# Category:Improvements

These are pages containing proofs that, although correct, are not the best they could be.

See the Improve template.

## Pages in category "Improvements"

The following 99 pages are in this category, out of 99 total.

### A

### B

### C

- Cantor's Theorem (Strong Version)/Proof 2
- Characteristic of Ordered Integral Domain is Zero
- Definition:Class (Descriptive Statistics)
- Compact First-Countable Space is Sequentially Compact
- Compact Subspace of Linearly Ordered Space
- Compact Subspace of Linearly Ordered Space/Reverse Implication
- Compact Subspace of Linearly Ordered Space/Reverse Implication/Proof 2
- Compactness Theorem
- Condition for Ideal to be Total Ring
- Conditions for Strong Minimum of Functional
- Continuum Property/Proof 1
- Definition:Contravariant Hom Functor
- Cosine of Sum/Proof 4
- Countable Union of Finite Sets is Countable
- Definition:Covariant Hom Functor

### D

- De Morgan's Laws imply Uniquely Complemented Lattice is Boolean Lattice
- Definite Integral from 0 to Half Pi of Even Power of Sine x
- Definite Integral from 0 to Half Pi of Odd Power of Sine x
- User:Dfeuer/thought
- Diagonals of Rhombus Bisect Angles
- Disjunction has no Inverse
- Divergent Series/Examples/n over n^2 + i

### E

- Eigenvalues of Normal Operator have Orthogonal Eigenspaces
- Equation for Perpendicular Bisector of Two Points
- Equivalence of Definitions of Transitive Closure (Set Theory)
- Equivalence of Subobjects is Equivalence
- Euler Polyhedron Formula
- Euler's Equation for Vanishing Variation is Invariant under Coordinate Transformations
- Euler's Number: Limit of Sequence implies Base of Logarithm
- Exponential of Sum/Real Numbers/Corollary

### F

### G

### I

- Image of Small Class under Mapping is Small
- Increasing Sequence in Ordered Set Terminates iff Maximal Element
- Indexed Summation of Multiple of Mapping
- Intersection of Ordinals is Smallest
- Inverse of Vandermonde Matrix
- Definition:Irreducible (Representation Theory)
- Definition:Irreducible (Representation Theory)/G-Module

### L

### M

### N

### O

### 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
- Perpendicular Bisector of Triangle is Altitude of Medial Triangle
- Primary Decomposition Theorem
- Primitive of Reciprocal of x squared plus a squared/Proof 3
- Primitive of x over Root of a x + b by Root of p x + q
- Product of Sigma and Euler Phi Functions
- Projection from Product Category
- Pullback of Quotient Group Isomorphism/Examples/C6 with A4

### R

- Rational Numbers with Denominators Coprime to Prime under Addition form Group
- 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
- Residue Field of P-adic Norm on Rationals/Lemma 1

### S

- Seifert-van Kampen Theorem
- Shape of Cosecant Function
- Shape of Secant Function
- Sign of Composition of Permutations
- Sine to Power of Odd Integer
- Solution to Legendre's Differential Equation
- Strictly Increasing Sequence induces Partition
- Strictly Increasing Sequence of Natural Numbers
- Subband of Induced Operation is Set of Subbands
- Subset Relation is Compatible with Subset Product
- Subset Relation is Compatible with Subset Product/Corollary 2
- Sufficient Conditions for Uncountability
- Sum of Indexed Suprema
- Sum of Sequence of Seventh Powers
- Sums of Squares of Diagonals of Order 3 Magic Square
- Supremum of Absolute Value of Difference equals Supremum of Difference