Category:Proofread

A

• User:Abcxyz/Sandbox/Dedekind Completions of Archimedean Ordered Groups
• User:Abcxyz/Sandbox/Dedekind Completions of Ordered Sets
• Absolute Value of Powers
• Absolutely Convergent Generalized Sum Converges
• Addition of Real and Imaginary Parts
• Definition:Aleph Function
• All Convergent Sequence in Space have Unique Limit iff Hausdorff
• Alternative Differentiability Condition/Proof 1
• Alternative Differentiability Condition/Proof 2
• Definition:Arc Length
• Arens-Fort Space is Not Countably Compact
• Arens-Fort Space is Not Extremally Disconnected
• Arens-Fort Space is Not First-Countable
• Axiom of Choice Implies Zorn's Lemma
• Axiom:Axiom of Continuity
• Axiom of Foundation (Strong Form)/Proof 2
• Axiom:Axiom of Triangle Existence

B

• Banach-Alaoglu Theorem
• Binomial Theorem/General Binomial Theorem
• Binomial Theorem/Multiindex
• ProofWiki:Books/Antoni Zygmund/Trigonometrical Series
• Boolean Prime Ideal Theorem
• Boubaker's Theorem
• Boubaker's Theorem/Proof of Uniqueness

C

• Carroll Paradox
• Cauchy Integral Formula
• Central Limit Theorem
• Chain Rule for Real-Valued Functions
• Characterisation of Non-Archimedean Absolute Values
• Characteristic of Ordered Integral Domain
• Characterization of Minimal Element
• Definition:Class/Zermelo-Fraenkel
• Classical Probability is Probability Measure
• Classification of Compact One-Manifolds
• Compact Subspace of Linearly Ordered Space
• Compact Subspace of Linearly Ordered Space/Reverse Implication/Proof 1
• Completion of Valued Field
• Complex Integration by Substitution
• Composition of Compatible Closure Operators
• Condition for Straight Lines in Plane to be Parallel
• Definition:Connected (Topology)/Subset
• Continuous Complex Function is Complex Riemann Integrable
• Continuous Image of Connected Space is Connected/Proof 2
• Contour Integral along Reversed Contour
• Contour Integral is Well-Defined
• Cowen-Engeler Lemma

D

• Definition:Definite Integral
• Definition:Degenerate Case
• Definition:Depressed Polynomial
• Derivative of Arc Length
• Derivative of Arccosecant Function
• Derivative of Product of Real Function and Vector-Valued Function
• Derivatives of PGF of Shifted Geometric Distribution
• Determinant with Rows Transposed
• User:Dfeuer/Compact Subspace of Linearly Ordered Space strengthened
• User:Dfeuer/Open Set may not be Open Ball
• User:Dfeuer/Totally Ordered Group with Order Topology is Topological Group
• Definition:Dicyclic Group
• Dimension Theorem for Vector Spaces
• Directed Set has Strict Successors iff Unbounded Above
• Disjunction and Implication

E

• Edges of Polyhedra have no Curvature
• Einstein's Mass-Velocity Equation
• Embedding Theorem
• Equidistance Independent of Betweenness
• Equivalence of GO-Space Definitions/One implies Three
• Equivalence of GO-Space Definitions/Three implies One

E cont.

• Equivalence of GO-Space Definitions/Two implies One
• Equivalence of Join Definitions
• Equivalence of Transitive Closure Definitions (Relation Theory)/Union of Compositions is Smallest
• Equivalent Absolute Values
• Equivalent Definition of Irreducible G-module
• Equivalent Matrices have Equal Rank
• Existence of Logarithm
• Existence of Positive Root/Negative Exponent
• Existence of Positive Root/Positive Exponent
• Exponential Generating Function for Boubaker Polynomials

F

• Ferrari's Method
• Field of Characteristic Zero has Unique Prime Subfield/Proof 2
• Field of Prime Characteristic has Unique Prime Subfield
• Finite Group has Composition Series
• Finite Intersection of Regular Open Sets is Regular Open
• Finite Tree has Leaf Nodes
• Finite Tree has Leaf Nodes/Proof 1
• Finite Union of Regular Closed Sets is Regular Closed
• Finitely Satisfiable Theory has Maximal Finitely Satisfiable Extension/Lemma
• First Derivative of PGF of Negative Binomial Distribution/First Form
• First Derivative of PGF of Negative Binomial Distribution/Second Form
• Fisher's Inequality
• Frobenius's Theorem
• Function Obtained by Minimization from URM Computable Functions
• Fundamental Theorem of Algebra/Proof 3
• Fundamental Theorem of Calculus/First Part/Proof 2

G

• Gelfond-Schneider Theorem
• General Associativity Theorem/Formulation 2
• General Euclidean Metrics are Topologically Equivalent
• Definition:Gradient

H

• Heine-Borel iff Dedekind Complete
• Heine-Borel Theorem/Dedekind-Complete Space
• Hilbert Space Direct Sum is Hilbert Space

I

• Definition:Implicit Function
• Implicitly Defined Real-Valued Function
• Independent Events are Independent of Complement/General Result
• Definition:Inductive Argument
• Definition:Infinite Limit at Infinity
• Integral of Arcsecant Function
• Integral of One Over Square Root of Binomial
• Integral Resulting in Arcsecant
• Integral Resulting in Arctangent
• Internal Group Direct Product Injective
• Intersection of Closed Sets is Closed/Closure Operator
• Intersection of Closure Operators (Order Theory)
• Inverse of Relation Isomorphism
• Inverse of Vandermonde's Matrix
• Inverse Trigonometric Function of Reciprocral

K

• Kernel of Linear Transformation is Null Space of Matrix Representation

L

• Laplace's Expansion Theorem
• Law of Quadratic Reciprocity
• Left Distributive and Commutative Implies Distributive
• Legendre's Differential Equation
• Lexicographic Order Initial Segments
• Limit of Sequence is Limit of Real Function
• Linear Combination of Complex Integrals
• Linear Combination of Contour Integrals
• Linear Transformations Isomorphic to Matrix Space
• Linear Transformations Isomorphic to Matrix Space/Corollary
• Linearly Independent Subset of Basis of Vector Space
• Linearly Ordered Space is Connected iff Linear Continuum
• Logarithm Tends to Infinity
• User:Lord Farin/Sandbox/Archive
• User:Lord Farin/SandboxTemplate
• Lucas-Lehmer Test

M

• Mapping Induced on Power Set by Surjection
• Mappings Between Residue Classes

M cont.

• ProofWiki:Mathematicians/Paolo Ruffini
• Matrix Multiplication Homogeneous of Degree 1
• Maximal Ideal WRT Filter Complement is Prime in Distributive Lattice
• Maximal Spectrum of Ring Nonempty
• Measurable Image
• Modulus and Argument of Complex Exponential
• Morera's Theorem
• Motion of a Pendulum
• Multiplication of Real and Imaginary Parts
• Definition:Multiplication/Real Numbers

N

• Non-Empty Class has Element of Least Rank
• Non-Equivalence as Equivalence with Negation/Formulation 1/Forward Implication/Proof

O

• Odd Power Function is Strictly Increasing/General Result
• Odd Power Function is Strictly Increasing/Real Numbers
• Open Set may not be Open Ball
• Orbit-Stabilizer Theorem/Proof 2
• Order Isomorphism on Foundational Relations
• Order-Extension Principle/Proof 1
• Ordering can be Expanded to Compare Additional Pair/Proof 1
• Axiom:Outer Connectivity of Betweenness

P

• Axiom:Pasch's Axiom (Tarski's Axioms)
• Pi+e is Transcendental
• Points of a Transcendental Slope
• Polynomials Closed under Addition/Polynomial Forms
• Polynomials Closed under Ring Product
• Power Rule for Derivatives/Real Number Index
• Praeclarum Theorema/Formulation 1/Proof 3
• Primary Decomposition Theorem
• Prime Ideal in Lattice
• User:Prime.mover/Sandbox
• Principal Ideal Domain fulfills Ascending Chain Condition
• Product Form of Sum on Completely Multiplicative Function
• Product of Discrete Random Variables
• Product of Positive Strictly Increasing Mappings is Strictly Increasing
• Pseudometric induces Topology

Q

• Quadratic Nature by Sum of Floors of Multiples of Fractions
• Quaternion Group not Dihedral Group
• Quotient Group of Direct Products
• Quotient Mapping of Inverse Completion
• Quotient Space of Real Line may be Indiscrete
• Quotient Structure of Inverse Completion

R

• Real and Imaginary Part Projections are Continuous
• Real Multiplication is Well-Defined
• Real Number Line
• Real Numbers are Uncountable
• Real Numbers are Uncountable/Cantor's Diagonal Argument
• Reciprocal Function Strictly Decreasing
• Definition:Relative Frequency Model
• Reparameterization of Contour is Contour
• Restricted Tukey-Teichmüller Theorem/Strong Form
• Reversed Contour is Contour
• Reversed Directed Smooth Curve is Directed Smooth Curve
• Right and Left Multiplications in Topological Group are Homeomorphism
• Row Equivalent Matrix for Homogeneous System Has Same Solutions

S

• Schur's Lemma (Representation Theory)/Corollary
• Second Derivative of Concave Downward Function
• Second Derivative of Concave Upward Function
• Second Derivative of PGF of Negative Binomial Distribution/Second Form
• Second Principle of Finite Induction
• Set has Rank
• Set of Finite Subsets of Countable Set is Countable/Proof 2
• Sigma-Algebra Closed under Finite Intersection
• Sorgenfrey Line fulfills All Separation Axioms
• Sorgenfrey Line is Perfectly Normal
• Spectrum of Ring Nonempty
• Strictly Positive Integer Power Function Strictly Succeeds Each Element