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PlanetMath Encyclopedia

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5 - 4 entries

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9 - 2 entries

A - 1166 entries

B - 695 entries

C - 2325 entries

D - 974 entries

E - 948 entries

F - 856 entries

G - 687 entries

H - 737 entries

I - 925 entries

J - 178 entries

K - 249 entries

L - 1001 entries

M - 907 entries

N - 638 entries

O - 458 entries

O(2) owned by rspuzio

object (in category) owned by mathcam

objectification (=hypostatic abstraction) owned by Jon Awbrey

objective function (in linear programming) owned by mathcam

oblate (in spheroid) owned by rspuzio

oblong number owned by CompositeFan

observability owned by GeraW

observable operator algebra (in Grassmann-Hopf algebras and coalgebras\gebras) owned by bci1

observation (in data types in statistics) owned by CWoo

obtuse (in convex angle) owned by pahio

obtuse angle (in angle) owned by CWoo

obtuse angle (in convex angle) owned by pahio

obtuse triangle (in triangle) owned by Wkbj79

obvious owned by rspuzio

Occam's razor owned by CWoo

occur in (in word) owned by juanman

occurrence (in word) owned by juanman

Ockham algebra owned by CWoo

octad (in miracle octad generator) owned by monster

octahedron owned by evin290

octahedron (in regular polyhedron) owned by mathwizard

octant owned by pahio

octic group owned by Daume

octonion owned by CWoo

octonion algebra (in octonion) owned by CWoo

octuplet (in ordered tuplet) owned by rspuzio

odd (in even number) owned by mathcam

the odd Bernoulli numbers are zero owned by alozano

odd element (=supercommutative) owned by rmilson

odd fence (in fence) owned by CWoo

odd function (in even and odd functions) owned by yark

odd integer (in even number) owned by mathcam

odd multiple (in general associativity) owned by pahio

odd number (in even number) owned by mathcam

odd number owned by PrimeFan

odd permutation (in signature of a permutation) owned by rspuzio

odd power (in general associativity) owned by pahio

odds (in odds ratio) owned by CWoo

odds ratio owned by CWoo

ODE (in differential equation) owned by rspuzio

ODE types reductible to the variables separable case owned by pahio

ODE types solvable by two quadratures owned by pahio

OEIS (=On-Line Encyclopedia of Integer Sequences) owned by CompositeFan

off-diagonal entry owned by mathcam

offset curve (=parallel curve) owned by stitch

proof ofZorn's lemma (=Zorn's lemma and the well-ordering theorem equivalence of Hausdorff's maximum principle) owned by mathcam

Oka coherence theorem owned by jirka

Oka's coherence theorem (=Oka coherence theorem) owned by jirka

Oka's theorem (=Oka coherence theorem) owned by jirka

Oka theorem (=Oka coherence theorem) owned by jirka

Ol'ga Alexandrovna Ladyzhenskaya (=Olga Ladyzhenskaya) owned by Mravinci

Olga Alexandrovna Ladyzhenskaya (=Olga Ladyzhenskaya) owned by Mravinci

Ol'ga Alexandrowna Ladyzhenskaya (=Olga Ladyzhenskaya) owned by Mravinci

Olga Alexandrowna Ladyzhenskaya (=Olga Ladyzhenskaya) owned by Mravinci

Olga Arsenievna Oleinik (=Olga Oleinik) owned by Mravinci

Ol'ga Arsen'ievna Oleinik (=Olga Oleinik) owned by Mravinci

Olga Ladyzhenskaya owned by Mravinci

Olga Oleinik owned by Mravinci

oligomorphic automorphism group (in oligomorphic permutation group) owned by amador

oligomorphic permutation group owned by amador

$\omega$ -accumulation points (in types of limit points) owned by mathcam

$\omega$ -categorical (=countably categorical structures) owned by amador

Omega-Consistency (in beyond formalism: Gödel's incompleteness) owned by gribskoff

proof that $\omega$ has the tree property owned by Henry

proof that omega has the tree property (=proof that $\omega$ has the tree property) owned by Henry

$\omega$ -limit (in $\omega$ -limit set) owned by Koro

omega-limit (in $\omega$ -limit set) owned by Koro

$\omega$ -limit cycle (=limit cycle) owned by Daume

$\omega$ -limit set (=omega limit set) owned by mathcam

omega limit set owned by mathcam

$\omega$ -limit set owned by Koro

omega-limit set (= $\omega$ -limit set) owned by Koro

omega notation (=Landau notation) owned by Mathprof

Omega spectrum (in $\Omega$ -spectrum) owned by bci1

$\Omega$ --spectrum (in $\Omega$ -spectrum) owned by bci1

Omega spectrum (= $\Omega$ -spectrum) owned by bci1

$\Omega$ -spectrum owned by bci1

$\Omega$ -stability (in $\Omega$ -stability theorem) owned by Koro

omega-stability (in $\Omega$ -stability theorem) owned by Koro

$\Omega$ -stability theorem owned by Koro

omega-stability theorem (= $\Omega$ -stability theorem) owned by Koro

$\Omega$ -stable (in $\Omega$ -stability theorem) owned by Koro

omega-stable (in $\Omega$ -stability theorem) owned by Koro

$\omega$ -word (in word) owned by juanman

o-minimal (in o-minimality) owned by Timmy

o-minimality owned by Timmy

omnific integers (in surreal number) owned by Henry

one-dimensional Banach-Tarski paradox (=pseudoparadox in measure theory) owned by rspuzio

one-dimensional CW complex (=graph topology) owned by mps

one-dimensional $CW$

-complexes and category of $CW$

complexes (=spin networks and spin foams) owned by bci1

one hundred and sixty-three (=one hundred sixty-three) owned by PrimeFan

one hundred sixty-three owned by PrimeFan

one-line notation (in one-line notation for permutations) owned by mps

one-line notation for permutations owned by mps

one-parameter subgroup owned by CWoo

one-pass algorithm to compute sample variance owned by stevecheng

one-periodic (in periodicity of exponential function) owned by pahio

one-periodic (in periodic functions) owned by pahio

one-point compactification (=Alexandrov one-point compactification) owned by yark

one relator products of cyclic groups (=Scott-Wiegold conjecture) owned by whm22

one-sheeted hyperboloid (in quadratic surfaces) owned by pahio

one-sided continuity owned by pahio

one-sided continuity by series owned by pahio

one-sided continuity of series with terms one-sidedly continuous (=one-sided continuity by series) owned by pahio

one-sided derivatives owned by pahio

one-sided error (in random Turing machine) owned by Henry

one sided error (in random Turing machine) owned by Henry

one-sided limit owned by CWoo

one-sided normal form (in Kuroda normal form) owned by CWoo

one-sided normality of subsemigroup owned by lars_h

one-stage cluster sampling (=cluster sampling) owned by CWoo

one-to-one (=injective function) owned by drini

one-to-one and onto correspondence (=Borel isomorphism) owned by bci1

one to one correspondence (=bijection) owned by mathcam

one-to-one correspondence (=bijection) owned by mathcam

one-to-one function from onto function owned by mathcam

one-way (=one-way function) owned by Henry

one way (=one-way function) owned by Henry

one way function (=one-way function) owned by Henry

one-way function owned by Henry

examples on how to find Taylor series from other known series owned by alozano

Online Encyclopedia of Integer Sequences (=On-Line Encyclopedia of Integer Sequences) owned by CompositeFan

On-Line Encyclopedia of Integer Sequences owned by CompositeFan

the only compact metric spaces that admit a positively expansive homeomorphism are discrete spaces owned by Koro

O notation (=Landau notation) owned by Mathprof

onto (=surjective) owned by drini

definition of onto linear transformation owned by Mathprof

ontology (=logicism) owned by gribskoff

op. cit. (in terms from foreign languages used in mathematics (html version)) owned by Wkbj79

open (in open question) owned by rspuzio

open (in classification of topological properties according to behaviour under mapping) owned by rspuzio

open (=open set) owned by mathwizard

open (in topological space) owned by djao

open (in topology of the complex plane) owned by matte

open and closed intervals have the same cardinality owned by mps

open annulus (=annulus) owned by Wkbj79

open ball (=ball) owned by CWoo

open ball (in metric space) owned by djao

open cell (in cell attachment) owned by yark

open chain (in (closed) walk / trek / trail / path) owned by marijke

open cover (in cover) owned by mps

open disk (in topology of the complex plane) owned by matte

open function (=open mapping) owned by Koro

open half plane (in ordered geometry) owned by CWoo

open interval (in interval) owned by PrimeFan

open interval (=ordered geometry) owned by CWoo

open line segment (in ordered geometry) owned by CWoo

open line segment (in line segment) owned by matte

open mapping owned by Koro

open mapping theorem owned by Koro

proof of open mapping theorem owned by Statusx

open path (in (closed) walk / trek / trail / path) owned by marijke

OpenPFGW owned by PrimeFan

open polydisc (=polydisc) owned by jirka

open problem (in open question) owned by rspuzio

open question owned by rspuzio

open ray (=ray) owned by CWoo

open refinement (in cover) owned by mps

open set owned by mathwizard

open set in $\mathbb{R}^n$ contains an open rectangle owned by matte

open subcover (in cover) owned by mps

open subgroup (=full subgroup) owned by Mathprof

open submanifold (in submanifold) owned by jirka

open subset (=open set) owned by mathwizard

open trail (in (closed) walk / trek / trail / path) owned by marijke

open trek (in (closed) walk / trek / trail / path) owned by marijke

open unit disk (in unit disc) owned by PrimeFan

open walk (in (closed) walk / trek / trail / path) owned by marijke

operation owned by rspuzio

operational logic of super-complex systems (in fuzzy logics of living systems) owned by bci1

operations on consequence operators owned by rspuzio

operations on relations owned by CWoo

operations with events owned by polarbear

operator owned by rmilson

operator algebras in mathematical physics and AQFT-A to K owned by bci1

example of an operator owned by Mathprof

operator induced by a measure preserving map owned by asteroid

operator monotone owned by mathcam

$\operatorname{arc tan}$ with two arguments owned by matte

$\operatorname{cf}(\operatorname{cf} \alpha) = \operatorname{cf} \alpha$ owned by yesitis

proof that $\operatorname{exp}~G$ divides $| G |$

owned by Wkbj79

$\operatorname{ker} L=\{0\}$ if and only if $L$

is injective owned by Mathprof

$\operatorname{p.\!v.}(\frac{1}{x})$ is a distribution of first order owned by Koro

proof that $\operatorname{Spec}(R)$ is quasi-compact owned by Wkbj79

operator norm owned by asteroid

operator norm of multiplication operator on $L^2$

owned by rspuzio

operator ordering problem (in canonical quantization) owned by bci1

operator precedence (=order of operations) owned by akrowne

operator set (in algebraic system) owned by CWoo

operator substitution rule (in canonical quantization) owned by bci1

operator symbol (in algebraic system) owned by CWoo

operator topologies owned by asteroid

opere citato (in terms from foreign languages used in mathematics (html version)) owned by Wkbj79

Oppenheim inequality (in Hadamard product) owned by bbukh

opposing angles in a cyclic quadrilateral are supplementary owned by rm50

opposite owned by Wkbj79

opposite (=dual category) owned by CWoo

opposite algebra (in Brauer group) owned by djao

opposite arrow (in dual category) owned by CWoo

opposite category (=dual category) owned by CWoo

opposite functor (in dual category) owned by CWoo

opposite group owned by Wkbj79

opposite inverse (in condition of orthogonality) owned by pahio

opposite morphism (=dual category) owned by CWoo

opposite number owned by pahio

opposite ordering (in ordering relation) owned by djao

opposite polynomial owned by pahio

opposite ray (in ray) owned by CWoo

opposite ring owned by antizeus

opposite side (=opposite) owned by Wkbj79

opposite sides (in ordered geometry) owned by CWoo

opposite vector (in difference of vectors) owned by pahio

optimal approximation (=best approximation) owned by asteroid

optional (in optional process) owned by gel

optional process owned by gel

optional stopping (=stopped process) owned by gel

opus number owned by PrimeFan

oracle owned by Henry

orbifold owned by guffin

orbifold structure (in orbifold) owned by guffin

orbifold structure (=orbifold) owned by guffin

orbit (in Proof: The orbit of any element of a group is a subgroup) owned by drini

orbit owned by djao

orbits of a normal subgroup are equal in size when the full group acts transitively owned by rm50

orbit-stabilizer theorem owned by yark

order (=order (of a group)) owned by mathcam

order (in order in an algebra) owned by alozano

order (in discrete valuation ring) owned by djao

order (in matrix) owned by bbukh

order (in order and degree of polynomial) owned by jgade

order (=partial order) owned by mathcam

order (=order (of a graph)) owned by Mathprof

order (in zeros and poles of rational function) owned by pahio

order (=order (of a ring)) owned by Wkbj79

order (in B-tree) owned by Mathprof

order (in zero of polynomial) owned by pahio

order and degree of polynomial owned by jgade

Order Conjecture for non-commuting graph of a group owned by abdollahi

order contact (=order of contact) owned by rspuzio

order convergence (=meet continuous) owned by CWoo

order converges (in meet continuous) owned by CWoo

ordered bases (=matrix representation of a linear transformation) owned by CWoo

ordered basis (in matrix representation of a linear transformation) owned by CWoo

ordered field (in ordered ring) owned by djao

ordered geometry owned by CWoo

ordered group owned by pahio

ordered group equipped with zero (in ordered group) owned by pahio

ordered integral domain with well-ordered positive elements owned by Wkbj79

ordered linear space (=ordered vector space) owned by CWoo

ordered

-tuplet (=ordered tuplet) owned by rspuzio

ordered

-tupule (=ordered tuplet) owned by rspuzio

ordered pair owned by djao

ordered ring owned by djao

ordered space owned by CWoo

ordered topological linear space (=ordered topological vector space) owned by CWoo

ordered topological space (=ordered space) owned by CWoo

ordered topological vector space owned by CWoo

ordered tree owned by CWoo

ordered tuplet owned by rspuzio

ordered vector space owned by CWoo

order extension principle (in extension of a poset) owned by CWoo

order filter (in order ideal) owned by CWoo

order homomorphism (=order-preserving map) owned by porton

order ideal owned by CWoo

order in an algebra owned by alozano

ordering (=partial order) owned by mathcam

ordering of self-adjoints owned by asteroid

ordering on cardinalities owned by CWoo

ordering principle (in extension of a poset) owned by CWoo

ordering relation owned by djao

orderly number owned by PrimeFan

order morphism (in poset) owned by mps

order n constant coefficient differential equations and matrix exponential owned by gaillard

order of additive basis (in additive basis) owned by bbukh

order (of a graph) owned by Mathprof

order (of a group) owned by mathcam

order (of a group element) (in order (of a group)) owned by mathcam

order of an elliptic function owned by rspuzio

order of a number field (in orders in a number field) owned by pahio

order of a profinite group owned by mathcam

order of a ring (=order (of a ring)) owned by Wkbj79

order (of a ring) owned by Wkbj79

order of a supercategory (in supercategory) owned by bci1

order of asymptotic basis (in asymptotic basis) owned by bbukh

order of contact owned by rspuzio

order of derivative (in higher order derivatives) owned by PrimeFan

order of elements in finite groups owned by rm50

order of factors in infinite product owned by pahio

order of infinity (=formal definition of Landau notation) owned by paolini

order of operations owned by akrowne

order of products owned by pahio

order of rational function (in zeros and poles of rational function) owned by pahio

order of six means owned by pahio

order of the root (in equation) owned by pahio

order of the zero (=multiplicity) owned by pahio

order of vanishing owned by pahio

order of zero (=formal definition of Landau notation) owned by paolini

order of zero (in zero of polynomial) owned by pahio

order-preserving (=order-preserving map) owned by porton

order preserving (for ordinal functions) (in normal (ordinal) function) owned by florisje

order-preserving function (in poset) owned by mps

order-preserving map owned by porton

order-reversing (=order-preserving map) owned by porton

order reversing (=polarity) owned by Algeboy

orders and structure of classical groups owned by Algeboy

orders in a number field owned by pahio

orders of elements in integral domain owned by pahio

order statistics owned by CWoo

order topology owned by rspuzio

order type (in classes of ordinals and enumerating functions) owned by mathcam

order valuation owned by pahio

ordinal (=von Neumann ordinal) owned by Henry

ordinal (=ordinal number) owned by yark

ordinal arithmetic owned by Henry

ordinal category (in preorder as a category) owned by CWoo

ordinal exponentiation owned by CWoo

ordinal number owned by yark

ordinal space owned by CWoo

ordinal variable (in data types in statistics) owned by CWoo

ordinary cusp (in singular points of plane curve) owned by pahio

ordinary differential equation (in differential equation) owned by rspuzio

ordinary Dirichlet series (in Dirichlet series) owned by bbukh

ordinate (in Cartesian coordinates) owned by pahio

Ore condition owned by mclase

Ore domain owned by antizeus

Ore number owned by CompositeFan

Ore ring (in Ore condition) owned by mclase

Ore's theorem owned by mclase

Ore's theorem owned by Koro

organismic set (in organismic sets) owned by bci1

organismic set (in theory of organismic sets and mathematical relations) owned by bci1

organismic sets owned by bci1

organismic supercategories (=categorical dynamics) owned by bci1

organismic supercategories (=supercategory) owned by bci1

organismic supercategories and super-complex systems biodynamics owned by bci1

organismic supercategory (in supercategory theories) owned by bci1

organismic supercategory (=supercategory theories) owned by bci1

organismic supercategory (in categories and supercategories in relational biology) owned by bci1

organismic supercategory biodynamics (=natural transformations of organismic structures) owned by bci1

orientability with respect to a generalized homology theory (in Thom class) owned by antonio

orientable (in orientation) owned by PrimeFan

orientable manifold (in orientation) owned by PrimeFan

orientation owned by CWoo

orientation (in incidence matrix with respect to an orientation) owned by Mathprof

orientation owned by PrimeFan

orientation class (in orientation) owned by PrimeFan

orientation-preserving (=sense-preserving mapping) owned by jirka

oriented (in orientation) owned by PrimeFan

oriented cobordism owned by mathcam

oriented manifold (in orientation) owned by PrimeFan

oriented space curve (=space curve) owned by Mathprof

origin owned by jirka

origin of species (=biogroupoids: mathematical models of species evolution) owned by bci1

origins of Wedderburn's theorem owned by Algeboy

Ornstein-Uhlenbeck equation (=Ornstein-Uhlenbeck process) owned by stevecheng

Ornstein-Uhlenbeck process owned by stevecheng

or operator (=join) owned by yark

or `spectral (quantum) triples' (in noncommutative geometry) owned by bci1

or theoretical physics (=quantum chromodynamics (QCD)) owned by bci1

orthic triangle owned by drini

orthocenter owned by Mathprof

orthocentric tetrad (in orthocenter) owned by Mathprof

orthocomplement (in orthocomplemented lattice) owned by CWoo

orthocomplementation (in orthocomplemented lattice) owned by CWoo

orthocomplemented (in orthocomplemented lattice) owned by CWoo

orthocomplemented lattice owned by CWoo

orthocomplemented poset (in orthocomplemented lattice) owned by CWoo

orthodox semigroup (in regular semigroup) owned by yark

orthogonal owned by akrowne

orthogonal (in orthomodular lattice) owned by CWoo

orthogonal (in perpendicularity in Euclidean plane) owned by pahio

orthogonal (in orthogonal morphisms) owned by CWoo

orthogonal circle (in orthogonal circles) owned by pahio

orthogonal circles owned by pahio

orthogonal complement (in complementary subspace) owned by rmilson

orthogonal complement (in orthomodular lattice) owned by CWoo

orthogonal curve owned by pahio

orthogonal decomposition theorem owned by asteroid

orthogonal direct sum owned by CWoo

orthogonal group owned by djao

orthogonal idempotents (in idempotent) owned by mclase

orthogonal idempotents of the group ring owned by mathcam

orthogonality (in perpendicularity in Euclidean plane) owned by pahio

orthogonality of Chebyshev polynomials owned by pahio

orthogonality of Chebyshev polynomials from recursion owned by rspuzio

orthogonality of Laguerre polynomials owned by pahio

orthogonality of Legendre polynomials owned by pahio

orthogonality relations owned by mhale

orthogonalization (=proof of Gram-Schmidt orthogonalization procedure) owned by rspuzio

orthogonal Latin squares owned by CWoo

orthogonally commute (in commutativity relation in an orthocomplemented lattice) owned by CWoo

orthogonal matrices owned by akrowne

orthogonal morphisms owned by CWoo

orthogonal polynomials owned by akrowne

orthogonal projection (in projection) owned by rmilson

orthogonal projection (=projection of point) owned by pahio

orthogonal projections onto Hilbert subspaces (=projections and closed subspaces) owned by asteroid

orthogonal sum (=orthogonal direct sum) owned by CWoo

orthogonal trajectory (=orthogonal curve) owned by pahio

orthogonal transformation (in orthogonal group) owned by djao

orthogonal vectors owned by akrowne

ortholattice (=orthocomplemented lattice) owned by CWoo

orthomodular lattice owned by CWoo

orthomodular poset (in orthomodular lattice) owned by CWoo

orthonormal (in orthonormal set) owned by yark

orthonormal basis owned by yark

orthonormal basis of $\ell^2(X)$ have the cardinality of $X$

(in $\ell^p(X)$ space) owned by asteroid

orthonormal dyadic wavelet (in wavelet) owned by swiftset

orthonormal frame (in moving frame) owned by mathcam

orthonormal set owned by yark

oscillation of a function owned by perucho

osculating circle (=circle of curvature) owned by rspuzio

osculating curve owned by pahio

osculating plane (in Frenet frame) owned by rmilson

ostensibly discontinuous antiderivative owned by pahio

Ostrowski's valuation theorem owned by pahio

proof of Ostrowski's valuation theorem owned by rm50

Ostrowski theorem owned by Andrea Ambrosio

Otto Hoelder (=Otto Hölder) owned by Mravinci

Otto Holder (=Otto Hölder) owned by Mravinci

Otto Hölder owned by Mravinci

outcome (in game) owned by Henry

out-degree (in directed graph) owned by rm50

out degree (=directed graph) owned by rm50

outer (in inner automorphism) owned by rmilson

outer automorphism (in inner automorphism) owned by rmilson

outer automorphism group (in outer automorphism group) owned by Thomas Heye

outer automorphism group owned by Thomas Heye

examples of outer automorphism group owned by juanman

outer function (in inner function) owned by jirka

outer ideal (in quadratic Jordan algebra) owned by Algeboy

proof that the outer (Lebesgue) measure of an interval is its length owned by Simone

outer linear (=scalar map) owned by Algeboy

outer measure owned by mathcam

outer measure (=Lebesgue outer measure) owned by yark

outer measure generated by (in capacity generated by a measure) owned by gel

outer measure generated by a measure (=capacity generated by a measure) owned by gel

outer multiplication owned by rmilson

outer product (=cross product) owned by yark

outer regular owned by djao

outlier (in trimmed mean) owned by CWoo

an outline of Hilbert's programme owned by gribskoff

output controllability owned by GeraW

oval of Cassini (=Cassini oval) owned by pahio

overdetermined owned by akrowne

over-determined (=overdetermined) owned by akrowne

over determined (=overdetermined) owned by akrowne

overdispersion owned by CWoo

over-harmonic series (in examples using comparison test without limit) owned by pahio

$\overline{\mathbb{R}}$ (in extended real numbers) owned by matte

overload owned by Mravinci

overloaded (=overload) owned by Mravinci

overring owned by pahio

overview of the content of PlanetMath owned by matte

Oystein Ore (=Øystein Ore) owned by Mravinci

Øystein Ore owned by Mravinci

P - 1518 entries

Q - 323 entries

R - 1000 entries

S - 2058 entries

T - 852 entries

U - 400 entries

V - 260 entries

W - 328 entries

X - 8 entries

Y - 22 entries

Z - 99 entries

8694 entries total.
15221 concepts total.

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