 Page "Euclidean space" ¶ 38
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Any and subset Any subset of B is also well-ordered. :* Any subset of the identity relation on X has equivalence classes that are the singletons of X. Any one language has only a subset of the aspectual distinctions attested in the world's languages, and some languages ( such as Standard German ; see below ) do not have aspects. Any measurable subset of a null set is itself a null set. Any topological space which is itself finite or countably infinite is separable, for the whole space is a countable dense subset of itself. Any second-countable space is separable: if is a countable base, choosing any gives a countable dense subset. Any subset of resource, but typically at least the processor state, may be associated with each of the process ' threads in operating systems that support threads or ' daughter ' processes. Any function can be restricted to a subset of its domain. * Any open subset of a finite-dimensional real, and therefore complex, vector space is a diffeological space. Any ordinal is, of course, an open subset of any further ordinal. * Any subset of a meagre set is meagre ; any superset of a comeagre set is comeagre. Any discrete subset of Euclidean space is countable, since the isolation of each of its points ( together with the fact the rationals are dense in the reals ) means that it may be mapped 1-1 to a set of points with rational co-ordinates, of which there are only countably many. Any proposed inverse R of F ( reconstruction formula, in the lingo ) would have to map to some subset of. Any action of the group by continuous affine transformations on a compact convex subset of a ( separable ) locally convex topological vector space has a fixed point. Any induced subgraph of a comparability graph is itself a comparability graph, formed from the restriction of the partial order to a subset of its elements. * Any directed set A may be made into a Cauchy space by declaring a filter F to be Cauchy if, given any element n of A, there is an element U of F such that U is either a singleton or a subset of the tail Any subset of a group closed under multiplication, under inversion and under identity ( i. e. Any given neuron only responds to a subset of stimuli within its receptive field. * Any open subset of an n-manifold is a n-manifold with the subspace topology. Any set of five points in the plane in general position has a subset of four points that form the vertices of a convex quadrilateral.

Any and R * Any commutative ring R is an algebra over itself, or any subring of R. * Any ring of matrices with coefficients in a commutative ring R forms an R-algebra under matrix addition and multiplication. Brown continued releasing recordings: in 1993, he issued the album, Universal James, which included Brown's final Billboard charted single, " Can't Get Any Harder ", which peaked at # 76 on the US R & B chart and # 59 on the UK chart. Any formal series with has a composition inverse provided is an invertible element of R. The coefficients are found recursively from the above formula for the coefficients of a composition, equating them with those of the composition identity X ( that is 1 at degree 1 and 0 at every degree greater than 1 ). * Any positive multiple of the repunit R < sub > n </ sub >< sup >( b )</ sup > contains at least n nonzero digits in base b. Any binary relation R on a set A can generate a natural partial order on the R-cycle equivalence classes of set A, so that xRy implies ≥. * The Drug War in Mexico: By Any Other Name it's Terrorism, by Barnard R. Thompson ( MexiData. info ) Any totally ordered set that is not isomorphic to R but satisfies ( 1 )( 4 ) is known as a Suslin line. Any physical object whose radius R becomes less than or equal to the Schwarzschild radius will undergo gravitational collapse and become a black hole. * Any ring R can be considered as a one-object preadditive category ; the category of left modules over R is the same as the additive functor category Add ( R, Ab ) ( where Ab denotes the category of abelian groups ), and the category of right R-modules is Add ( R < sup > op </ sup >, Ab ). Any n-dimensional formal group law gives an n dimensional Lie algebra over the ring R, defined in terms of the quadratic part F < sub > 2 </ sub > of the formal group law. * Any two-sided ideal of a ring R is an R-bimodule. * Any module over a commutative ring R is automatically a bimodule. * Any slave who evades capture for 20 days or more is to be publicly whipped for the first offense ; branded with the letter R on the right cheek for the second offense ; and lose one ear if absent for thirty days for the third offense ; and castrated for the fourth offense. In early June, Banks released the second single off the album, " Any Girl " featuring R & B singer Lloyd. O. A. R., who grew up in nearby Rockville, Maryland, recorded the live album Any Time Now at the 9: 30 Club on November 23 – 24, 2001. Any non-singular matrix S of the same size is said to transform A into another symmetric matrix B = SAS < sup > T </ sup >, also of order n, where S < sup > T </ sup > is the transpose of S. If A is the coefficient matrix of some quadratic form of R < sup > n </ sup >, then B is the matrix for the same form after the change of coordinates defined by S. Lloyd C. Gardner, " Pay Any Price: Lyndon Johnson and the Wars for Vietnam ", Chicago: Ivan R. Dee, 1995.

Any and < Note: Any nonlinear electronic block driven by two signals with frequencies f < sub > 1 </ sub > and f < sub > 2 </ sub > would generate intermodulation ( mixing ) products. Any units of angular measure can be used for right ascension, but it is customarily measured in hours (< sup > h </ sup >), minutes (< sup > m </ sup >), and seconds (< sup > s </ sup >), with 24 < sup > h </ sup > being equivalent to a full circle. Any frequency component above f < sub > s </ sub >/ 2 is indistinguishable from a lower-frequency component, called an alias, associated with one of the copies. # Any pure element ( even if it forms diatomic molecules like chlorine, Cl < sub > 2 </ sub >) has an oxidation state ( OS ) of zero. Any Taylor series for this function converges not only for x close enough to x < sub > 0 </ sub > ( as in the definition ) but for all values of x ( real or complex ). Any polynomial written in standard form has a unique constant term, which can be considered a coefficient of x < sup > 0 </ sup >. < li > Any legislative measures and other measures calculated to prevent a racial group or groups from participation in the political, social, economic and cultural life of the country and the deliberate creation of conditions preventing the full development of such a group or groups, in particular by denying to members of a racial group or groups basic human rights and freedoms, including the right to work, the right to form recognised trade unions, the right to education, the right to leave and to return to their country, the right to a nationality, the right to freedom of movement and residence, the right to freedom of opinion and expression, and the right to freedom of peaceful assembly and association ;</ li > < li > Any measures including legislative measures, designed to divide the population along racial lines by the creation of separate reserves and ghettos for the members of a racial group or groups, the prohibition of mixed marriages among members of various racial groups, the expropriation of landed property belonging to a racial group or groups or to members thereof ;</ li > Any ( non-graded ) ring A can be given a gradation by letting A < sub > 0 </ sub > Any XML Schema can use the Point Profile by importing it and referencing the subject < gml: Point > instance: Any number b + 1 is written as " 11 < sub > b </ sub >" in base b, so 11 is trivially a palindrome in base 10. Any such sequence belongs to the Hilbert space ℓ < sub > 2 </ sub >, so the Hilbert cube inherits a metric from there. * Any two objects Y and Z of C have an exponential Z < sup > Y </ sup > in C. :: Theorem ( Lefschetz theorem on ( 1, 1 )- classes ) Any element of H < sup > 2 </ sup >( X, Z ) ∩ H < sup > 1, 1 </ sup >( X ) is the cohomology class of a divisor on X. Any n × n real symmetric matrix A determines a quadratic form q < sub > A </ sub > in n variables by the formula * Any open set is trivially a G < sub > δ </ sub > set Any sulfur in the fuel can be oxidized to SO < sub > 2 </ sub > ( sulfur dioxide ) or even SO < sub > 3 </ sub > ( sulfur trioxide ) in the combustion chamber. < TD > Ask Any Woman </ TD > Any non-zero vector v divides the Euclidean space into two half-spaces bounding the hyperplane v < sup >∧</ sup > orthogonal to v, namely v < sup >+</ sup > and v < sup >−</ sup >.

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