# Category:Unfinished Proofs

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This category lists pages which need finishing.

See the finish template.

## Subcategories

This category has only the following subcategory.

### A

## Pages in category "Unfinished Proofs"

The following 200 pages are in this category, out of 403 total.

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

- Ackermann Function/Examples
- Definition:Ackermann Function/Mistake 2
- Definition:Ackermann-Péter Function
- Ackermann-Péter Function/Examples
- Addition in Minimally Inductive Set is Unique
- Addition of Order Types/Examples/Example Ordering on Integers
- Alphabetic Substitution is Semantically Equivalent/Existential Quantifier
- Alphabetic Substitution is Semantically Equivalent/Universal Quantifier
- 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
- Antilexicographic Product of Totally Ordered Sets is Totally Ordered/General Result
- Approximation to Power of 7 by Power of 10
- Area of Circle/Proof 4
- Axioms of Hilbert Proof System Instance 1 for Predicate Logic are Tautologies

### B

- Definition:Balance
- Definition:Ball
- Banach-Alaoglu Theorem/Proof 1
- 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
- Carathéodory's Theorem (Convex Analysis)
- Casting Out 9s
- 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
- Characterization of Normal Operators
- 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
- Circle of Apollonius is Circle/Proof 2
- Classification of Compact One-Manifolds
- Closed Convex Set in terms of Bounded Linear Functionals
- Closed Linear Subspaces Closed under Setwise Addition
- Closure of Irreducible Subspace is Irreducible
- Closure of Irreducible Subspace is Irreducible/Proof 1
- 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
- Condition for Ordered Set of All Mappings to be Total Ordering
- 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 Regular Heptadecagon
- Construction of Triangle from Given Lengths
- Continuity of Mapping to Cartesian Product under Chebyshev Distance
- 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
- Curry's Paradox
- Cut Associated with 1 is Identity for Multiplication of Cuts

### D

- De Morgan's Laws imply Uniquely Complemented Lattice is Boolean Lattice
- Decomposition of Matrix Exponential
- 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
- Dicyclic Group is Non-Abelian Group
- Dido's Problem/Variant 2
- Discrete Category on Set is Discrete Category
- Dissection of Square into 9 Acute Triangles
- Distinct Lower Sections of Well-Ordered Class are not Order Isomorphic
- Distinct Ordinals are not Order Isomorphic
- Divisibility of Numerator of Sum of Sequence of Reciprocals/Lemma
- 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

- Endomorphisms on Entropic Structure whose Pointwise Product is Identity Automorphism
- Equation of Straight Line in Plane/Two-Point Form/Determinant Form
- Equidecomposable Nested Sets
- Equidistance is Independent of Betweenness
- Equivalence of Definitions of Abelian Category
- Equivalence of Definitions of Arborescence
- Equivalence of Definitions of Boundary
- Equivalence of Definitions of Complete Metric Space
- Equivalence of Definitions of Conjugate Point
- Equivalence of Definitions of Convex Polygon
- Equivalence of Definitions of Convex Polyhedron
- 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 Meromorphic Function
- Equivalence of Definitions of Ordered Integral Domain
- Equivalence of Definitions of Polynomial Function on Subset of Ring
- Equivalence of Definitions of Strictly Inductive Semigroup
- Equivalence of Definitions of Vector Cross Product
- Equivalent Characterizations of Invertible Matrix
- 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
- External Direct Product of Congruence Relations

### 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
- Field has Prime Characteristic p iff exists Monomorphism from Field of Integers Modulo p
- Template:Finish
- 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 Hausdorff Measure Implies Zero Higher Dimensional Measure
- Finite Product of Sigma-Compact Spaces is Sigma-Compact
- First Order ODE/y' + 2 x y = 1
- 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
- Gaussian Integers form Principal Ideal Domain
- 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:Grafting Number
- Definition:Gram-Equivalent
- Group Epimorphism Induces Bijection between Subgroups
- Group/Examples/inv x = 1 - x

### H

- Hausdorff's Maximal Principle implies Axiom of Choice
- Hausdorff's Maximal Principle implies Axiom of Choice/Proof
- Heine-Borel Theorem/Dedekind Complete Space
- Henry Ernest Dudeney/Modern Puzzles/73 - Alphabetical Arithmetic/Solution
- Henry Ernest Dudeney/Puzzles and Curious Problems/112 - Simple Division/Solution
- Henry Ernest Dudeney/Puzzles and Curious Problems/162 - Find the Triangle/Solution
- Henry Ernest Dudeney/Puzzles and Curious Problems/319 - The Ten Cards/Solution
- Henry Ernest Dudeney/Puzzles and Curious Problems/98 - Digital Money/Solution
- Higher Dimensional Hausdorff Measure than Euclidean Space is Zero
- Hilbert Cube is Separable
- Hilbert Sequence Space is Separable
- Homotopy Group is Group
- Homotopy Group is Homeomorphism Invariant

### 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
- Injective iff Projective in Dual Category
- 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
- Book:Ivan Niven/Maxima and Minima without Calculus

### K

### L

- Lagrange's Four Square Theorem
- Lagrange's Four Square Theorem/Proof 2
- Definition:Language of Predicate Logic/Bourbaki
- 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
- Lasota-Yorke Inequality/One-Sided Shift Space of Finite Type