Any non-trivial true statement about reality is necessarily an abstraction composed of a complex of objects and properties or relations.

Any algebra whose elements are idempotent is also power-associative.

* Any unital quantale is an idempotent semiring, or dioid, under join and multiplication.

* Any bounded, distributive lattice is a commutative, idempotent semiring under join and meet.

Any organism that falters or misperceives the signals or weakens is done.

Any information we have here in Taiwan is at your disposal ''.

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 alteration of one of these factors is distortion, although we generally use that word only for effects so pronounced that they can be stated quantitatively on the basis of standard tests.

Any musician playing Beethoven here, where Beethoven was born, is likely to examine his own interpretations with special care.

Any action is understood to create " seeds " in the mind that sprout into the appropriate results ( Pāli vipaka ) when they meet the right conditions.

** Any union of countably many countable sets is itself countable.

Any information may be conveyed by an analog signal ; often such a signal is a measured response to changes in physical phenomena, such as sound, light, temperature, position, or pressure.

Any quantity of energy absorbed by the electron in excess of this amount is converted to kinetic energy according to the conservation of energy.

Any breach of these laws is a criminal offence and can lead to fine of up to £ 5, 000 or six months in prison.

The prohibition against retaliation or coercion applies broadly to any individual or entity that seeks to prevent an individual from exercising his or her rights or to retaliate against him or her for having exercised those rights ... Any form of retaliation or coercion, including threats, intimidation, or interference, is prohibited if it is intended to interfere.

Any word or phrase that exactly reproduces the letters in another order is an anagram.

Any work ( δW ) done must be done at the expense of internal energy U, since no heat δQ is being supplied from the surroundings.

" Any threat of war Clovis could make would only be effective if they were neighbors ; " it is nowhere written that Syagrius was handed over in 486 or 487.

Any player may declare the game over at any time during his turn if either of two conditions is true: one chain has 41 or more tiles, or there is at least one chain on the board and every chain on the board has 11 or more tiles.

Any person who is seen as a threat to civil aviation is banned from flying.

* Any ring of characteristic n is a ( Z / nZ )- algebra in the same way.

* Any ring A is an algebra over its center Z ( A ), or over any subring of its center.

* Any commutative ring R is an algebra over itself, or any subring of R.

Any form of intelligent life would do ; so, specifying carbon-based life, per se, is irrelevant.

* Any base that is water-soluble and forms hydroxide ions or the solution of a base in water.

* Any vector space V endowed with the identically zero Lie bracket becomes a Lie algebra.

The blitter's block copying mode takes zero to three data sources in memory, called A, B and C, performs a programmable boolean function on the data sources and writes the result to a destination area, D. Any of these four areas can overlap.

Any chemical species that is regenerated, such as a catalyst, also has a stoichiometric coefficient of zero.

# Any pure element ( even if it forms diatomic molecules like chlorine, Cl < sub > 2 </ sub >) has an oxidation state ( OS ) of zero.

Any perfect conductor will prevent any change to magnetic flux passing through its surface due to ordinary electromagnetic induction at zero resistance.

Any polynomial can be easily expressed as a power series around any center c, albeit one with most coefficients equal to zero.

Any fixed time can be used in place of the present ( e. g., the end of one interval of an annuity ); the value obtained is zero if and only if the NPV is zero.

Any non-zero change of direction is possible: if this distance is zero the velocities are reversed in the collision ; if it is close to the sum of the radii of the spheres the two bodies are only slightly deflected.

Any new root growth is rapidly and heavily colonised, so that shoot growth is virtually zero.

Any number system that forms a commutative ring — for instance, the integers, the real numbers, and the complex numbers — can be extended to a wheel in which division by zero is always possible ; however, in such a case, " division " has a slightly different meaning.

Any such point P will contain zero area and so will have zero probability of being hit by the dart.

Any term p < sub > k </ sub > X < sup > k </ sup > with zero coefficient, p < sub > k </ sub > = 0, may be omitted.

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 genus zero handlebody is homeomorphic to the three-ball B < sup > 3 </ sup >.

* Any other pair scores zero

Any such velocity can be viewed as a zero velocity under a squeeze mapping called a Lorentz boost.

Any normal ordered operator therefore has a vacuum expectation value of zero.

Any point can correspond with 0 ( zero ) and any other point can correspond with 1 ( one ).

Any abelian group can be turned into a zero ring by defining the product of any two elements to be 0.

Any subgroup of the additive group of a zero ring is an ideal.

Any number plus 0 ( zero ) equals itself.