Axiom 2: Any property entailed by — i. e., strictly implied by — a positive property is positive

Any poles on the imaginary axis have real strictly positive residues, and similarly at any zeros on the imaginary axis, the function has a real strictly positive derivative.

Any positive divisor of is a product of prime divisors of raised to some power.

Any invertible matrix can be uniquely represented according to the polar decomposition as the product of a unitary matrix and a hermitian matrix with positive eigenvalues.

Any gas discharge lamp has a positive ( anode ) and a negative electrode.

for some p between 1 and n. Any two such expressions of q ( at the same point m of M ) will have the same number p of positive signs.

Any system where there is positive feedback together with a gain greater than one will result in a runaway situation.

* Any positive multiple of the repunit R < sub > n </ sub >< sup >( b )</ sup > contains at least n nonzero digits in base b.

Any fluctuations in food supply ( either positive, for example, due to technology improvements, or negative, due to droughts and pest invasions ) tend to translate directly into population fluctuations.

The theory, Any press is good press, has been coined to describe situations where bad behaviour by people involved with an organization or brand has actually resulted in positive results, due to the fame and press coverage accrued by such events.

Any positive immunological effect is thought to be the result of melatonin acting on high affinity receptors ( MT1 and MT2 ) expressed in immunocompetent cells.

* Any positive integer is a chain of length 1.

Any positive test result should be confirmed by a lab using the western blot.

Any hope towards positive relations with Russia ended in the late 18th and early 19th centuries when tensions with the Cossacks escalated and Russia began trying to conquer the Caucasus, starting with Georgia.

On 8 July 2011 on BBC Radio 4's Any Questions, at the height of the furore surrounding the alleged illegal and corrupt activities of News of the World journalists, Parris eulogised the newspaper and gave an enthusiastic appreciation of what he considered the virtues and positive achievements of Rupert Murdoch.

* Any open manifold admits a ( non-complete ) Riemannian metric of positive ( or negative ) curvature.

Any positive integer n has 2 < sup > n − 1 </ sup > distinct compositions.

Any element y ∈ Y := Ran ( S − I ) has a distance larger than or equal to 1 from u ( otherwise y < sub > i </ sub > = x < sub > i + 1 </ sub >-x < sub > i </ sub > would be positive and bounded away from zero, whence x < sub > i </ sub > could not be bounded ).

Any skew semistandard tableau of shape / with positive integer entries gives rise to a sequence of partitions ( or Young diagrams ), by starting with, and taking for the partition places further in the sequence the one whose diagram is obtained from that of by adding all the boxes that contain a value ≤ in ; this partition eventually becomes equal to.

Any voltage is a difference in electric potential between two points-for example, the separation of positive and negative electric charges on opposite sides of a resistive barrier.

Any open flame or electric sparks, including lit tobacco products like cigarettes, cigars or pipes, in the area also present a danger of ignition of any hydrogen gas emanating from a battery ( this is the reason, when recharging the battery in place in the vehicle or jump starting, that the negative cable of the recharger or attached to the other vehicle's jumping battery negative post is always attached away from the battery to ground on the engine or frame, and is always attached to complete the circuit only after the positive cable has been attached to the battery's positive terminal ( and is removed in the reverse order, i. e., negative cable first from the frame or engine, breaking the circuit, then positive cable from the battery )-in this fashion, any sparks which may occur will occur at the more distant location of the negative cable attachment point, away from the battery and potentially explosive gases, and no sparks will occur, as the circuit is no longer complete, when the positive cable is attached or detached from the battery ).

Any rational number with a denominator whose only prime factors are 2 and / or 5 may be precisely expressed as a decimal fraction and has a finite decimal expansion.

* 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 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 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.