# Category:Unfinished Proofs

This category lists pages which need finishing.

See the finish template.

## Pages in category "Unfinished Proofs"

The following 200 pages are in this category, out of 334 total.

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

- Achilles and the Tortoise
- 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
- Area of Circle/Proof 4

### B

- Definition:B-Algebra
- Bijection from Cartesian Product of Initial Segments to Initial Segment
- Binet-Cauchy Identity
- Binet-Cauchy Identity/Proof 2
- Binomial Theorem/Abel's Generalisation
- Binomial Theorem/Abel's Generalisation/Proof 2
- Binomial Theorem/Abel's Generalisation/Proof 3
- Boubaker's Theorem
- Definition:Braid Group

### C

- Cantor Set has Zero Lebesgue Measure
- Category Axioms are Self-Dual
- Category of Subobject Classes is Category
- Cauchy's Integral Formula/General Result/Corollary
- Central Product/Examples/D4 with Q
- Characteristic of Increasing Mapping from Toset to Order Complete Toset
- Characterization of Measures
- Characterization of Metacategory via Equations
- Mathematician:Charles Proteus Steinmetz
- 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
- Condition for Denesting of Square Root
- 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
- Consecutive Triples with Same Euler Phi value
- Construction of Triangle from Given Lengths
- Continuity of Mapping to Cartesian Product under Chebyshev Distance
- Continuous Mapping on Finite Union of Closed Sets
- Conversion of Number in Golden Mean Number System to Simplest Form
- Coproduct of Free Monoids
- Countable Union of Finite Sets is Countable

### D

- De Morgan's Laws imply Uniquely Complemented Lattice is Boolean Lattice
- Derivation of Hamilton-Jacobi Equation
- Dicyclic Group Dic3/Matrix Representation
- Discrete Category on Set is Discrete Category
- Division Algebra has No Zero Divisors
- Divisor Relation on Positive Integers is Partial Ordering
- Dual of Preordered Set is Preordered Set
- Definition:Dual Statement (Category Theory)
- 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 Consistent Set of Formulas
- Equivalence of Definitions of Countable Set
- Equivalence of Definitions of Curvature
- Equivalence of Definitions of Gamma Function
- Equivalence of Definitions of Locally Connected Space
- Equivalence of Definitions of Locally Path-Connected Space
- Equivalence of Definitions of Noetherian Ring
- Equivalence of Definitions of Polynomial Function on Subset of Ring
- Equivalence of Definitions of Quotient Field
- 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
- Existence and Uniqueness of Direct Limit of Sequence of Groups
- Existence of Ring of Polynomial Forms in Transcendental over Integral Domain
- External Direct Product Closure/General Result

### F

- 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
- Fermat Pseudoprime/Base 3/Examples/91
- 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 Product of Sigma-Compact Spaces is Sigma-Compact
- Definition:Floating Point Representation
- Fourier Series/1 over -1 to 0, Cosine of x over 0 to 1
- Fourier Series/x over 0 to 2, x-2 over 2 to 4
- Fréchet Space (Functional Analysis) is Metric Space
- Function Simple iff Positive and Negative Parts Simple

### G

- Gamma Difference Equation
- Gamma Difference Equation/Proof 2
- 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
- GO-Space Embeds as Closed Subspace of Linearly Ordered Space
- Gradient of Dot Product
- Group Epimorphism Induces Bijection between Subgroups
- Group/Examples/inv x = 1 - x

### H

### I

- Index of Intersection of Subgroups/Corollary
- Inductive Definition of Sequence
- Ingham's Theorem on Convergent Dirichlet Series
- Integer as Sum of 5 Non-Zero Squares
- Integers are Coprime iff Powers are Coprime
- Integers Expressible as Product of Number and Reversal in 2 Different Ways
- 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
- Inverse Cosine of Imaginary Number
- Inverse Hyperbolic Cosine of Imaginary Number
- Inverse Hyperbolic Secant of Imaginary Number
- Inverse Hyperbolic Sine Logarithmic Formulation
- Inverse Secant of Imaginary Number

### K

### L

- Lagrange's Four Square Theorem
- Lagrange's Four Square Theorem/Proof 2
- Law of Cosines
- Law of Cosines/Proof 2
- LCM from Prime Decomposition
- LCM from Prime Decomposition/General Result
- Length of Arc of Cycloid
- Length of Arc of Cycloid/Proof 2
- Limit Points in Fort Space
- Limit Points in T1 Space
- Limit Points in Uncountable Fort Space
- Locally Compact iff Open Neighborhood contains Compact Set
- Logarithm of Absolute Value of 2 times Sine of pi x is Replicative Function

### M

### N

- Naturally Ordered Semigroup is Unique
- Newton-Girard Formulas
- Non-Divisbility of Binomial Coefficients of n by Prime
- Non-Square Positive Integers not Sum of Square and Prime
- Normality Relation is not Transitive
- Normality Relation is not Transitive/Proof 2
- Number of Different Ways to play First n Moves in Chess
- Number Plus One divides Power Plus One iff Odd
- Numbers Not Expressible as Sum of no more than 5 Composite Numbers
- Numerator of p-1th Harmonic Number is Divisible by Prime p
- Numerator of p-1th Harmonic Number is Divisible by Prime p/Proof 2

### O

- Obtuse Triangle Divided into Acute Triangles
- Octonions form Algebra
- Omitting Types Theorem
- Open Continuous Image of Paracompact Space is not always Countably Metacompact
- Open Set in Partition Topology is also Closed
- Open Sets of Double Pointed Topology
- Order Isomorphism is Equivalence Relation
- Order Isomorphism is Equivalence Relation/Proof 1
- Orthogonal Trajectories/Parabolas with Focus at Origin

### P

- P-adic Valuation of Difference of Powers with Coprime Exponent
- P-adic Valuation of Difference of Powers with Coprime Exponent/Proof 2
- Parity Group is Group
- Partial Fractions Expansion of Cotangent
- Partial Fractions Expansion of Cotangent/Proof 1
- Paths from Vertex of Minimal Length form Tree
- Period of Reciprocal of 729 is 81
- Definition:Period of Recurrence
- Points Defined by Adjacent Pairs of Digits of Reciprocal of 13 lie on Hyperbola
- Polynomial is Linear Combination of Monomials
- Positive Integers Equal to Sum of Digits of Cube
- Poulet Number/Examples/341
- Power Series Expansion for Logarithm of 1 + x over 1 + x
- Power Set of Sample Space is Event Space
- Power Set of Sample Space is Event Space/Proof 1
- Prime Factors of One More than Power of 10