# Category:Proof Wanted

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These are pages containing theorems which do not have a proof posted.

See the `{{ProofWanted}}`

template.

## Pages in category "Proof Wanted"

The following 200 pages are in this category, out of 1,727 total.

(previous page) (next page)### 1

### 3

### 4

### A

- Abel's Limit Theorem
- Abel's Summation Formula
- Abel's Test
- Abel's Test for Uniform Convergence
- Abel-Ruffini Theorem
- Abi-Khuzam Inequality
- Absolute Value of Trigonometric Function
- Absolute Value of Uniformly Convergent Product
- Additivity of Riemannian Length of Admissible Curve
- Adjoint of Finite Rank Operator
- Admissible Curve in Riemannian Manifold has Unique Forward Reparametrization by Arc Length
- Admissible Family of Curves Symmetry Lemma
- Alexander Polynomial is a Knot Invariant
- Alexandroff Extension of Rational Number Space is Sequentially Compact
- Algebra Defined by Ring Homomorphism is Algebra
- Algebraic Closure of Field is Unique
- Algebraic Numbers form Field
- Algorithm to determine whether Polynomial Diophantine Equation has Integer Solution
- All Nontrivial Zeroes of Riemann Zeta Function are on Critical Strip
- Alternating Groups that are Ambivalent
- Alternating Sum and Difference of Factorials to Infinity
- Analytic Basis is Analytic Sub-Basis
- Angle of Tangent to Radius in Polar Coordinates
- Angles with Parallel or Perpendicular Arms are Equal or Supplementary
- Angular Momentum Commutation Rules
- Anisotropic Vector Gives Composition of Bilinear Space
- Approximate Formula for Number of Partitions
- Approximate Size of Sum of Harmonic Series
- Apéry's Constant in terms of Central Binomial Coefficients
- Apéry's Theorem
- Archimedes' Limits to Value of Pi
- Are All Perfect Numbers Even?/Progress/Form
- Are All Perfect Numbers Even?/Progress/Minimum Size
- Are All Perfect Numbers Even?/Progress/Prime Factors
- Are All Triperfect Numbers Even?/Progress/Form
- Are All Triperfect Numbers Even?/Progress/Minimum Size
- Are All Triperfect Numbers Even?/Progress/Prime Factors
- Area of Circle
- Area of Circle/Proof 7
- Area of Smallest Rectangle accommodating Re-Entrant Knight's Tour
- Area of Smallest Square accommodating Re-Entrant Knight's Tour
- Area under Curve
- Arnauld's Paradox
- Arrow Paradox
- Asymptotic Expansion for Complementary Error Function
- Asymptotic Expansion for Cosine Integral Function
- Asymptotic Expansion for Error Function
- Asymptotic Expansion for Exponential Integral Function/Formulation 1
- Asymptotic Expansion for Fresnel Cosine Integral Function
- Asymptotic Expansion for Fresnel Sine Integral Function
- Asymptotic Expansion for Sine Integral Function
- At Least One Third of Zeros of Riemann Zeta Function on Critical Line
- Atlas is Contained in Unique Maximal Atlas
- Autocorrelation Matrix is Positive Definite
- Autocovariance Matrix is Positive Definite
- Automorphism Group of Complex Numbers over Real Numbers
- Automorphism Group/Examples/Klein Four-Group
- Axiom of Choice is Independent of ZF
- Axiom of Choice/Examples/Russell's Socks and Shoes

### B

- B-Algebra/Examples/S3
- Babbage's Congruence
- Baer's Criterion
- Baire Characterisation Theorem
- Banach-Alaoglu Theorem/Lemma 3
- Banach-Alaoglu Theorem/Lemma 4
- Barbier's Theorem
- Bases of Finitely Generated Free Module have Equal Cardinality
- Basic Inequality/One-Sided Shift Space of Finite Type
- Basis (Hilbert Space)/Examples/L-2 Space over Interval of Zero to Two Pi
- Basis (Hilbert Space)/Examples/Real Vector Space
- Basis (Hilbert Space)/Examples/Space of Square Summable Mappings
- Basis for Open Ordinal Topology
- Bendixson-Dulac Theorem
- Bernoulli Number in terms of Euler Numbers
- Bernoulli's Hanging Chain Problem
- Bessel Function of the First Kind for Imaginary Argument
- Best Approximation from Below to 1 as Sum of Minimal Number of Unit Fractions
- Beta Function as Integral of Power of t by Power of 1 minus t over Power of r plus t
- Beta Function is Continuous and Positive on Positive Reals
- Big-O Notation for Sequences Coincides with General Definition
- Binet's Formula for Logarithm of Gamma Function/Formulation 1
- Binet's Formula for Logarithm of Gamma Function/Formulation 2
- Binomial Form of Relation between Riemann Zeta Function and Dirichlet Eta Function
- Binomial Theorem/Approximations/1st Order
- Binomial Theorem/Approximations/2nd Order
- Binomial Theorem/Extended
- Binomial Theorem/Hurwitz's Generalisation
- Birkhoff's Ergodic Theorem
- Blaschke-Lebesgue Theorem
- Bloch's Theorem
- Body behaves as Particle under Gravitation
- Body in Free Fall moves in Parabolic Path
- Bonnet-Myers Theorem
- Boolean Prime Ideal Theorem
- Boolean Prime Ideal Theorem/Proof 2
- Boolean Prime Ideal Theorem/Proof 3
- Borel-Carathéodory Lemma
- Borel-TIS inequality
- Borsuk Null-Homotopy Lemma
- Borsuk Null-Homotopy Lemma/Corollary
- Borsuk-Ulam Theorem
- Bott-Milnor-Kervaire 1,2,4,8 Theorem
- Bound on Riemannian Distance Inside Coordinate Neighborhood
- Bound on Riemannian Distance Outside Coordinate Neighborhood
- Bounds for Weierstrass Elementary Factors
- Bounds of Riemannian Metric by Euclidean Metric on Euclidean Space
- Bounds on Number of Odd Terms in Pascal's Triangle
- Box Topology may not form Categorical Product in the Category of Topological Spaces
- Brianchon's Theorem
- Brianchon's Theorem is Projective Dual to Pascal's Theorem
- Brouncker's Formula
- Brun's Theorem
- Burnout Height of Upward Rocket under Constant Gravity
- Burnout Velocity of Upward Rocket under Constant Gravity
- Burnside's Theorem
- Bézout's Theorem

### C

- Canonical Basis of Free Module on Set is Basis
- Canonical Homomorphism to Polynomial Ring is Ring Monomorphism
- Carathéodory's Theorem (Measure Theory)
- Carathéodory's Theorem (Measure Theory)/Corollary
- Cardinality is Additive Function
- Cardinality of Cartesian Product of Finite Sets/General Result
- Cardinality of Set of All Mappings
- Cardinality of Set of All Mappings/Infinite Sets
- Carmichael's Theorem
- Cartan-Hadamard Theorem
- Cartesian Product of Homeomorphisms is Homeomorphism
- Cartesian Product of Mappings is Continuous iff Factor Mappings are Continuous
- Cartesian Product of Unions/General Result
- Catalan's Conjecture
- Category Axioms are Self-Dual/Morphisms-Only Category Theory
- Category of Finite Sets is Cartesian Closed
- Category of Posets is Cartesian Closed
- Category of Subobject Classes is Order Category
- Category of Vector Spaces is Category
- Cauchy Product of Absolutely Convergent Series
- Cavalieri's Principle
- Cavalieri's Principle/Extension
- Center of Gravity of Cycloid
- Central Product/Examples/D4 with D4
- Central Product/Examples/Q with Q
- Champernowne Constant is Normal
- Champernowne Constant is Transcendental
- Change of Coordinate Vector Under Change of Basis
- Change of Index Variable of Summation
- Change of Index Variable of Supremum
- Change of Lead in Prime Number Race 4n+1 vs. 4n-1
- Characterisation of UFDs
- Characteristic Function of Limit Inferior of Sequence of Sets
- Characteristic Function of Limit Superior of Sequence of Sets
- Characteristics of Pentatope
- Characteristics of Regular 4-Dimensional Polytopes
- Characterization of Bases (Hilbert Spaces)
- Characterization of Constant-Curvature Metrics
- Characterization of Cosine Integral Function
- Characterization of Finite Rank Operators
- Characterization of Invariant Subspaces
- Characterization of Normal Operators
- Characterization of Pre-Measures
- Characterization of Projections
- Characterization of Reducing Subspaces
- Characterization of Unit Tangent Bundle
- Characterization of Unitary Operators
- Characterizations of Metric Connections
- Chen's Theorem
- Chinese Remainder Theorem/General Result 2
- Choice Function for Power Set implies Choice Function for Set
- Choice Function for Set implies Choice Function for Union of Set
- Christoffel Symbols vanish at Origin of Normal Neighborhood
- Chu-Vandermonde Identity for Gaussian Binomial Coefficients
- Clairaut's Theorem
- Class Mapping has Minimally Superinductive Class
- Classical Runge-Kutta Method
- Classification of Bounded Sesquilinear Forms
- Classification of Compact Three-Manifolds Supporting Zero-Curvature Geometry
- Classification of Compact Two-Manifolds/Lemma
- Closed Sets in Noetherian Topological Space
- Closure of Range of Compact Linear Transformation is Separable
- Coefficients of Product of Two Polynomials
- Columns of Pascal's Triangle contain Simplicial Polytopic Numbers
- Combination Theorem for Continuous Mappings/Topological Ring/Combined Rule
- Definition:Commutative B-Algebra
- Compact Complement Topology is Second-Countable