# Category:Tidy

Jump to navigation
Jump to search
(previous page) (next page)

This category is for pages that need to be fixed up aesthetically and brought into conformance with $\mathsf{Pr} \infty \mathsf{fWiki}$ house style.

## Pages in category "Tidy"

The following 200 pages are in this category, out of 218 total.

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

### A

- Abel's Limit Theorem
- Abel's Limit Theorem/Proof 2
- Abel's Test for Uniform Convergence
- Abi-Khuzam Inequality
- Alternating Group is Generated by 3-Cycles
- Area between Radii and Curve in Polar Coordinates
- Definition:Arithmetical Hierarchy
- Associative Idempotent Anticommutative
- Automorphism Group/Examples/Klein Four-Group

### B

### C

- Cantor-Bernstein-Schröder Theorem/Lemma/Proof 3
- Cardano's Formula/Examples/x^3 - 15x - 4
- Cardinality of Cartesian Product of Finite Sets/General Result
- Cauchy's Group Theorem/Proof 1
- Cauchy's Integral Formula/General Result
- Change of Base of Logarithm/Proof 2
- Change of Variables Theorem (Multivariable Calculus)
- Characterisation of UFDs
- Characteristics of Floor and Ceiling Function
- Characterization of Ergodicity in terms of Koopman Operator
- Characterization of Prime Ideal by Finite Infima
- Chinese Remainder Theorem (Groups)
- Closed Form for Triangular Numbers/Combinatorial Proof
- Closure for Finite Collection of Relations and Operations
- Closure of product equals product of closures
- Cofactor Sum Identity
- Cofinal Ordinal Relation is Transitive
- Collatz Conjecture/Failed Proof
- Column Rank of Matrix equals Row Rank/Proof using Orthogonality
- Column Rank of Matrix equals Row Rank/Proof using Rank Factorization
- Compact Idempotent is of Finite Rank
- Complement of Irreducible Topological Subset is Prime Element
- Constructible numbers
- Continued Fraction Expansion of Limit of Simple Infinite Continued Fraction equals Expansion Itself
- Continuity of Linear Transformation/Normed Vector Space
- Contour Integral of Gamma Function
- Correspondence between Rational Numbers and Simple Finite Continued Fractions
- Countable Product of Sequentially Compact Spaces is Sequentially Compact
- Crossbar Theorem
- Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n/Lemma
- Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n/Proof 1
- Cyclic Group of Order 8 is not isomorphic to Group of Units of Integers Modulo n/Proof 2
- Cyclicity Condition for Units of Ring of Integers Modulo n

### D

- Decomposition of Field Extension as Separable Extension followed by Purely Inseparable
- Definitions of Genera are Equivalent
- Degenerate Linear Operator Plus Identity is Fredholm Operator
- Derivative of Derivative is Subset of Derivative in T1 Space
- Derivative of Exponential Function/Complex
- Derivative of Product of Operator-Valued Functions
- Determinant of Block Diagonal Matrix
- Dirichlet Integral/Proof 2
- Division Ring is Vector Space over Prime Subfield
- Dual Representation Preserves Natural Pairings Between Vectors and Their Duals
- Duplicated Triangle Forms a Kite or a Parallelogram
- Definition:Dynamical Systems

### E

- Epsilon Induction
- Equivalence of Definitions of Absolute Convergence of Product
- Equivalence of Definitions of Affine Space
- Equivalence of Definitions of Closed Linear Span
- Equivalence of Definitions of Contractible Space
- Equivalence of Definitions of Limit of Vector-Valued Function
- Equivalence of Definitions of Normal Subset/3 iff 4
- Equivalence of Definitions of Projective Module
- Equivalent Conditions for Dedekind-Infinite Set
- Erdős-Moser Equation
- Euler Phi Function by Argument is Injective
- Euler's Formula/Real Domain/Proof 3
- Euler's Homogeneous Function Theorem
- Exchange Principle
- Existence and Uniqueness of Direct Limit of Sequence of Groups
- Existence and Uniqueness of Direct Limit of Sequence of Groups/Lemma 2
- Existence of Abscissa of Convergence/General
- Existence of Base-N Representation
- Existence of Chebyshev Polynomials of the First Kind
- Existence of Chebyshev Polynomials of the Second Kind
- Existence of Matrix Logarithm
- Exponential Tends to Zero and Infinity

### F

### G

- Galois Field of Order q Exists iff q is Prime Power
- Galois Group Acts Faithfully on Generating Set
- Gauss's Lemma on Irreducible Polynomials
- Gauss-Lucas Theorem
- Gilmer-Parker Theorem
- Goursat's Integral Lemma
- Definition:Grafting Number
- Group of Unitary Matrices under Multiplication is not Abelian
- Group of Units Ring of Integers Modulo p^2 is Cyclic

### H

### I

- Ideal Contained in Finite Union of Prime Ideals
- Ideals form Complete Lattice
- Improper Integral of Partial Derivative
- Intersection Condition for Direct Sum of Subspaces
- Definition:Invariant Set of a Map
- Inverse of a Line Through Circle Center is a Line
- Inverse of Cauchy Matrix
- Inverse of Vandermonde Matrix/Eisinberg Formula
- Inverse of Vandermonde Matrix/Proof 2
- Invertibility of Identity Minus Operator
- Definition:Isolated Singularity
- Definition:Isolated Singularity/Riemann Surface
- Isomorphism between Group of Units Ring of Integers Modulo 2^n and C2 x C2^(n-2)
- Isomorphism Classes for Order 4 Size 3 Simple Graphs

### L

- L'Hôpital's Rule/Proof 1
- Definition:Lagrange multiplier
- Lagrange's Theorem (Number Theory)/Examples/Non-Prime Index
- Laplace Transform of Bessel Function of the First Kind/Proof 2
- Laplace Transform of Derivative with Finite Discontinuities
- Largest Prime Factor of Euler Phi Function
- Length of Arc of Cycloid/Proof 3
- Local Uniform Convergence Implies Compact Convergence
- Axiom:Lower Dimensional Axiom

### M

### N

- N over 2 times Reciprocal of 1 Plus n Squared x Squared to the Power of 3/2 Delta Sequence
- Napoleon's Theorem/Proof 2
- Definition:Negatively Invariant Set of a Map
- Newton's Identities
- Newton's Identities/Proof 1
- Newton's Identities/Proof 2
- Noetherian Topological Space is Compact/Proof 1
- Nondeterministic Turing Machine Equivalent to Deterministic Turing Machine
- Nonzero Eigenvalue of Compact Operator has Finite Dimensional Eigenspace

### O

### P

- Phi in the Pentagon
- Phi is 8 has only 5 solutions
- Pi Squared is Irrational/Proof 2
- Poisson Brackets of Classical Particle in Radial Potential on Plane
- Definition:Positively Invariant Set of a Map
- Power Series Expansion for Exponential of Cosine of x/Proof 2
- Prefix of WFF of Predicate Logic is not WFF
- Prime-Counting Function in terms of Eulerian Logarithmic Integral/Riemann Hypothesis Holds
- Primitive Element Theorem
- Product of Summations is Summation Over Cartesian Product of Products
- Product Sigma-Algebra Generated by Projections
- Projector has Norm 1
- Proper and Prime iff Ultrafilter in Boolean Lattice
- Ptolemy's Theorem/Proof 2

### R

- Definition:Radical of Integer
- Definition:Ramification
- Rational Root Theorem
- Recursively Enumerable Set is Image of Primitive Recursive Function
- Regular Heptagon is Smallest with no Compass and Straightedge Construction
- Regular Heptagon is Smallest with no Compass and Straightedge Construction/Proof 2
- Relation of Boubaker Polynomials to Fermat Polynomials
- Resolvent Mapping is Continuous/Bounded Linear Operator
- Riemann-Hurwitz Formula
- Riesz-Markov-Kakutani Representation Theorem/Lemma 4

### S

- Sample Matrix Independence Test
- Saturated Models of same Cardinality are Isomorphic
- Semidirect Product of Groups is Group
- Separable Degree of Field Extensions is Multiplicative
- Sequence Lemma
- Smallest n needing 6 Numbers less than n so that Product of Factorials is Square
- Definition:Smith-Volterra-Cantor Set
- Sobolev Space is Banach Space
- Spectrum of Bounded Linear Operator is Non-Empty
- Stabilizer is Normal iff Stabilizer of Each Element of Orbit
- Statements Equivalent to Non-Dividing Type
- Steinitz's Theorem
- Stone's Representation Theorem for Boolean Algebras
- Straight Line Segment is Shortest Path between Two Points
- Sturm-Liouville Problem
- Subgroup of Solvable Group is Solvable/Proof 2
- Subspace of Complete Metric Space is Closed iff Complete
- Sum of Elements in Inverse of Vandermonde Matrix
- Summation of Powers over Product of Differences/Proof 3
- Surgery for Rings
- Surjective Monotone Function is Continuous

### T

- Theories with Infinite Models have Models with Order Indiscernibles
- There are no 120 consecutive numbers which all have exactly 120 divisors
- Template:Tidy
- Triangle Right-Angle-Hypotenuse-Side Congruence/Proof 2
- Triangle Side-Side-Side Congruence
- Triangle Side-Side-Side Congruence/Proof 2
- Tutte's Wheel Theorem
- Tutte's Wheel Theorem/Lemma