# 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 1,529 total.

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

### 3

### 4

### A

- Abel's Limit Theorem
- Abel's Test
- Abel's Test for Uniform Convergence
- Abel-Ruffini Theorem
- Abi-Khuzam Inequality
- Absolute Value of Uniformly Convergent Product
- Adjoint of Finite Rank Operator
- 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
- Algebraically Closed Field is Perfect
- Algorithm to determine whether Polynomial Diophantine Equation has Integer Solution
- All Nontrivial Zeroes of Riemann Zeta Function are on Critical Strip
- Alternating Even-Odd Digit Palindromic Prime
- Alternating Group is Generated by 3-Cycles
- 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
- Annihilator is Submodule of Algebraic Dual
- 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 between Radii and Curve in Polar Coordinates
- 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
- 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
- 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 C Over R
- Automorphism Group/Examples/Klein Four-Group
- Axiom of Choice is Independent of ZF

### B

- Baire Characterisation Theorem
- Banach-Alaoglu Theorem/Lemma 3
- Banach-Alaoglu Theorem/Lemma 4
- Banach-Steinhaus Theorem
- Barbier's Theorem
- Bases of Finitely Generated Free Module have Equal Cardinality
- 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
- Bessel's Inequality
- Best Approximation from Below to 1 as Sum of Minimal Number of Unit Fractions
- Best Rational Approximations to Root 2 generate Pythagorean Triples
- 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/Extended
- Binomial Theorem/Hurwitz's Generalisation
- Body behaves as Particle under Gravitation
- Body in Free Fall moves in Parabolic Path
- Boolean Prime Ideal Theorem
- Borel-Carathéodory Lemma
- Borel-TIS inequality
- Borsuk-Ulam Theorem
- Bott-Milnor-Kervaire 1,2,4,8 Theorem
- Bounded Linear Transformation Induces Bounded Sesquilinear Form
- Bounds for Weierstrass Elementary Factors
- 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)
- Cardinality is Additive Function
- Cardinality of Cartesian Product/General Result
- Cardinality of Power Set of Natural Numbers Equals Cardinality of Real Numbers
- Cardinality of Set of All Mappings
- Cardinality of Set of All Mappings/Infinite Sets
- Carmichael's Theorem
- Cartesian Product Exists and is Unique
- 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 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
- Cayley-Menger Determinant
- 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 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 Unitary Operators
- Chen's Theorem
- Chinese Remainder Theorem/General Result 2
- Chu-Vandermonde Identity for Gaussian Binomial Coefficients
- Chu-Vandermonde Identity/Extended
- Classical Runge-Kutta Method
- Classification of Bounded Sesquilinear Forms
- Classification of Compact Three-Manifolds Supporting Zero-Curvature Geometry
- Classification of Compact Two-Manifolds
- Closure of Complement of Closure is Regular Closed
- Closure of Range of Compact Linear Transformation is Separable
- Coefficients of Product of Two Polynomials
- Collection of All Ordered Sets is not Set
- Collection of Sets Equivalent to Set Containing Empty Set is Proper Class
- 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
- Compact Idempotent is of Finite Rank
- Compact Linear Transformation is Bounded
- Compact Linear Transformations Composed with Bounded Linear Operator
- Compact Operator on Hilbert Space Direct Sum
- Compact Self-Adjoint Operator has Countable Point Spectrum
- Compact Set of Irrational Numbers is Nowhere Dense
- Compactness Properties in Hausdorff Spaces
- Complete Archimedean Valued Field is Real or Complex Numbers
- Complete Factorizations of Proper Element in Principal Ideal Domain are Equivalent
- Completeness Theorem for Hilbert Proof System Instance 2 and Boolean Interpretations
- Completion Theorem (Inner Product Space)
- Complex Roots of Unity are Vertices of Regular Polygon Inscribed in Circle
- Components of Vector in Terms of Dot Product
- Composite of Homomorphisms is Homomorphism/R-Algebraic Structure
- Composition of Identification Mappings is Identification Mapping
- Conclusion of Valid Categorical Syllogism is Negative iff one Premise is Negative
- Condition for Complex Number to be in Right Half Plane
- Condition for Existence of Fourth Number Proportional to Three Numbers
- Condition for Expectation of Non-Negative Random Variable to be Zero