# Category:Tidy

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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 324 total.

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

- Additive Function is Linear for Rational Factors
- Analytic Continuation of Generating Function of Dirichlet Series
- Analytic Continuation of Riemann Zeta Function using Mellin Transform of Fractional Part
- Area between Smooth Curve and Line is Maximized by Semicircle
- Area between Smooth Curve and Line with Fixed Endpoints is Maximized by Arc of Circle

### B

- Basis has Subset Basis of Cardinality equal to Weight of Space
- Bernstein's Theorem on Unique Global Solution to y''=F(x,y,y')
- Bijection in Yoneda Lemma for Covariant Functors
- Definition:Bilinear Functional
- Definition:Binary Biproduct
- Bolzano-Weierstrass Theorem/General Form
- Boolean Interpretation is Well-Defined/Proof 2
- Borel-TIS inequality
- Bounded Subspace of Euclidean Space is Totally Bounded
- Bounds for Complex Exponential

### C

- Cardinality of Infinite Sigma-Algebra is at Least Cardinality of Continuum
- Cauchy's Convergence Criterion for Series
- Definition:Central Field
- Central Field is Field of Functional
- Change of Coordinate Vector Under Change of Basis
- Characteristic Function of Normal Distribution
- Characteristics of Floor and Ceiling Function
- Characterization of N-Cube
- Characterization of Prime Filter by Finite Suprema
- Characterization of Prime Ideal
- Characterization of Prime Ideal by Finite Infima
- Characterization of Strictly Increasing Mapping on Woset
- Circle Group is Infinite Abelian Group/Proof 2
- Closed Elements Uniquely Determine Closure Operator
- Closure is Smallest Closed Successor
- Closure of Irreducible Subspace is Irreducible
- Definition:Coefficient of Polynomial
- Combination Theorem for Complex Derivatives/Product Rule
- Combination Theorem for Complex Derivatives/Quotient Rule
- Compact First-Countable Space is Sequentially Compact
- Compact in Subspace is Compact in Topological Space
- Definition:Complete Ritz Sequence
- Complex Exponential is Uniformly Continuous on Half-Planes
- Concentration of Lipschitz functionals of Gaussian vector
- Condition for Differentiable Functional to have Extremum
- Conditions for C^1 Smooth Solution of Euler's Equation to have Second Derivative
- Conditions for Extremal Embedding in Field of Functional
- Conditions for Functional to be Extremum of Two-variable Functional over Canonical Variable p
- Conditions for Integral Functionals to have same Euler's Equations
- Conditions for Limit Function to be Limit Minimizing Function of Functional
- Conditions for Strong Minimum of Functional
- Conditions for Transformation to be Canonical
- Definition:Conjugate Point
- Definition:Conjugate Point/wrt original Functional
- Connected iff no Proper Clopen Sets
- Continued Fraction Algorithm
- Continuity of Linear Transformations
- Continuous Function on Compact Space is Bounded
- Contour Integral of Gamma Function
- Convergence a.u. Implies Convergence a.e.
- Convergence of Complex Sequence in Polar Form
- Convex Set is Contractible
- Convexity of Function implies Convexity of its Legendre Transform
- Definition:Conway Life
- Correspondence between Rational Numbers and Simple Finite Continued Fractions
- Cyclotomic Polynomial has Integer Coefficients

### D

- Derivation of Hamilton-Jacobi Equation
- Derivative of Complex Power Series/Proof 1
- Derivative of Derivative is Subset of Derivative in T1 Space
- Derivative of Exponential Function/Complex
- Derivative of Sequence of Holomorphic Functions
- Descartes' rule of signs
- Determinant of Matrix Product/Proof 2
- Determinant of Matrix Product/Proof 4
- Diameter of N-Cube
- Difference of Abscissae of Convergence
- Definition:Differentiable Functional
- Definition:Differential/Functional
- Direct Product iff Nontrivial Idempotent
- Dirichlet Series Absolute Convergence Lemma
- Dirichlet Series Convergence Lemma/General
- Discrete Subgroup of Real Numbers is Closed
- Double Angle Formulas/Sine/Proof 3

### E

- Egorov's Theorem
- Epic Equalizer is Isomorphism
- Equality of Towers in Set
- Equivalence of Definitions of Absolute Convergence of Product
- Equivalence of Definitions of Conjugate Point
- Equivalence of Definitions of Contractible Space
- Equivalence of Definitions of Euler's Number
- Equivalence of Definitions of Normal Subset/3 iff 4
- Equivalence of Definitions of Topology Generated by Synthetic Basis
- Equivalence of Definitions of Unital Associative Commutative Algebra/Correspondence
- Equivalence of Definitions of Weierstrass E-Function
- Equivalence of Versions of Axiom of Choice
- Equivalent Definition for Alternating Bilinear Mapping
- Euler Buckling Formula
- Definition:Euler's Equation for Vanishing Variation
- Euler's Equation for Vanishing Variation in Canonical Variables
- Euler's Equation for Vanishing Variation is Invariant under Coordinate Transformations
- Definition:Euler-Lagrange Equation
- Exchange Principle
- Existence of Abscissa of Convergence/General
- Existence of Base-N Representation
- Existence of Matrix Logarithm
- Existence of Minimal Uncountable Well-Ordered Set/Proof Without Using Choice
- Existence of Subfamily of Cardinality not greater than Weight of Space and Unions Equal
- Exponential Function is Continuous/Real Numbers/Proof 1
- Exponential Function is Well-Defined/Real/Proof 2
- Exponential of Real Number is Strictly Positive/Proof 5/Lemma
- Exponential Tends to Zero and Infinity
- Definition:Extremal Embedding in Field of Functional
- Definition:Extremum/Functional

### F

- Definition:Field of Directions
- Definition:Field of Directions/Functional
- Finite Rank Operator is Compact
- Definition:First Integral of System of Differential Equations
- Fisher-Tippet-Gnedenko theorem
- For Complete Ritz Sequence Continuous Functional approaches its Minimal Value
- Foundational Relation is Asymmetric
- Definition:Functional Invariant under Transformation
- Definition:Functional/Weak Extremum
- Futurama Theorem

### G

- Gauss's Lemma on Irreducible Polynomials
- Gauss-Lucas Theorem
- Gaussian Isoperimetric Inequality
- Gelfond-Schneider Theorem
- General Periodicity Property
- General Variation of Integral Functional/Dependent on N Functions
- General Variation of Integral Functional/Dependent on N Functions/Canonical Variables
- General Variation of Integral Functional/Dependent on n Variables
- Generators of Special Linear Group of Order 2 over Integers
- Geodesic Equation/2d Surface Embedded in 3d Euclidean Space
- Definition:Geodetic Distance
- Graph of Nonlinear Additive Function is Dense in the Plane
- Group of Unitary Matrices under Multiplication is not Abelian

### H

- Definition:Hamilton-Jacobi Equation
- Harmonic Series is Divergent/Proof 5
- Hausdorff Maximal Principle implies Well-Ordering Theorem
- Hensel's Lemma for Composite Numbers
- Hilbert's Basis Theorem
- Definition:Hilbert's Invariant Integral
- Definition:Hom Bifunctor
- Definition:Homomorphism Ring between Modules
- Homotopy Group is Group

### I

- Ideal Contained in Finite Union of Prime Ideals
- Ideals are Continuous Lattice Subframe of Power Set
- Ideals form Complete Lattice
- If Definite Integral of a(x)h(x) vanishes for any C^0 h(x) then C^0 a(x) vanishes
- If Ideal and Filter are Disjoint then There Exists Prime Ideal Including Ideal and Disjoint from Filter
- Image of Ultrafilter is Ultrafilter
- Implicit Function Theorem
- Implicit Function Theorem/Real Functions
- Implicit Function Theorem/Real Functions/Proof 1
- Indexed Summation does not Change under Permutation
- Infinite Limit Theorem
- Initial Part of WFF of Predicate Logic is not WFF
- Integer to Rational Power is Irrational iff not Integer or Reciprocal
- Integrability Theorem for Functions Continuous on Open Intervals
- Integral Domain iff Zero Ideal is Prime
- Intersection Condition for Direct Sum of Subspaces
- Intersection of Closed Sets is Closed/Closure Operator
- Inverse of Vandermonde Matrix/Eisinberg Formula
- Definition:Isolated Singularity

### J

### L

- Lagrange's Four Square Theorem/Proof 2
- Definition:Lagrangian
- Laplace's Expansion Theorem
- Definition:Lattice (Group Theory)/Definition 2
- Legendre Transform of Strictly Convex Real Function is Strictly Convex
- Legendre's Condition
- Legendre's Condition/Lemma 1
- Legendre's Condition/Lemma 1/Dependent on N functions
- Legendre's Condition/Lemma 2
- Legendre's Condition/Lemma 2/Dependent on N Functions
- Logarithm of Dirichlet L-Functions
- Logarithm of Infinite Product of Complex Functions
- Logarithm of Infinite Product of Complex Functions/Corollary
- Lower Bound of Natural Logarithm/Proof 3

### M

- Meet is Intersection in Set of Ideals
- Minimal Polynomial of Element with Finite Orbit under Group of Automorphisms over Fixed Field in terms of Orbit
- Minimal Smooth Surface of Revolution
- Minimal Uncountable Well-Ordered Set Unique up to Isomorphism
- Minimum Degree Bound for Simple Planar Graph
- Monotone Function is Riemann Integrable
- Monotone Real Function with Everywhere Dense Image is Continuous
- Monotone Real Function with Everywhere Dense Image is Continuous/Lemma
- Multiplication On The Parabola
- Definition:Mutually Consistent Boundary Conditions

### N

- Definition:N-Ary Operation Induced by Binary Operation
- Necessary and Sufficient Condition for Boundary Conditions to be Self-adjoint
- Necessary and Sufficient Condition for First Order System to be Field for Functional
- Necessary and Sufficient Condition for First Order System to be Field for Second Order System
- Necessary and Sufficient Condition for First Order System to be Mutually Consistent
- Necessary and Sufficient Condition for Integral Parametric Functional to be Independent of Parametric Representation
- Necessary and Sufficient Condition for Quadratic Functional to be Positive Definite
- Necessary and Sufficient Condition for Quadratic Functional to be Positive Definite/Dependent on N Functions