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Page "Decimal" ¶ 13
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Any and rational
* Any field, including fields of rational numbers, real numbers, and complex numbers.
Any process of evaluation or analysis, that may be called rational, is expected to be highly objective, logical and " mechanical ".
Any rational function of a real variable can be written as the sum of a polynomial function and a finite number of algebraic fractions.
Roger Ebert's review for the Chicago Sun-Times was :" Any attempt to defend this movie on rational grounds is futile.
Any conic section defined over F with a rational point in F is a rational curve.
Any one of these models must be explicitly constructed, and most of these models are built using the basic properties of the rational number system as an ordered field.
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 other cost price would yield an arbitrage opportunity and riskless profit ( see rational pricing for the arbitrage mechanics ).
Any positive rational number can be written as the sum of unit fractions, in multiple ways.
Any Heronian triangle can be split into two right-angled triangles whose side lengths form Pythagorean triples with rational values.
Any such field is either equal to K or is also rational, i. e. L = K ( F ) for some rational function F. In geometrical terms this states that a non-constant rational map from the projective line to a curve C can only occur when C also has genus 0.
Any pairing function can be used in set theory to prove that integers and rational numbers have the same cardinality as natural numbers.
Any polynomial, and more generally any rational function p ( x )/ q ( x ) where p and q are polynomials, transforms the Riemann sphere by mapping it to itself.
For example, can be written as Any positive rational number can be written as a sum of unit fractions in infinitely many ways.

Any and number
Any number of other ways exist to be rich.
* Any expression formed using any combination of the basic arithmetic operations and extraction of nth roots gives an algebraic number.
Any number of players may be replaced by substitutes during the course of the game.
Any season ticket holder could put themselves forward for election, with a certain number of nominations, and votes were cast by all season ticket holders over the age of 18.
# Any real number can be added to both sides.
# Any real number can be subtracted from both sides.
# Any real number can be multiplied to both sides.
# Any non-zero real number can divide both sides.
Any complex number z = x + iy can be written as
* Any two finite fields with the same number of elements are isomorphic.
# Any player who would qualify from the Interzonal to play in the Candidates but who was excluded because of a limitation on the number of participants from his Federation.
* Any of a number of plants in the family Poaceae with narrow blade-shaped leaves, or other unrelated plants of similar appearance
Any decision involves a choice selected from a number of alternatives, directed toward an organizational goal or subgoal.
Any number of these monomer units may be indicated by the appropriate Greek prefix ; e. g. a decamer is formed from 10 monomers.
Any overbid or underbid loses the number of points their bid was off ( a player bidding 3 tricks that wins only 2 would lose a point, as would a player bidding 2 and winning 3 ).
Simple Plan, from Montréal, climbed to number three in the United States with Still Not Getting Any ... in 2004.
Any meaningful theory of quantum gravity that makes sense and is predictive at all energy scales must have some deep principle that reduces the infinitely many unknown parameters to a finite number that can then be measured.
Any number of players can play, using differently coloured pens, if required.
* Any topological space which is the union of a countable number of separable subspaces is separable.
Any number of other alternate forms may be used, many of which are variations on the term " gamemaster "; these variants are especially common in storytelling games derived from or similar to role-playing games.
Any Liouville number must have unbounded partial quotients in its continued fraction expansion.
Any finite number of initial terms of the Taylor series of a function is called a Taylor polynomial.
Any modulated signal will have an infinite number of sidebands and hence an infinite bandwidth but in practice all significant sideband energy ( 98 % or more ) is concentrated within the bandwidth defined by Carson's rule.
Any type or number of topologies may be used -- star, bus, ring, etc.

Any and with
Any posse riding down the street to demand Blue Throat's surrender would be wiped out with one deadly burst of fire.
Any abilities I may have were achieved in their present shape from experience in sharing in the growth and control of my business, coupled with raising my family.
Any attempt to reconcile this statement of the central issue in the campaign of 1956 with the nature of the man who could not conceive it as the central issue will at least resolve our confusions about the chaotic and misleading results of the earnestness of both doctors and President in a situation which should never have arisen.
Any claimant whose claim is denied, or is approved for less than the full amount of such claim, shall be entitled, under such regulations as the Commission may prescribe, to a hearing before the Commission, or its duly authorized representatives, with respect to such claim.
Any irregularity on the piston heads will make it impossible, with normal means, to determine the final combustion chamber volume because the volume displaced by the piston heads cannot be readily computed.
Any reputable French interne can supply you with a dozen similar instances, and I'll presently recount a case out of my own personal experience, but, for the moment, let's resume our catalogue.
Any of the antithyroid drugs, of either type, if given in large enough doses for a long period of time will cause goitre, owing to inhibition of thyroid hormone synthesis, with production of hypothyroidism.
Any adjustments which are made, Mr. Grenier said earlier this month, will appear on the balance of the tax bill since most of the town's taxpayers take the option of paying quarterly with the balance due next year.
Any shareholder of any of these funds who finds a mistake in his account certainly should get in touch with the bank.
Any musician playing Beethoven here, where Beethoven was born, is likely to examine his own interpretations with special care.
* Any ring of matrices with coefficients in a commutative ring R forms an R-algebra under matrix addition and multiplication.
Most of the C code being written nowadays is based on ANSI C. Any program written only in standard C and without any hardware dependent assumptions is virtually guaranteed to compile correctly on any platform with a conforming C implementation.
Any company incorporating Bluetooth wireless technology into products, using the technology to offer goods and services or simply re-branding a product with Bluetooth technology must become a member of the Bluetooth SIG.
Any codex of Bede's Easter cycle is normally found together with a codex of his " De Temporum Ratione ".
Love and Erlandson continued to pursue with the band, and released the single " Be A Man "— an outtake from the Celebrity Skin sessions — for the soundtrack of the Oliver Stone film Any Given Sunday ( 1999 ).
Any differential area with normal vector of a given internal surface area, bounding a portion of the body, experiences a contact force arising from the contact between both portions of the body on each side of, and it is given by
# Any collection of closed subsets of X with the finite intersection property has nonempty intersection.
Any pellets which are too small to be finished granules of couscous and fall through the sieve will be again rolled and sprinkled with dry semolina and rolled into pellets.
Any successes that the Nationalists did make, however, were met with constant political and military upheavals.
Any piece of DNA with the point centromere DNA sequence on it will typically form a centomere if present in the appropriate species.
# Any experience which is inconsistent with the organization of the structure of the self may be perceived as a threat, and the more of these perceptions there are, the more rigidly the self structure is organized to maintain itself.
Any units of angular measure can be used for declination, but it is customarily measured in the degrees ( ° ), minutes ( ' ), and seconds ( " ) of sexagesimal measure, with 90 ° equivalent to circle.
Any ellipse can be obtained by rotation and translation of a canonical ellipse with the proper semi-diameters.

0.790 seconds.