Category:Improvements
Jump to navigation
Jump to search
These are pages containing proofs that, although correct, are not the best they could be.
See the Improve template.
Subcategories
This category has the following 13 subcategories, out of 13 total.
C
- Category of Ordered Sets (4 P)
D
- Definitions/Transforms (1 P)
E
H
L
- Legendre Transforms (empty)
S
T
- Transforms (empty)
Pages in category "Improvements"
The following 200 pages are in this category, out of 220 total.
(previous page) (next page)A
B
- Banach-Alaoglu Theorem/Lemma 3
- Banach-Alaoglu Theorem/Lemma 4
- Binomial Theorem Approximations/Examples/Arbitrary Example 1
- Binomial Theorem Approximations/Examples/Arbitrary Example 2
- Binomial Theorem Approximations/Examples/Arbitrary Example 3
- Binomial Theorem Approximations/Examples/Arbitrary Example 4
- Binomial Theorem Approximations/Examples/Arbitrary Example 5
- Binomial Theorem Approximations/Examples/Arbitrary Example 6
- Bolzano-Weierstrass Theorem/General Form
- Definition:Boolean Lattice/Definition 3
C
- Definition:Canonical Preordering of C*-Algebra
- Cardinal Equal to Collection of All Dominated Ordinals
- Cardinality of Infinite Sigma-Algebra is at Least Cardinality of Continuum
- Definition:Category of Ordered Sets
- Characteristic of Ordered Integral Domain is Zero
- Characteristics of Traversable Graph
- Characterization of Lipschitz Continuity on Shift of Finite Type by Variations
- Definition:Chess
- Chord Length for Regular Polygon
- Circle of Apollonius is Circle
- Circle of Apollonius is Circle/Proof 2
- Definition:Class Interval
- Definition:Classical Propositional Logic
- Compact First-Countable Space is Sequentially Compact
- Compact Subspace of Linearly Ordered Space/Reverse Implication
- Compact Subspace of Linearly Ordered Space/Reverse Implication/Proof 2
- Compactness Theorem/Proof using Henkin Construction
- Condition for Ideal to be Total Ring
- Condition on Congruence Relations for Cancellable Monoid to be Group/Counterexample
- Conditions for Strong Minimum of Functional
- Definition:Connection on Manifold
- Definition:Consistent (Logic)/Set of Formulas/Propositional Logic
- Definition:Contravariant Hom Functor
- Definition:Convex Polygon/Definition 3
- Cosine of Sum/Proof 4
- Countable Union of Finite Sets is Countable
- Definition:Covariant Hom Functor
- Cycle does not Contain Subcycles
D
- Definition:Darboux Function
- Definite Integral from 0 to Half Pi of Even Power of Sine x
- Definite Integral from 0 to Half Pi of Even Power of Sine x/Proof 1
- Definite Integral from 0 to Half Pi of Odd Power of Sine x
- Definite Integral from 0 to Half Pi of Odd Power of Sine x/Proof 1
- Denial of Universality/Formulation 2/Forward Implication/Proof 2
- Descartes's Rule of Signs
- Determinant of Linear Operator is Well Defined
- Dimension of R-Module R is 1
- Definition:Discrete Random Variable/Definition 1
- Definition:Distribution
- Dixon's Theorem (Group Theory)
E
- Einstein's Mass-Velocity Equation
- Elementary Amalgamation Theorem
- Empty Set is Well-Ordered
- Endomorphism Ring of Abelian Group is Ring with Unity
- Epimorphism Preserves Associativity
- Equation for Perpendicular Bisector of Two Points
- Equivalence of Definitions of Normal Subgroup
- Equivalence of Definitions of Transitive Closure of Set
- Equivalence of Subobjects is Equivalence
- Euler's Equation for Vanishing Variation is Invariant under Coordinate Transformations
- Definition:Exact
- Definition:Exact Sequence of Modules
- Existential Instantiation/Informal Statement
- Exponential of Sum of Real Numbers/Corollary
F
- Fatou's Lemma for Measures/Corollary/Examples/Union of Disjoint Real Intervals
- Final Topology with respect to Mapping
- Definition:Finite Path
- Finite Sequences in Set Form Acyclic Graph
- Fixed-Point Property is Topological
- Fontené Theorems/First
- Definition:Formal Semantics
- Fourth Sylow Theorem/Proof 2
- Fréchet Product Space is Metric Space
- Fundamental Theorem of Line Integrals
- Fundamental Theorem on Equivalence Relations
G
- Definition:Gaussian Elimination/Procedure
- Gaussian Integers form Euclidean Domain
- Gaussian Integers form Euclidean Domain/Proof 1
- General Variation of Integral Functional/Dependent on n Variables
- Generating Function for Elementary Symmetric Function
- Generating Function for Elementary Symmetric Function/Proof 2
- Gradient of Dot Product
H
I
- Image of Small Class under Mapping is Small
- Image of Successor Mapping forms Peano Structure
- Template:Improve
- Increasing Sequence in Ordered Set Terminates iff Maximal Element
- Increasing Sequence of Sets forms Nest
- Indexed Summation of Multiple of Mapping
- Inequality of Height of Proper Ideal
- Intersection of Ordinals is Smallest
- Definition:Inverse Sine/Real/Arcsine
- Definition:Irreducible (Representation Theory)
- Definition:Irreducible (Representation Theory)/G-Module
L
- L'Hôpital's Rule
- L'Hôpital's Rule/Corollary 2
- Laplace Expansion Theorem for Determinants
- Definition:Laurent Series
- Least Upper Bound Property/Proof 1
- Left Quasigroup if (2-3) Parastrophe of Magma is Magma
- Legendre Polynomial in terms of Gaussian Hypergeometric Function
- Definition:Legendre Transform
- Lexicographic Product of Family of Ordered Sets is Ordered Set
- Limit Ordinal Equals its Union
- Linear Combination of Measures
- Linearity of Function with Translation Property
- Linearly Ordered Space on Order-Convex Subset is Subspace Topology
- Liouville's Theorem (Complex Analysis)
- Liouville's Theorem (Complex Analysis)/Proof 1
- Liouville's Theorem (Hamiltonian Mechanics)
- Logarithmic Integral as Non-Convergent Series
M
- Definition:Magma of Sets
- Mapping from Totally Ordered Set is Order Embedding iff Strictly Increasing/Reverse Implication
- Definition:Measurable Set/Arbitrary Outer Measure
- Medians of Triangle Meet at Centroid/Corollary
- Mittag-Leffler Expansion for Cotangent Function
- Mittag-Leffler Expansion for Cotangent Function/Proof 3
- Definition:Modulus of Element of C*-Algebra
N
- Nagata-Smirnov Metrization Theorem
- Nagata-Smirnov Metrization Theorem/Necessary Condition
- Necessary and Sufficient Condition for Quadratic Functional to be Positive Definite
- Necessary and Sufficient Conditions for Continuous Linear Transformation Space to be Banach Space/Corollary 1
- Necessary Condition for Integral Functional to have Extremum for given function/Dependent on N Functions
- Necessary Condition for Integral Functional to have Extremum for given Function/Dependent on Nth Derivative of Function
- Newton-Girard Identities/Proof 1
- Non-Equivalence as Equivalence with Negation/Formulation 1/Forward Implication/Proof
- Norm on Vector Space is Quasinorm
- Definition:Number Base/Integers
- Number of Arrangements of n Objects of m Types
O
- Open Sets of Double Pointed Topology/Corollary
- Order Isomorphism iff Strictly Increasing Surjection
- Order Topology equals Dual Order Topology
- Order-Extension Principle/Strict/Proof 2
- Ordinal Subset is Well-Ordered
- Orthocenter, Centroid and Circumcenter Coincide iff Triangle is Equilateral
- Orthonormal Subset of Hilbert Space Extends to Basis
- Outer Jordan Content of Right Triangle
P
- P-Product Metrics on Real Vector Space are Topologically Equivalent
- P-Product Metrics on Real Vector Space are Topologically Equivalent/Inequality for General Case
- Power of Generator of Cyclic Group is Generator iff Power is Coprime with Order
- Primary Decomposition Theorem
- Prime Magic Square/Examples/Order 3/Smallest
- Primitive of x over Root of a x + b by Root of p x + q
- Product of Divisor Sum and Euler Phi Functions
- Products of 2-Digit Pairs which Reversed reveal Same Product
- Definition:Projection
- Projection from Product Category
- Definition:Proper Relational Structure
- Ptolemy's Theorem
- Ptolemy's Theorem/Proof 2
- Pullback of Quotient Group Isomorphism/Examples/C6 with A4
- Pythagoras's Theorem
- Pythagoras's Theorem/Short Algebraic Proof
R
- Real Numbers of Type Rational a plus b root 2 form Field
- Reciprocal of Function of Bounded Variation Bounded away from Zero is of Bounded Variation
- Recursively Defined Sequence/Examples/Term is Term of Index less 1 plus 6 times Term of Index less 2
- Relation between Two Ordinals
- Relationship between Transitive Closure Definitions
- Resolvent Mapping is Analytic/Banach Algebra
- Riesz-Markov-Kakutani Representation Theorem
S
- Scheffé's Lemma/Corollary
- Definition:Schwartz Distribution
- Seifert-van Kampen Theorem
- Definition:Separable Degree
- Definition:Set of Literals
- Shape of Cosecant Function
- Shape of Cosine Function
- Shape of Secant Function
- Sigma-Algebra Generated by Finite Partition is Finite Sub-Sigma-Algebra
- Sign of Composition of Permutations
- Sine and Cosine are Periodic on Reals/Corollary/Cosine
- Sine and Cosine are Periodic on Reals/Corollary/Sine
- Definition:Smallest Field
- Smallest Field is Field
- Smallest Field/Cayley Tables
- Stabilizer of Subgroup Action on Left Coset Space
- Stopped Supermartingale is Supermartingale
- Strictly Increasing Sequence induces Partition
- Strictly Increasing Sequence of Natural Numbers
- Subband of Induced Operation is Set of Subbands
- Subgroup is Subset of Conjugate iff Normal
- Subgroup is Superset of Conjugate iff Normal
- Sufficient Conditions for Uncountability
- Sum of Indexed Suprema