# 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 given individual or organization attempting to implement this model in a real situation would be unable to comply with the three requirements.

* Any Lie group G defines an associated real Lie algebra.

* Any closed interval b of real numbers is Lebesgue measurable, and its Lebesgue measure is the length b − a.

Any real mode operating system ( such as Xenix ) could also be made to run using OS / 2's virtual machine capabilities, subject to certain direct hardware access limitations.

Any Dedekind-complete ordered field is isomorphic to the real numbers.

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 field, including fields of rational numbers, real numbers, and complex numbers.

Any non-negative real number can be represented as a base-φ numeral using only the digits 0 and 1, and avoiding the digit sequence " 11 "-this is called a standard form.

* Any polynomial ( real or complex ) is an analytic function.

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 real analytic function on some open set on the real line can be extended to a complex analytic function on some open set of the complex plane.

Any destruction by the Occupying Power of real or personal property belonging individually or collectively to private persons, or to the State, or to other public authorities, or to social or cooperative organizations, is prohibited, except where such destruction is rendered absolutely necessary by military operations.

Furthermore, in the opening credits there is a mock disclaimer which reads ( in translation ): “ Any resemblance to real events, to persons dead or living, is not accidental.

Any rational function of a real variable can be written as the sum of a polynomial function and a finite number of algebraic fractions.

Any hope of real progress by the Poles was then lost.

Any entity from the real or virtual world that lends itself to dramatic interpretation may be taken up as a subject.

* Any open subset of a finite-dimensional real, and therefore complex, vector space is a diffeological space.

Any public employee who fell under his power would be replaced by someone in whom he saw real ability instead of a mere useful recipient of a favor.

Any resident could be member and enjoy its privileges, including dining services, games, lawn tennis, and the entire social advantages attendant thereto.

Any device that can display text on a screen can act as an e-book reader, but without the advantages of the e-paper technology.

Any advantages for the Austrians however were canceled out by the crushing defeat on 3 July at Königgrätz, where Ludwig von Benedek was surprised by the speed of Helmuth von Moltke's concentric advance into Bohemia.

Any approach toward such a system looks toward saving and security.

Any type of focal lesion of the central nervous system ( such as stroke, brain tumour, multiple sclerosis ) will cause the type of ataxia corresponding to the site of the lesion: cerebellar if in the cerebellum, sensory if in the dorsal spinal cord ( and rarely in the thalamus or parietal lobe ), vestibular if in the vestibular system ( including the vestibular areas of the cerebral cortex ).

Any heat that isn't translated into work is normally considered a waste product and is removed from the engine either by an air or liquid cooling system.

Any customer who opted to keep theirs was required to sign a waiver indicating their understanding that no more software would be written for the system and which absolved Intellivision of any future responsibility for technical support.

: Premise: Any cognitive state occurs as part of a set of cognitive states and within a cognitive system

Any individual workflow within a system of workflows can be subject to some type of operational latency.

Any object gravitationally held by the rotating Earth – Moon system will be attracted to the barycenter to an equal and opposite degree as its tendency to fly off into space.

Any communication to another system in the galaxy has to be recorded on a physical disc which is transported through the wormhole ; chains of these are referenced in Diplomatic Immunity ( Chapter 9 ) where messages are ' squirted ' to a station on one side of a wormhole, flown ( on a physical medium ) through the wormhole and re-squirted to a similar arrangement at the next wormhole in the sequence.

Eugene Odum, a founder of ecology, stated: " Any unit that includes all of the organisms ( ie: the " community ") in a given area interacting with the physical environment so that a flow of energy leads to clearly defined trophic structure, biotic diversity, and material cycles ( i. e.: exchange of materials between living and nonliving parts ) within the system is an ecosystem.

* Extensibility: Any database system has its own predefined set of data types which we can use to build new types ( see Complex Objects ), but a purely extensible system is designed such that there are no logical differences between built-in ( or ' primitive ') data types and ' custom ' data types, though there may be strong differences in the way the two are implemented.

Any decidable type system involves a trade-off: while it rejects many incorrect programs, it can also prohibit some correct, albeit unusual programs.

Any two-level quantum system can be used as a qubit.

* Any system that implements records management

Any automated reasoning system will have to deal with truly huge inputs.

: Any change in status quo prompts an opposing reaction in the responding system.

Any decrease in the Gibbs function of a system is the upper limit for any isothermal, isobaric work that can be captured in the surroundings, or it may simply be dissipated, appearing as T times a corresponding increase in the entropy of the system and / or its surrounding.

Any CTCSS system that has compatible tones is interchangeable.

Any object radiating sound, including a loudspeaker system, can be thought of as being composed of combinations of such simple point sources.

Any direction can potentially serve as the plane of reference, as long as it is clearly defined for everyone using that system.

Any security system depends crucially on keeping some things secret.

Any foreigner wishing to visit Ming China could only do so via the tribute system.