Relation)
 * 1236) Definition:System of Sets
 * 1237) Definition:Tangent Bundle
 * 1238) Definition:Tangent Map
 * 1239) Definition:Tangent Space
 * 1240) Definition:Tangent Function/Complex
 * 1241) Definition:Tangent Circles
 * 1242) Definition:Tarski's Geometry
 * 1243) Definition:Tautology/Formal Semantics
 * 1244) Definition:Term (Natural Language)
 * 1245) Definition:Time Period
 * 1246) Definition:Time-Constructible Function
 * 1247) Definition:Top of Lattice/Definition 1
 * 1248) Definition:Top of Lattice/Definition 2
 * 1249) Definition:Top of Lattice
 * 1250) Definition:Topological Division Ring
 * 1251) Definition:Topological Field
 * 1252) Definition:Topological Group/Definition 2
 * 1253) Definition:Topological Manifold/Complex Manifold
 * 1254) Definition:Topological Manifold/Differentiable Manifold
 * 1255) Definition:Topological Manifold/Smooth Manifold
 * 1256) Definition:Topological Manifold
 * 1257) Definition:Topological Ring
 * 1258) Definition:Topological Semigroup
 * 1259) Definition:Topology Generated by Synthetic Basis
 * 1260) Definition:Topology on Extended Real Numbers
 * 1261) Definition:Torus (Topology)
 * 1262) Definition:Total Derivative
 * 1263) Definition:Total Function
 * 1264) Definition:Total Preordering
 * 1265) Definition:Total Recursive Function
 * 1266) Definition:Totally Bounded Metric Space/Definition 2
 * 1267) Definition:Totally Bounded Metric Space
 * 1268) Definition:Totally Ordered Commutative Semigroup
 * 1269) Definition:Totally Ordered Group
 * 1270) Definition:Totally Ordered Semigroup
 * 1271) Definition:Totally Ordered Structure
 * 1272) Definition:Tower of Fields
 * 1273) Definition:Trace (Linear Algebra)
 * 1274) Definition:Trace Table
 * 1275) Definition:Transcendence Degree
 * 1276) Definition:Transcendental Field Extension
 * 1277) Definition:Transcendental Element of Field Extension
 * 1278) Definition:Transcendental
 * 1279) Definition:Transfer Function
 * 1280) Definition:Transitive Closure (Relation Theory)/Intersection of Transitive Supersets
 * 1281) Definition:Transitive Closure (Relation Theory)/Union of Compositions
 * 1282) Definition:Transitive Closure
 * 1283) Definition:Transitive Reduction
 * 1284) Definition:Transitive with Respect to a Relation
 * 1285) Definition:Transitivity (Relation Theory)
 * 1286) Definition:Translation Invariant Measure
 * 1287) Definition:Tree (Graph Theory)/Definition 1
 * 1288) Definition:Tree (Set Theory)
 * 1289) Definition:Triangle (Geometry)/Adjacent
 * 1290) Definition:Triangle (Geometry)/Isosceles/Apex
 * 1291) Definition:Triangle (Geometry)/Isosceles/Legs
 * 1292) Definition:Triangle (Geometry)/Nomenclature
 * 1293) Definition:Triangle (Graph Theory)
 * 1294) Definition:Trichotomy
 * 1295) Definition:Triplicate Ratio
 * 1296) Definition:Trivial Character
 * 1297) Definition:Trivial G-Module
 * 1298) Definition:Trivial Gradation
 * 1299) Definition:Trivial Norm
 * 1300) Definition:Trivial Partition
 * 1301) Definition:Trivial Topological Space
 * 1302) Definition:Trivial
 * 1303) Definition:Truth Function/Connective
 * 1304) Definition:Two (Ordinal)
 * 1305) Definition:Type Space
 * 1306) Definition:Type
 * 1307) Definition:Ultrafilter on Set
 * 1308) Definition:Ultraproduct
 * 1309) Definition:Unambiguous
 * 1310) Definition:Unbounded Divergent Sequence
 * 1311) Definition:Unbounded Divergent Sequence/Complex Sequence
 * 1312) Definition:Underlying Graph
 * 1313) Definition:Underlying Set Functor
 * 1314) Definition:Undirected Graph
 * 1315) Definition:Uniform Convergence Almost Everywhere
 * 1316) Definition:Uniform Equivalence
 * 1317) Definition:Union of Relations/General Definition
 * 1318) Definition:Union of Relations
 * 1319) Definition:Union Relation
 * 1320) Definition:Unique Parsability
 * 1321) Definition:Uniquely Complemented Lattice
 * 1322) Definition:Unit Arithmetic Function
 * 1323) Definition:Unit of System of Sets
 * 1324) Definition:Unital Subalgebra
 * 1325) Definition:Universal Graph
 * 1326) Definition:Universal Model
 * 1327) Definition:Universal Net
 * 1328) Definition:Universally Compatible Relation
 * 1329) Definition:Universally Congruent
 * 1330) Definition:Unsatisfiable/Boolean Interpretations
 * 1331) Definition:Unsatisfiable/Formula
 * 1332) Definition:Unsatisfiable/Set of Formulas
 * 1333) Definition:Upper Closure of Element
 * 1334) Definition:Upper Section/Definition 1
 * 1335) Definition:Upper Section/Definition 2
 * 1336) Definition:Upper Section/Definition 3
 * 1337) Definition:URM Computability
 * 1338) Definition:Valuation Ring
 * 1339) Definition:Valuation
 * 1340) Definition:Vector Space Automorphism
 * 1341) Definition:Vector Space Monomorphism
 * 1342) Definition:Vectorialization of Affine Space
 * 1343) Definition:Veridical Paradox
 * 1344) Definition:Vertex Cut
 * 1345) Definition:Von Mangoldt Function
 * 1346) Definition:Walk (Graph Theory)/Open
 * 1347) Definition:Wedge Product
 * 1348) Definition:Weight Function
 * 1349) Definition:Well-Founded Class
 * 1350) Definition:Witness Property
 * 1351) Definition:Word Metric
 * 1352) Definition:Zariski Topology
 * 1353) Definition:Zero (Ordinal)
 * 1354) Definition:Zero Divisor/Algebra
 * 1355) Definition:Zero Locus
 * 1356) Definition:Zero Subspace