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Page "Category (mathematics)" ¶ 17
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Any and set
Any such totality would itself have to be a set, thus lying somewhere within the hierarchy and thus failing to contain every set.
* Any finite topological space, including the empty set, is compact.
Any definition that attempts to set out the essence of something, such as that by genus and differentia, is an intensional definition.
Any consistent set of units may be used, although SI units are preferred.
* Any singleton set
Any regional variety of English has a set of political, social and cultural connotations attached to it, even the so-called ' standard ' forms.
Any partially ordered set I can be considered as a small category where the morphisms consist of arrows i → j if and only if i j.
: Premise: Any cognitive state occurs as part of a set of cognitive states and within a cognitive system
Any measurable subset of a null set is itself a null set.
* 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 slight initial imbalance between taste and tails may set off an explosion in tail lengths.
Any byte with the high bit set was a special Telnet character.
* Any attempt to set up a telecommunication circuit
Any given instruction set can be implemented in a variety of ways.
Any discussion of Muslim magic poses a double set of problems.
Any other cogenerator ( or cogenerating set ) can be used in this construction.
Any ordinal number can be seen as a category when viewed as an ordered set.
Any given animal uses a relatively restricted set of gaits, and different species use different gaits.
Any statement that has a Y following the command letter is processed only if the match flag is set.
Any collection of subsets of a set X satisfying these properties forms a base for the closed sets of a topology on X.
* Any partially ordered set can be interpreted as a category: the objects are the elements of, and there is a single morphism from to if and only if.
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 and P
Other notable roles include Mary Elizabeth ( O ' Brien ) Sims on the Lifetime Television drama series Any Day Now ( 1998 – 2002 ), for which she was nominated for two Screen Actors Guild Award for Outstanding Performance by a Female Actor in a Drama Series, the voice of Little Bo Peep in the first two Toy Story films, a supporting role in the John Hughes's Pretty in Pink as well as guest-starring roles on such CBS's television series as Magnum, P. I., Joan of Arcadia, Close to Home, Two and a Half Men and ABC ' Men in Trees, Ugly Betty and Boston Legal.
Any such point P will contain zero area and so will have zero probability of being hit by the dart.
His novel Babylon (" Generation П " or " Generation P " is the Russian title ) bears on its cover the inscription, " Any thought that occurs in the process of reading this book is subject to copyright.
Any strongly NP-hard optimization problem with a polynomially bounded objective function cannot have an FPTAS unless P = NP.
Any other sequence satisfying this recurrence relation can be represented as a linear combination of the Lucas sequences U < sub > n </ sub >( P, Q ) and V < sub > n </ sub >( P, Q ).
Comfort In Any Climate, Taos: Solar Survival P. ISBN 0-9626767-4-8
Any canonical transformation involving a type-2 generating function G < sub > 2 </ sub >( q, P, t ) leads to the relations
Any friction would result in a pressure build-up in the syringe and would lead to an inaccurate measurement, that is, a lower amount of gas would be determined, than really obtained .< ref > Schmid, H. P. " Pressure and Gas Laws.
* Any four points on C span P < sup > 3 </ sup >.
Any M / E section can be selected as a source in the P / P stage, making the mixer operations much more versatile, since effects or keys can be composed " offline " in an M / E and then go " live " at the push of one button.
2000 Primetime Emmy Awards — ( Nominated ) Outstanding Costumes for a Series: Mary Anne Aston ( Costume Supervisor ); Elizabeth P. Palmer ( Costume Designer )< ref >" Any Day Now.
Any subgraph P in node n may be copied into any node depending on n. Likewise, any subgraph P in node n may be erased if there exists a copy of P in some node ancestral to n ( i. e., some node on which n depends ).

Any and forms
* Any ring of matrices with coefficients in a commutative ring R forms an R-algebra under matrix addition and multiplication.
* Any base that is water-soluble and forms hydroxide ions or the solution of a base in water.
Alfred Korzybski criticized the use of the verb " to be ", and stated that, " Any proposition containing the word ' is ' its other forms ' are ,' ' be ', etc.
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 pure element ( even if it forms diatomic molecules like chlorine, Cl < sub > 2 </ sub >) has an oxidation state ( OS ) of zero.
Any of these forms can be used to display a fraction.
Any monoid ( any algebraic structure with a single associative binary operation and an identity element ) forms a small category with a single object x.
Any context-free grammar that does not generate the empty string can be represented in CNF using only production rules of the forms and.
Any particular Boolean function can be represented by one and only one full disjunctive normal form, one of the two canonical forms.
Any planar cross section passing through the center of an ellipsoid forms an ellipse on its surface: this degenerates to a circle for sections normal to the symmetry axis of an ellipsoid of revolution ( or all sections when the ellipsoid degenerates to a sphere.
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 conversion of energy between forms results in loss.
* Any speech deemed as instigative can be regarded as illegal, including oral, written and electronic forms ; it is a crime both to express, and to hear such speech and fail to report it.
Any non-rotating and non-charged mass that is smaller than its Schwarzschild radius forms a black hole.
# Any US vessel travelling on the Great Lakes, connecting waters or the Saint Lawrence River ( where that river forms part of the Canada – United States border )
Any animals living above the snowline are obliged to do this as snow and ice are the only forms of water during winter, and by doing so their range is greatly enlarged.
Any material misstatements on the insurance application ( which generally forms a part of the contract ) cannot be used as a reason for the insurer not to pay the death benefit, as long as it does not constitute fraud on the part of the insured.
Any payoff symmetric 2x2 game will take one of these three forms.
Any finite graph has a finite ( though perhaps exponential ) number of distinct simple cycles, and if the graph is embedded into three-dimensional space then each of these cycles forms a simple closed curve.
Any character or class can use the most basic forms of these, but to master any one of them requires a large commitment in skill points.
Any number of styles can be used to convey these forms.
To comply with the new law, " Any Money Order Office " was rubber-stamped or hand written in place of a specific paying city on the Type II forms.

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