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The following pages link to Mathematician:Writer/Thomas A. Whitelaw:

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• Mathematician:Writer (transclusion) ‎ (← links)
• Mathematician:Thomas A. Whitelaw (redirect page) ‎ (← links)
  • One-Step Subgroup Test ‎ (← links)
  • Two-Step Subgroup Test ‎ (← links)
  • Fundamental Theorem of Arithmetic ‎ (← links)
  • Euclid's Lemma ‎ (← links)
  • Fermat's Little Theorem ‎ (← links)
  • Divisibility by 9 ‎ (← links)
  • Center of Symmetric Group is Trivial ‎ (← links)
  • Double Negation ‎ (← links)
  • Set is Subset of Union ‎ (← links)
  • Set is Subset of Itself ‎ (← links)
  • Subset Relation is Transitive ‎ (← links)
  • Intersection is Subset ‎ (← links)
  • Union Distributes over Intersection ‎ (← links)
  • Intersection Distributes over Union ‎ (← links)
  • Set Difference with Set Difference ‎ (← links)
  • Set Difference as Intersection with Relative Complement ‎ (← links)
  • Symmetric Difference with Empty Set ‎ (← links)
  • Complement of Empty Set is Universe ‎ (← links)
  • Complement of Universe is Empty Set ‎ (← links)
  • Complement of Complement ‎ (← links)
  • Symmetric Difference with Universe ‎ (← links)
  • Symmetric Difference with Self is Empty Set ‎ (← links)
  • Symmetric Difference with Complement ‎ (← links)
  • Symmetric Difference is Associative ‎ (← links)
  • Cartesian Product is Empty iff Factor is Empty ‎ (← links)
  • Cartesian Product is Anticommutative ‎ (← links)
  • Cartesian Product of Intersections ‎ (← links)
  • Cartesian Product Distributes over Union ‎ (← links)
  • Cartesian Product of Unions ‎ (← links)
  • Diagonal Relation is Equivalence ‎ (← links)
  • Element in its own Equivalence Class ‎ (← links)
  • Equivalence Class is not Empty ‎ (← links)
  • Equivalence Class holds Equivalent Elements ‎ (← links)
  • Fundamental Theorem on Equivalence Relations ‎ (← links)
  • Equivalence Class is Unique ‎ (← links)
  • Equality of Mappings ‎ (← links)
  • Image of Element under Inverse Mapping ‎ (← links)
  • Injection if Composite is Injection ‎ (← links)
  • Restriction of Mapping to Image is Surjection ‎ (← links)
  • Surjection if Composite is Surjection ‎ (← links)
  • Identity Mapping is Permutation ‎ (← links)
  • Composite of Bijection with Inverse is Identity Mapping ‎ (← links)
  • Composite of Permutations is Permutation ‎ (← links)
  • Inverse of Permutation is Permutation ‎ (← links)
  • Image of Intersection under Injection ‎ (← links)
  • Cantor's Theorem ‎ (← links)
  • Union of Power Sets ‎ (← links)
  • Intersection of Power Sets ‎ (← links)
  • Subset Product within Semigroup is Associative ‎ (← links)
  • Subsemigroup Closure Test ‎ (← links)
  • More than one Left Identity then no Right Identity ‎ (← links)
  • Element under Right Operation is Left Identity ‎ (← links)
  • Product of Semigroup Element with Left Inverse is Idempotent ‎ (← links)
  • Left Inverse for All is Right Inverse ‎ (← links)
  • Inverse of Identity Element is Itself ‎ (← links)
  • Power Set with Union is Commutative Monoid ‎ (← links)
  • Power Set with Intersection is Commutative Monoid ‎ (← links)
  • Monomorphism Image is Isomorphic to Domain ‎ (← links)
  • Isomorphism is Equivalence Relation ‎ (← links)
  • Group Product Identity therefore Inverses ‎ (← links)
  • Inverse of Product of Subsets of Group ‎ (← links)
  • Regular Representations in Group are Permutations ‎ (← links)
  • Set Equivalence of Regular Representations ‎ (← links)
  • Commutation Property in Group ‎ (← links)
  • Group is Subgroup of Itself ‎ (← links)
  • Identity of Subgroup ‎ (← links)
  • Inverses in Subgroup ‎ (← links)
  • Intersection of Subgroups is Subgroup ‎ (← links)
  • Union of Subgroups ‎ (← links)
  • Product of Subgroup with Itself ‎ (← links)
  • Inverse of Subgroup ‎ (← links)
  • Subset Product of Subgroups ‎ (← links)
  • Group Homomorphism Preserves Subgroups ‎ (← links)
  • Image of Group Homomorphism is Subgroup ‎ (← links)
  • Conjugacy is Equivalence Relation ‎ (← links)
  • Kernel of Group Homomorphism is Subgroup ‎ (← links)
  • Ring Product with Zero ‎ (← links)
  • Product with Ring Negative ‎ (← links)
  • Ring Less Zero is Semigroup for Product iff No Proper Zero Divisors ‎ (← links)
  • Subring Test ‎ (← links)
  • Center of Ring is Commutative Subring ‎ (← links)
  • Ring is Ideal of Itself ‎ (← links)
  • Ideal of Unit is Whole Ring ‎ (← links)
  • Test for Ideal ‎ (← links)
  • Element of Integral Domain Divides Zero ‎ (← links)
  • Unit of Integral Domain divides all Elements ‎ (← links)
  • Divisor of Unit is Unit ‎ (← links)
  • Associatehood is Equivalence Relation ‎ (← links)
  • Field is Subfield of Itself ‎ (← links)
  • Cosets are Equivalent ‎ (← links)
  • Cosets in Abelian Group ‎ (← links)
  • Conjugate of Subgroup is Subgroup ‎ (← links)
  • Subgroup of Abelian Group is Normal ‎ (← links)
  • Kernel is Normal Subgroup of Domain ‎ (← links)
  • Kernel of Inner Automorphism Group is Center ‎ (← links)
  • Normalizer is Subgroup ‎ (← links)
  • Subgroup is Normal Subgroup of Normalizer ‎ (← links)
  • Normalizer of Subgroup is Largest Subgroup containing that Subgroup as Normal Subgroup ‎ (← links)
  • Quotient Group of Ideal is Coset Space ‎ (← links)
  • Quotient Ring is Ring/Quotient Ring Product is Well-Defined ‎ (← links)
  • Quotient Ring of Commutative Ring is Commutative ‎ (← links)
  • Quotient Ring of Ring with Unity is Ring with Unity ‎ (← links)
  • Quotient Epimorphism is Epimorphism/Ring ‎ (← links)
  • Kernel of Ring Homomorphism is Subring ‎ (← links)
  • Kernel of Ring Homomorphism is Ideal ‎ (← links)
  • Equivalence of Mappings between Sets of Same Cardinality ‎ (← links)
  • General Associativity Theorem ‎ (← links)
  • External Direct Product of Groups is Group ‎ (← links)
  • Integers form Integral Domain ‎ (← links)
  • Invertible Integers under Multiplication ‎ (← links)
  • Cardinality of Cartesian Product ‎ (← links)
  • Cardinality of Set of Injections ‎ (← links)
  • Set of Integers Bounded Below by Integer has Smallest Element ‎ (← links)
  • Set of Integers Bounded Above by Integer has Greatest Element ‎ (← links)
  • Principle of Least Counterexample ‎ (← links)
  • Absolute Value of Integer is not less than Divisors ‎ (← links)
  • Euclidean Algorithm ‎ (← links)
  • Set of Integer Combinations equals Set of Multiples of GCD ‎ (← links)
  • Divisor of Sum of Coprime Integers ‎ (← links)
  • Product of Coprime Factors ‎ (← links)
  • Integer is Congruent Modulo Divisor to Remainder ‎ (← links)
  • Integer is Congruent to Integer less than Modulus ‎ (← links)
  • Modulo Addition is Well-Defined ‎ (← links)
  • Modulo Multiplication is Well-Defined ‎ (← links)
  • Congruence of Product ‎ (← links)
  • Congruence of Powers ‎ (← links)
  • Modulo Addition is Associative ‎ (← links)
  • Modulo Addition is Commutative ‎ (← links)
  • Modulo Addition has Identity ‎ (← links)
  • Modulo Addition has Inverses ‎ (← links)
  • Modulo Multiplication is Closed ‎ (← links)
  • Modulo Multiplication is Commutative ‎ (← links)
  • Modulo Multiplication has Identity ‎ (← links)
  • Modulo Multiplication Distributes over Modulo Addition ‎ (← links)
  • GCD from Congruence Modulo m ‎ (← links)
  • Prime not Divisor implies Coprime ‎ (← links)
  • Real Number minus Floor ‎ (← links)
  • Real Number is Floor plus Difference ‎ (← links)
  • Sum of Floor and Floor of Negative ‎ (← links)
  • Floor defines Equivalence Relation ‎ (← links)
  • Cancellable Finite Semigroup is Group ‎ (← links)
  • Element has Idempotent Power in Finite Semigroup ‎ (← links)
  • Power of Conjugate equals Conjugate of Power ‎ (← links)
  • Homomorphism of Power of Group Element ‎ (← links)
  • Powers of Element form Subgroup ‎ (← links)
  • Intersection of Subgroups of Prime Order ‎ (← links)
  • Identity is Only Group Element of Order 1 ‎ (← links)
  • Group Element is Self-Inverse iff Order 2 ‎ (← links)
  • Powers of Infinite Order Element ‎ (← links)
  • Order of Element Divides Order of Finite Group ‎ (← links)
  • Element to Power of Group Order is Identity ‎ (← links)
  • Boolean Group is Abelian ‎ (← links)
  • Order of Group Element equals Order of Inverse ‎ (← links)
  • Even Order Group has Order 2 Element ‎ (← links)
  • Order of Conjugate Element equals Order of Element ‎ (← links)
  • Order of Homomorphic Image of Group Element ‎ (← links)
  • No Group has Two Order 2 Elements ‎ (← links)
  • Odd Order Group Element is Square ‎ (← links)
  • Cyclic Groups of Same Order are Isomorphic ‎ (← links)
  • Subgroup of Finite Cyclic Group is Determined by Order ‎ (← links)
  • Prime Group is Cyclic ‎ (← links)
  • Group of Order less than 6 is Abelian ‎ (← links)
  • Power of Generator of Cyclic Group is Generator iff Power is Coprime with Order ‎ (← links)
  • Order of Conjugate of Subgroup ‎ (← links)
  • Subgroup of Index 2 is Normal ‎ (← links)
  • Intersection of Normal Subgroups is Normal ‎ (← links)
  • Union of Conjugacy Classes is Normal ‎ (← links)
  • Unique Subgroup of a Given Order is Normal ‎ (← links)
  • Subset Product of Normal Subgroups is Normal ‎ (← links)
  • Prime Group has no Proper Subgroups ‎ (← links)
  • Quotient of Group by Center Cyclic implies Abelian ‎ (← links)
  • Inner Automorphism Group is Isomorphic to Quotient Group with Center ‎ (← links)
  • Conjugates of Elements in Centralizer ‎ (← links)
  • Number of Conjugates is Number of Cosets of Centralizer ‎ (← links)
  • Conjugacy Class of Element of Center is Singleton ‎ (← links)
  • Group of Order Prime Squared is Abelian ‎ (← links)
  • Center of Group of Prime Power Order is Non-Trivial ‎ (← links)
  • External Direct Product of Abelian Groups is Abelian Group ‎ (← links)
  • Group Direct Product of Cyclic Groups ‎ (← links)
  • Complex Numbers under Addition form Infinite Abelian Group ‎ (← links)
  • Non-Zero Complex Numbers under Multiplication form Infinite Abelian Group ‎ (← links)
  • Real Numbers under Addition form Infinite Abelian Group ‎ (← links)
  • Non-Zero Real Numbers under Multiplication form Abelian Group ‎ (← links)
  • Rational Numbers under Addition form Infinite Abelian Group ‎ (← links)
  • Non-Zero Rational Numbers under Multiplication form Infinite Abelian Group ‎ (← links)
  • Multiplicative Group of Rationals is Normal Subgroup of Reals ‎ (← links)
  • Inverse of Generator of Cyclic Group is Generator ‎ (← links)
  • Generators of Infinite Cyclic Group ‎ (← links)
  • Quotient Group of Reals by Integers is Circle Group ‎ (← links)
  • Ring of Integers Modulo Prime is Field ‎ (← links)
  • Symmetry Group is Group ‎ (← links)
  • Stabilizer is Subgroup ‎ (← links)
  • Square Matrices over Real Numbers under Multiplication form Monoid ‎ (← links)
  • General Linear Group is Group ‎ (← links)
  • Principal Ideals of Integers ‎ (← links)
  • Principal Ideal Domain is Unique Factorization Domain ‎ (← links)
  • Integral Domain with Characteristic Zero ‎ (← links)
  • Field of Prime Characteristic has Unique Prime Subfield ‎ (← links)
  • Set of Polynomials over Integral Domain is Subring ‎ (← links)
  • Unique Representation in Polynomial Forms ‎ (← links)
  • Ring of Polynomial Forms is Integral Domain ‎ (← links)
  • Rings of Polynomials in Ring Elements are Isomorphic ‎ (← links)
  • Epimorphism from Polynomial Forms to Polynomial Functions ‎ (← links)
  • Polynomial Factor Theorem ‎ (← links)
  • Complex Numbers form Field ‎ (← links)
  • Indirect Proof ‎ (← links)
  • Composition of Mappings is Associative ‎ (← links)
  • Quaternion Group is Hamiltonian ‎ (← links)
  • Gaussian Integers form Subring of Complex Numbers ‎ (← links)
  • Intersection with Subset is Subset ‎ (← links)
  • Union with Superset is Superset ‎ (← links)
  • Associativity on Four Elements ‎ (← links)
  • Proof by Counterexample ‎ (← links)
  • Equivalence of Well-Ordering Principle and Induction ‎ (← links)
  • Common Divisor Divides GCD ‎ (← links)
  • Square Modulo 5 ‎ (← links)
  • Square Modulo 3 ‎ (← links)
  • Division Laws for Groups ‎ (← links)
  • Center is Intersection of Centralizers ‎ (← links)
  • Subset Product with Normal Subgroup is Subgroup ‎ (← links)
  • Ring Homomorphism Preserves Zero ‎ (← links)
  • Relation Induced by Mapping is Equivalence Relation ‎ (← links)
  • Factoring Mapping into Quotient and Injection ‎ (← links)
  • Quotient Group is Group ‎ (← links)
  • Principal Ideal is Ideal ‎ (← links)
  • Equality of Ordered Tuples ‎ (← links)
  • Subtraction on Numbers is Not Associative ‎ (← links)
  • Element to Power of Remainder ‎ (← links)
  • Element to Power of Multiple of Order is Identity ‎ (← links)
  • List of Elements in Finite Cyclic Group ‎ (← links)
  • Equivalence of Definitions of Order of Group Element ‎ (← links)
  • Special Linear Group is Subgroup of General Linear Group ‎ (← links)
  • One-Step Subgroup Test using Subset Product ‎ (← links)
  • Integers form Commutative Ring ‎ (← links)
  • Properties of Prime Subfield ‎ (← links)
  • Quaternions Defined by Matrices ‎ (← links)
  • Matrix Form of Quaternion ‎ (← links)
  • Quaternions form Skew Field ‎ (← links)
  • Cancellation Law of Ring Product of Integral Domain ‎ (← links)
  • Triangular Matrices forms Subring of Square Matrices ‎ (← links)
  • Real Numbers form Subfield of Complex Numbers ‎ (← links)
  • Real Numbers form Ring ‎ (← links)
  • Complex Numbers form Ring ‎ (← links)
  • Prime Ideal iff Quotient Ring is Integral Domain ‎ (← links)
  • Maximal Ideal of Commutative and Unitary Ring is Prime Ideal ‎ (← links)
  • Quotient Ring of Integers with Principal Ideal ‎ (← links)
  • Ring Homomorphism Preserves Negatives ‎ (← links)
  • Units of Gaussian Integers ‎ (← links)
  • Ring of Square Matrices over Real Numbers ‎ (← links)
  • Ring Homomorphism from Field is Monomorphism or Zero Homomorphism ‎ (← links)
  • Rational Square Root of Integer is Integer ‎ (← links)
  • Union of Equivalence Classes is Whole Set ‎ (← links)
  • Cardinality of Image of Injection ‎ (← links)
  • Composition of Mappings is not Commutative ‎ (← links)
  • Intersection of Injective Image with Relative Complement ‎ (← links)
  • Cardinality of Set of Induced Equivalence Classes of Injection ‎ (← links)
  • Cardinality of Set of Induced Equivalence Classes of Surjection ‎ (← links)
  • Index Laws/Sum of Indices/Semigroup ‎ (← links)
  • Index Laws/Product of Indices/Semigroup ‎ (← links)
  • Semigroup is Subsemigroup of Itself ‎ (← links)
  • Identity of Monoid is Unique ‎ (← links)
  • Units of Gaussian Integers form Group ‎ (← links)
  • Quaternion Group/Complex Matrices ‎ (← links)
  • Gaussian Integer Units form Multiplicative Subgroup of Complex Numbers ‎ (← links)
  • Permutation Group is Subgroup of Symmetric Group ‎ (← links)
  • Multiplicative Group of Positive Rationals is Non-Cyclic ‎ (← links)
  • General Linear Group to Determinant is Homomorphism ‎ (← links)
  • Logarithm on Positive Real Numbers is Group Isomorphism ‎ (← links)
  • Kernel is Trivial iff Monomorphism/Group ‎ (← links)
  • Kernel is Trivial iff Monomorphism/Ring ‎ (← links)
  • First Isomorphism Theorem/Groups ‎ (← links)
  • First Isomorphism Theorem/Rings ‎ (← links)
  • Subgroup is Subgroup of Normalizer ‎ (← links)
  • Powers of Group Elements/Negative Index ‎ (← links)
  • Powers of Group Elements/Sum of Indices ‎ (← links)
  • Powers of Group Elements/Product of Indices ‎ (← links)
  • Injection iff Left Inverse/Proof 1 ‎ (← links)
  • Center of Group is Subgroup ‎ (← links)
  • Inner Automorphism is Automorphism ‎ (← links)
  • Bijection iff Left and Right Inverse/Corollary ‎ (← links)
  • Left and Right Inverse Mappings Implies Bijection ‎ (← links)
  • Left and Right Inverses of Mapping are Inverse Mapping/Proof 1 ‎ (← links)
  • Inverse of Inverse of Bijection/Proof 1 ‎ (← links)
  • Automorphism Group is Subgroup of Symmetric Group ‎ (← links)
  • Cayley's Representation Theorem/Proof 2 ‎ (← links)
  • Central Subgroup is Normal/Proof 2 ‎ (← links)
  • Coset Product is Well-Defined/Proof 4 ‎ (← links)
  • Group Homomorphism Preserves Identity/Proof 1 ‎ (← links)
  • Group Homomorphism Preserves Inverses/Proof 1 ‎ (← links)
  • Quotient Ring is Ring ‎ (← links)
  • Null Ring is Ideal ‎ (← links)
  • Characteristic of Finite Ring with No Zero Divisors/Proof 2 ‎ (← links)
  • Field of Characteristic Zero has Unique Prime Subfield/Proof 2 ‎ (← links)
  • Cyclic Group is Abelian/Proof 1 ‎ (← links)
  • Lagrange's Theorem (Group Theory)/Proof 2 ‎ (← links)
  • Subgroup of Cyclic Group is Cyclic/Proof 1 ‎ (← links)
  • Fermat's Little Theorem/Proof 3 ‎ (← links)
  • Center of Group is Subgroup/Proof 2 ‎ (← links)
  • Center of Group is Subgroup/Proof 1 ‎ (← links)
  • Integer is Expressible as Product of Primes/Proof 1 ‎ (← links)
  • Expression for Integer as Product of Primes is Unique/Proof 1 ‎ (← links)
  • Modulo Addition is Closed/Integers ‎ (← links)
  • Reduced Residue System under Multiplication forms Abelian Group/Corollary ‎ (← links)
  • Ring Homomorphism Preserves Subrings/Corollary ‎ (← links)
  • Ring Homomorphism Preserves Subrings/Proof 3 ‎ (← links)
  • Cross-Relation on Natural Numbers is Equivalence Relation ‎ (← links)
  • Cardinality of Power Set of Finite Set/Informal Proof ‎ (← links)
  • Cardinality of Set Union/Corollary ‎ (← links)
  • Image of Subset under Mapping is Subset of Image ‎ (← links)
  • Identity Mapping is Right Identity/Proof 1 ‎ (← links)
  • Identity Mapping is Left Identity/Proof 1 ‎ (← links)
  • Composite of Bijections is Bijection/Proof 1 ‎ (← links)
  • Modulo Subtraction is Well-Defined ‎ (← links)
  • Inverse of Group Product/General Result ‎ (← links)
  • Element of Finite Group is of Finite Order/Proof 2 ‎ (← links)
  • Cancellation Laws/Proof 1 ‎ (← links)
  • Order of Conjugate Element equals Order of Element/Corollary ‎ (← links)
  • Product of Subset with Intersection/Proof 1 ‎ (← links)
  • Product of Subset with Intersection/Corollary ‎ (← links)
  • Tower Law for Subgroups/Proof 2 ‎ (← links)
  • Subset Product of Subgroups/Sufficient Condition/Proof 2 ‎ (← links)
  • Subset Product of Subgroups/Necessary Condition/Proof 2 ‎ (← links)
  • Trivial Subgroup is Subgroup ‎ (← links)
  • Trivial Subgroup is Normal ‎ (← links)
  • Group is Normal in Itself ‎ (← links)
  • Matrix Similarity is Equivalence Relation/Proof 2 ‎ (← links)
  • Quotient Group is Group/Corollary ‎ (← links)
  • Euclid's Lemma for Prime Divisors/Proof 2 ‎ (← links)
  • Euclid's Lemma for Prime Divisors/General Result/Proof 2 ‎ (← links)
  • Common Divisor Divides Integer Combination/Proof 2 ‎ (← links)
  • Divisor Relation is Transitive ‎ (← links)
  • Polynomial Forms over Field form Principal Ideal Domain/Corollary 3 ‎ (← links)
  • Polynomial Forms over Field form Principal Ideal Domain/Corollary 1 ‎ (← links)
  • Polynomial Forms over Field form Principal Ideal Domain/Proof 1 ‎ (← links)
  • Division Theorem for Polynomial Forms over Field/Proof 1 ‎ (← links)
  • Identity of Group is Unique/Proof 1 ‎ (← links)
  • Left Identity while exists Left Inverse for All is Identity ‎ (← links)
  • Inverse in Group is Unique/Proof 1 ‎ (← links)
  • Exponential on Complex Plane is Group Homomorphism ‎ (← links)
  • Symmetric Group is Group/Proof 1 ‎ (← links)
  • Bézout's Lemma/Proof 1 ‎ (← links)
  • Left and Right Coset Spaces are Equivalent/Proof 1 ‎ (← links)
  • Intersection of Subgroups is Subgroup/General Result ‎ (← links)
  • Existence of Unique Subgroup Generated by Subset/Singleton Generator ‎ (← links)
  • Subgroup is Normal iff Contains Conjugate Elements ‎ (← links)
  • Modulo Addition is Well-Defined/Proof 2 ‎ (← links)
  • Inverse of Group Isomorphism is Isomorphism/Proof 2 ‎ (← links)
  • Composite of Group Homomorphisms is Homomorphism/Proof 2 ‎ (← links)
  • Projection on Group Direct Product is Epimorphism ‎ (← links)
  • Non-Abelian Group has Order Greater than 4/Proof 2 ‎ (← links)
  • Idempotent Ring is Commutative ‎ (← links)
  • Product of Ring Negatives ‎ (← links)
  • Field is Integral Domain/Proof 1 ‎ (← links)
  • Quotient Epimorphism is Epimorphism/Group ‎ (← links)
  • Ideal of Unit is Whole Ring/Corollary ‎ (← links)
  • Unity Divides All Elements/Proof 2 ‎ (← links)
  • Rule of Transposition/Formulation 1 ‎ (← links)
  • Power Structure of Group is Semigroup/Proof 1 ‎ (← links)
  • Element in Left Coset iff Product with Inverse in Subgroup ‎ (← links)
  • Element in Right Coset iff Product with Inverse in Subgroup ‎ (← links)
  • Empty Set is Subset of All Sets/Proof 1 ‎ (← links)
  • Group of Units is Group ‎ (← links)
  • Principal Ideal of Principal Ideal Domain is of Irreducible Element iff Maximal/Forward Implication ‎ (← links)
  • Subring of Polynomials over Integral Domain Contains that Domain ‎ (← links)
  • Subring of Polynomials over Integral Domain is Smallest Subring containing Element and Domain ‎ (← links)
  • Quadratic Integers over 2 form Subdomain of Reals/Proof 2 ‎ (← links)
  • Set of all Self-Maps under Composition forms Semigroup ‎ (← links)
  • Existence of Ring of Polynomial Forms in Transcendental over Integral Domain ‎ (← links)
  • Union of Subsets is Subset/Proof 2 ‎ (← links)
  • Set Complement inverts Subsets/Proof 2 ‎ (← links)
  • Injection iff Left Cancellable/Necessary Condition ‎ (← links)
  • Inverse of Composite Bijection/Proof 2 ‎ (← links)
  • Equivalence of Definitions of Set Equality ‎ (← links)
  • De Morgan's Laws (Predicate Logic)/Denial of Existence ‎ (← links)
  • De Morgan's Laws (Predicate Logic)/Denial of Universality ‎ (← links)
  • Common Divisor Divides Difference ‎ (← links)
  • Division Theorem/Positive Divisor/Existence/Proof 2 ‎ (← links)
  • Division Theorem/Positive Divisor/Uniqueness/Proof 2 ‎ (← links)
  • Infinite Number of Primes of form 4n - 1 ‎ (← links)
  • Modulo Multiplication is Well-Defined/Proof 1 ‎ (← links)
  • Integers under Multiplication form Semigroup ‎ (← links)
  • Integers under Addition form Abelian Group ‎ (← links)
  • Real Numbers form Field ‎ (← links)
  • Rational Numbers form Field ‎ (← links)
  • Integers Modulo m under Addition form Abelian Group ‎ (← links)
  • Multiplicative Group of Field is Abelian Group/Proof 2 ‎ (← links)
  • Centralizer of Group Element is Subgroup/Proof 1 ‎ (← links)
  • Composition of Left Regular Representations ‎ (← links)
  • Composition of Right Regular Representations ‎ (← links)
  • Composition of Left Regular Representation with Right ‎ (← links)
  • Existence of Group of Finite Order ‎ (← links)
  • Equivalence of Definitions of Surjection ‎ (← links)
  • Equivalence of Definitions of Abelian Group ‎ (← links)
  • Euclid's Theorem/Corollary 1/Proof 1 ‎ (← links)
  • Square Modulo 3/Corollary 2 ‎ (← links)
  • Square Modulo 3/Corollary 1 ‎ (← links)
  • Equivalence Classes are Disjoint/Proof 1 ‎ (← links)
  • Modulo Multiplication is Associative/Proof 1 ‎ (← links)
  • Symmetry Group of Equilateral Triangle/Cayley Table ‎ (← links)
  • De Morgan's Laws (Set Theory)/Set Complement/General Case/Complement of Intersection ‎ (← links)
  • De Morgan's Laws (Set Theory)/Set Complement/General Case/Complement of Union ‎ (← links)
  • Group of Gaussian Integer Units/Cayley Table ‎ (← links)
  • Surjection iff Right Cancellable/Necessary Condition/Proof 1 ‎ (← links)
  • Surjection iff Right Cancellable/Sufficient Condition/Proof 1 ‎ (← links)
  • Left Coset Space forms Partition ‎ (← links)
  • Right Coset Space forms Partition ‎ (← links)
  • Right Cosets are Equal iff Product with Inverse in Subgroup ‎ (← links)
  • Left Cosets are Equal iff Product with Inverse in Subgroup ‎ (← links)
  • Left Congruence Class Modulo Subgroup is Left Coset ‎ (← links)
  • Right Congruence Class Modulo Subgroup is Right Coset ‎ (← links)
  • Left Congruence Modulo Subgroup is Equivalence Relation ‎ (← links)
  • Right Congruence Modulo Subgroup is Equivalence Relation ‎ (← links)
  • Cardinality of Set of All Mappings/Finite Sets ‎ (← links)
  • Inverse in Monoid is Unique ‎ (← links)
  • Equivalence of Definitions of Injection/Definition 1 iff Definition 1 a ‎ (← links)
  • Natural Numbers under Multiplication form Semigroup ‎ (← links)
  • Bound Variable/Examples/Universal Statement ‎ (← links)
  • Bound Variable/Examples/Existential Statement ‎ (← links)
  • Cardinality of Set of Injections/Corollary ‎ (← links)
  • Equivalence of Definitions of Floor Function ‎ (← links)
  • Left Coset Equals Subgroup iff Element in Subgroup ‎ (← links)
  • Right Coset Equals Subgroup iff Element in Subgroup ‎ (← links)
  • Elements in Same Left Coset iff Product with Inverse in Subgroup ‎ (← links)
  • Elements in Same Right Coset iff Product with Inverse in Subgroup ‎ (← links)
  • Euclidean Algorithm/Demonstration ‎ (← links)
  • Inverse of Group Product/Proof 1 ‎ (← links)
  • Cancellable Infinite Semigroup is not necessarily Group ‎ (← links)
  • Klein Four-Group/Cayley Table ‎ (← links)
  • Order of Cyclic Group equals Order of Generator ‎ (← links)
  • Square Modulo 5/Corollary ‎ (← links)
  • 16 ‎ (← links)
  • 17 ‎ (← links)
  • 1980 ‎ (← links)
  • Nilpotent Elements of Commutative Ring form Ideal ‎ (← links)
  • 504 ‎ (← links)
  • Increasing Union of Ideals is Ideal/Sequence ‎ (← links)
  • Prime Ideal of Principal Ideal Domain is Maximal ‎ (← links)
  • Congruence Modulo Integer is Equivalence Relation ‎ (← links)
  • Relative Complement/Examples/Even Integers ‎ (← links)
  • Set Difference/Examples/1, 2, 3 less 2, 4, 5, 6 ‎ (← links)
  • Set Intersection/Examples/3 Arbitrarily Chosen Sets ‎ (← links)
  • Set Union/Examples/3 Arbitrarily Chosen Sets ‎ (← links)
  • Cartesian Product of Subsets/Corollary 3 ‎ (← links)
  • Denial of Universality/Examples/x less than or equal to 3 ‎ (← links)
  • Denial of Existence/Examples/x less than or equal to 3 ‎ (← links)
  • Denial of Universality/Examples/x less than or equal to 3/Examples/2, 3, 4 ‎ (← links)
  • Denial of Universality/Examples/x less than or equal to 3/Examples/0 to 3 ‎ (← links)
  • Denial of Existence/Examples/x less than or equal to 3/Examples/2, 3, 4 ‎ (← links)
  • Denial of Existence/Examples/x less than or equal to 3/Examples/0 to 3 ‎ (← links)
  • Converse and Contrapositive Statements/Examples/x less than 5 and x less than or equal to 5 ‎ (← links)
  • Quotients of 3 Unequal Numbers are Unequal ‎ (← links)
  • Cardinality/Examples ‎ (← links)
  • Cardinality/Examples/-1,0,1 ‎ (← links)
  • Cardinality/Examples/0 less than x less than 6 ‎ (← links)
  • Cardinality/Examples/x^2-x ‎ (← links)
  • Cardinality/Examples/Powerset of Arbitrary Set ‎ (← links)
  • Cardinality/Examples/Powerset of Empty Set ‎ (← links)
  • Empty Intersection iff Subset of Complement/Proof 2 ‎ (← links)
  • Empty Intersection iff Subset of Complement/Corollary ‎ (← links)
  • Union of Power Sets not always Equal to Powerset of Union ‎ (← links)
  • Limit of Intersection of Closed Intervals from Zero to Positive Integer Reciprocal ‎ (← links)
  • Distributive Laws/Examples/A cap B cap (C cup D) subset of (A cap D) cup (B cap C) ‎ (← links)
  • Distributive Laws/Examples/A cap B cap (C cup D) subset of (A cap D) cup (B cap C)/Corollary ‎ (← links)
  • Set Theory/Examples/A cup (X cap B) = C, (A cup X) cap B = D ‎ (← links)
  • Set Theory/Examples/A cup (X cap B) = C, (A cup X) cap B = D/Converse ‎ (← links)
  • Total Number of Set Partitions/Examples/2 ‎ (← links)
  • Total Number of Set Partitions/Examples/3 ‎ (← links)
  • Total Number of Set Partitions/Examples/4 ‎ (← links)
  • Bounded Below Subset of Real Numbers/Examples/Open Interval from 1 to Infinity ‎ (← links)
  • Bounded Above Subset of Real Numbers/Examples/Closed Interval from Minus Infinity to 2 ‎ (← links)
  • Floor Function/Examples/Floor of 5 over 2 ‎ (← links)
  • Floor Function/Examples/Floor of Minus 5 over 2 ‎ (← links)
  • Floor Function/Examples/Floor of 14 ‎ (← links)
  • Floor Function/Examples/Floor of Root 10 ‎ (← links)
  • Common Divisor Divides Integer Combination/Corollary ‎ (← links)
  • Euclidean Algorithm/Examples/2190 and 465 ‎ (← links)
  • 1978 ‎ (← links)
  • Euclidean Algorithm/Examples/9n+8 and 6n+5 ‎ (← links)
  • Chinese Remainder Theorem/Examples/n = 7 mod 12 so n = 3 mod 4 ‎ (← links)
  • Modulo Arithmetic/Examples/11 Divides 3^3n+1 + 2^2n+3 ‎ (← links)
  • Euclidean Algorithm/Examples/31x = 1 mod 56 ‎ (← links)
  • Coprime Divisors of Square Number are Square ‎ (← links)
  • Set of Residue Classes/Examples/5 ‎ (← links)
  • Congruent Integers in Same Residue Class ‎ (← links)
  • Residue Classes form Partition of Integers ‎ (← links)
  • Cardinality of Set of Residue Classes ‎ (← links)
  • Modulo Addition/Cayley Table/Modulo 5 ‎ (← links)
  • Modulo Multiplication/Cayley Table/Modulo 6 ‎ (← links)
  • Modulo Multiplication/Cayley Table/Modulo 5 ‎ (← links)
  • Equivalence Relation on Power Set induced by Intersection with Subset ‎ (← links)
  • Equivalence Relation on Power Set induced by Intersection with Subset/Equivalence Class of Empty Set ‎ (← links)
  • Equivalence Relation on Power Set induced by Intersection with Subset/Cardinality of Set of Equivalence Classes ‎ (← links)
  • Reflexive and Symmetric Relation is not necessarily Transitive/Proof 2 ‎ (← links)
  • Reflexive and Transitive Relation is not necessarily Symmetric/Proof 2 ‎ (← links)
  • Symmetric and Transitive Relation is not necessarily Reflexive/Proof 2 ‎ (← links)
  • Equivalence Relation on Natural Numbers such that Quotient is Power of Two ‎ (← links)
  • Equivalence Relation on Natural Numbers such that Quotient is Power of Two/Equivalence Class of Prime ‎ (← links)
  • Equivalence Relation on Natural Numbers such that Quotient is Power of Two/Smallest Equivalence Class with no Prime ‎ (← links)
  • Equivalence Relation on Square Matrices induced by Positive Integer Powers ‎ (← links)
  • Modulo Arithmetic/Examples/Solutions to x^2 = x Modulo 6 ‎ (← links)
• Mathematician:Writer/W (transclusion) ‎ (← links)

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