# Category:Unfinished Proofs

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This category lists pages which need finishing.

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## Pages in category "Unfinished Proofs"

The following 200 pages are in this category, out of 361 total.

(previous page) (next page)### A

- Achilles Paradox
- Definition:Ackermann Function/Examples
- Definition:Ackermann Function/Mistake 2
- Definition:Ackermann-Péter Function
- Definition:Ackermann-Péter Function/Examples
- Alternating Group on 4 Letters/Conjugacy Classes
- Analytic Continuation of Riemann Zeta Function using Jacobi Theta Function
- Analytic Continuations of Riemann Zeta Function to Complex Plane
- Approximation to Power of 7 by Power of 10
- Area of Circle/Proof 4

### B

- Definition:B-Algebra
- Definition:Ball
- Mathematician:Barry Mitchell
- Bijection from Cartesian Product of Initial Segments to Initial Segment
- Bijection/Examples/Negative Functions
- Binet-Cauchy Identity
- Binet-Cauchy Identity/Proof 2
- Binomial Theorem/Abel's Generalisation
- Binomial Theorem/Abel's Generalisation/Proof 2
- Bolzano-Weierstrass Theorem/General Form
- Boubaker's Theorem
- Definition:Braid Group

### C

- Cantor Set has Zero Lebesgue Measure
- Category Axioms are Self-Dual
- Category of Subobject Classes is Category
- Central Product/Examples/D4 with Q
- Characteristic of Increasing Mapping from Toset to Order Complete Toset
- Characteristics of Cycle Graph
- Characterization of Measures
- Characterization of Metacategory via Equations
- Mathematician:Charles Proteus Steinmetz
- Definition:Chess
- Definition:Chess/Draw/Insufficient Pieces
- Church's Thesis
- Circle of Apollonius in Complex Plane
- Circle of Apollonius is Circle
- Classification of Compact One-Manifolds
- Closed Linear Subspaces Closed under Setwise Addition
- Compact Subspace of Linearly Ordered Space
- Compactness Properties in T3 Spaces
- Compactness Properties Preserved under Projection Mapping
- Compatibility of Atlases is Equivalence Relation
- Completeness Criterion (Metric Spaces)
- Completeness Criterion (Metric Spaces)/Proof 1
- Composite Fibonacci Numbers with Prime Index
- Composite of Three Mappings in Cycle forming Injections and Surjection
- Condition for Increasing Binomial Coefficients
- Condition for Increasing Binomial Coefficients/Proof 2
- Conditions for Function to be First Integral of Euler's Equations for Vanishing Variation
- Conditions for Function to be Maximum of its Legendre Transform Two-variable Equivalent
- Conditions for Transformation to be Canonical
- Conditions Satisfied by Linear Code
- Congruence Relation and Ideal are Equivalent
- Connecting Homomorphism is Functorial
- Construction of Triangle from Given Lengths
- Continuity of Mapping to Cartesian Product under Chebyshev Distance
- Continuous Mapping on Finite Union of Closed Sets
- Convergent Real Sequence/Examples/x (n+1) = k over 1 + x n/Lemma 2
- Convergent Real Sequence/Examples/x n = root x n-1 y n-1, 1 over y n = half (1 over x n + 1 over y n-1)
- Conversion of Number in Golden Mean Number System to Simplest Form
- Coproduct of Free Monoids
- Cosine of 36 Degrees
- Cosine of 36 Degrees/Proof 2
- Countable Union of Finite Sets is Countable
- Cut Associated with 1 is Identity for Multiplication of Cuts

### D

- De Morgan's Laws imply Uniquely Complemented Lattice is Boolean Lattice
- Definite Integral of Fourier Series at Ends of Interval
- Definite Integral to Infinity of Exponential of -a x^2 by Cosine of b x
- Derivation of Hamilton-Jacobi Equation
- Dicyclic Group Dic3/Matrix Representation
- Dido's Problem/Variant 2
- Discrete Category on Set is Discrete Category
- Dissection of Square into 9 Acute Triangles
- Division Algebra has No Zero Divisors
- Dual of Preordered Set is Preordered Set
- Definition:Dual Statement (Category Theory)
- Dudeney's Property of 2592
- Dynkin System Closed under Intersections is Sigma-Algebra

### E

- Equalizer as Limit
- Equidecomposable Nested Sets
- Equidistance is Independent of Betweenness
- Equivalence of Definitions of Complete Metric Space
- Equivalence of Definitions of Conjugate Point
- Equivalence of Definitions of Countable Set
- Equivalence of Definitions of Curvature
- Equivalence of Definitions of Field of Quotients
- Equivalence of Definitions of Gamma Function
- Equivalence of Definitions of Noetherian Ring
- Equivalence of Definitions of Ordered Integral Domain
- Equivalence of Definitions of Polynomial Function on Subset of Ring
- Equivalence of Definitions of Unsigned Stirling Numbers of the First Kind
- Eratosthenes' Measurement of Earth
- Euclid's Lemma for Prime Divisors/General Result/Proof 1
- Euclid's Lemma for Unique Factorization Domain/General Result
- Euclid's Lemma/Proof 1
- Euclidean Algorithm/Algorithmic Nature
- Exchange of Order of Summations over Finite Sets/Cartesian Product
- Exchange of Order of Summations over Finite Sets/Cartesian Product/Proof 3
- Existence of Ring of Polynomial Forms in Transcendental over Integral Domain
- External Direct Product Closure/General Result

### F

- Factorial as Product of Consecutive Factorials
- Faà di Bruno's Formula
- Faà di Bruno's Formula/Proof 1
- Faà di Bruno's Formula/Proof 3
- Faà di Bruno's Formula/Proof 4
- Fibonacci Number by Power of 2
- Fibonacci Number by Power of 2/Proof 1
- Fibonacci Number of Even Index by Golden Mean Modulo 1
- Finished Branch Lemma/Corollary
- Finite Cartesian Product of Non-Empty Sets is Non-Empty
- Finite Chain is Order-Isomorphic to Finite Ordinal
- Finite Character for Sets of Mappings
- Finite Fourier Series
- Finite Group with One Sylow p-Subgroup per Prime Divisor is Isomorphic to Direct Product
- Finite Product of Sigma-Compact Spaces is Sigma-Compact
- Definition:Floating Point Representation
- Focus of Hyperbola from Transverse and Conjugate Axis
- Fourier Series/Sawtooth Wave
- Fourier Series/Triangle Wave
- Function Simple iff Positive and Negative Parts Simple

### G

- Gaussian Integers form Euclidean Domain
- Gaussian Integers form Euclidean Domain/Proof 1
- GCD from Prime Decomposition
- GCD from Prime Decomposition/General Result
- Generating Function for Elementary Symmetric Function
- Generating Function for Elementary Symmetric Function/Proof 3
- Gibbs Phenomenon
- GO-Space Embeds as Closed Subspace of Linearly Ordered Space
- Gradient of Dot Product
- Definition:Gram-Equivalent
- Group Epimorphism Induces Bijection between Subgroups
- Group/Examples/inv x = 1 - x

### H

### I

- Image of Composite Relation
- Index of Intersection of Subgroups/Corollary
- Inductive Definition of Sequence
- Infinite Number of Integers which are Sum of 3 Sixth Powers in 2 Ways
- Ingham's Theorem on Convergent Dirichlet Series
- Integers whose Ratio between Sigma and Phi is Square
- Internal and External Group Direct Products are Isomorphic
- Internal Direct Product Theorem/General Result/Proof 2
- Intersection of Normal Subgroup with Center in p-Group
- Inverse Hyperbolic Sine Logarithmic Formulation
- Inverse of Element in Semidirect Product
- Irrational Number Space is Complete Metric Space
- Isomorphism Classes for Order 4 Size 3 Simple Graphs

### K

### L

- Lagrange's Four Square Theorem
- Lagrange's Four Square Theorem/Proof 2
- Laplace Transform of Bessel Function of the First Kind
- Laplace Transform of Bessel Function of the First Kind/Proof 1
- Laplace Transform of Null Function
- Largest Integer not Sum of Two Abundant Numbers
- Largest Pandigital Square including Zero
- Law of Cosines
- Law of Cosines/Proof 2
- Law of Tangents/Corollary
- LCM from Prime Decomposition/General Result
- Definition:Left
- Length of Arc of Cycloid
- Length of Arc of Cycloid/Proof 2
- Length of Median of Triangle
- Length of Median of Triangle/Proof 2
- Linear Second Order ODE/y'' + 2 y' + 5 y = x sin x
- Linear Transformations form Abelian Group
- Lévy's Continuity Theorem

### M

### N

- Naturally Ordered Semigroup is Unique
- Necessary and Sufficient Condition for Quadratic Functional to be Positive Definite/Dependent on N Functions
- Non-Commutative Ring with Unity and 2 Ideals not necessarily Division Ring
- Non-Square Positive Integers not Sum of Square and Prime
- Nonnegative Quadratic Functional implies no Interior Conjugate Points
- Norm on Vector Space is Continuous Function
- Number of Different Ways to play First n Moves in Chess
- Numbers for which Sixth Power plus 1091 is Composite
- Numbers Not Expressible as Sum of no more than 5 Squares of Composite Numbers
- Numbers not Sum of Distinct Squares
- Numerator of p-1th Harmonic Number is Divisible by Prime p
- Numerator of p-1th Harmonic Number is Divisible by Prime p/Proof 2