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Page "Category (mathematics)" ¶ 16
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Any and class
:* Any total order on X has exactly one equivalence class, X itself, because x ~ y for all x and y ;
Any definition which focuses on amusement leaves us unsatisfied since the feelings experienced by a world class chess player are very different from those of a circle of children playing Duck Duck Goose.
Any class that needs a " polymorphic constructor " capability derives itself from the abstract base class, and implements the clone () operation.
:: Theorem ( Lefschetz theorem on ( 1, 1 )- classes ) Any element of H < sup > 2 </ sup >( X, Z ) ∩ H < sup > 1, 1 </ sup >( X ) is the cohomology class of a divisor on X.
Any masculinity project aimed at restoring or reclaiming a ' traditional ' male role for privileged white, heterosexual males has a political impact within the tapestry of class, race, and gender power.
Any asteroid with this trait is considered an Amor class asteroid, regardless of its semi-major axis, eccentricity, aphelion, inclination, physical properties, orbital stability, or place of origin.
Any class is permitted to join, as the guild focus is mostly social.
Any system in a large class known as linear, time-invariant ( LTI ) is completely characterized by its impulse response.
With calls by students to occupy the UC Berkeley campus, Chancellor Birgeneau sent a letter, dated November 7, 2011, to the campus community stating " Any activities such as pulling fire alarms, occupying buildings, setting up encampments, graffiti, or other destructive actions that disrupt with anyone's ability to conduct regular activities -- go to class, study, carry out their research, etc.
Any bounded operator L that has finite rank is a compact operator ; indeed, the class of compact operators is a natural generalisation of the class of finite-rank operators in an infinite-dimensional setting.
Any student of Christian Science who has taken two-week class instruction in Christian Science healing may use the initials ' C. S .,' and take patients as a practitioner.
Any ring homomorphism A → B gives a map K < sub > 0 </ sub >( A ) → K < sub > 0 </ sub >( B ) by mapping ( the class of ) a projective A-module M to M ⊗< sub > A </ sub > B, making K < sub > 0 </ sub > a covariant functor.
Any investment in services that help lift Latinos into the middle class is an investment in the future of the entire country .”
Any proper complexity function can be used to define a complexity class, but only certain classes are useful to study.
He released two singles, the Alchemist-produced " The Man, The Icon ", and the DJ Premier-produced " Any Type of Way " ( on which he discusses urban collapse in post-9 / 11 New York City (" Giuliani got New York lookin ' like it's Amistad ") and the erosion of the middle class.
Any following reallocation of tram classes between depots, including the mooted retirement of the unpopular ( due to numerous noise and ongoing safety / maintenance issues ) and now more than four decades-old Z1 / 2 class trams, is currently in a state of contention until plans are formally announced.
* Interfaces: Any interfaces in the class
* Fields: Any fields in the class
* Methods: Any methods in the class
* Attributes: Any attributes of the class ( for example the name of the sourcefile, etc.
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 race can be any class ( with some conditions ).

Any and can
He merely said, `` Any good decorator these days can make you a tasteful home ''.
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 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 needy family living in San Francisco can obtain toys by writing to Christmas Toys, 676 Howard street, San Francisco 5, and listing the parent's name and address and the age and sex of each child in the family between the ages of 1 and 12.
Any breach of these laws is a criminal offence and can lead to fine of up to £ 5, 000 or six months in prison.
Any use of antibiotics can increase selective pressure in a population of bacteria to allow the resistant bacteria to thrive and the susceptible bacteria to die off.
* Any ring A can be considered as a Z-algebra in a unique way.
Any of these body styles can optionally incorporate a " cutaway ".
Any Latin-American country can join the 1980 Montevideo Treaty.
Any given bookmaker will weight their odds so that no one customer can cover all outcomes at a profit against their books.
Any node in the data structure can be reached by starting at root node and repeatedly following references to either the left or right child.
Any Banach algebra ( whether it has an identity element or not ) can be embedded isometrically into a unital Banach algebra so as to form a closed ideal of.
Any of these ways can be criticized for ...
* Any locally compact Hausdorff space can be turned into a compact space by adding a single point to it, by means of Alexandroff one-point compactification.
Any Sangiovese-based wine made according to the Chianti guidelines from these vineyards can be labelled and marked under the basic Chianti DOCG should the producer wish to use the designation.
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 convex polyhedron can be distorted into a canonical form, in which a midsphere ( or intersphere ) exists tangent to every edge, such that the average position of these points is the center of the sphere, and this form is unique up to congruences.
Any person who uses the Spanish title of " Doctor " ( or " Dr .") without being included in this Government database can be prosecuted for fraud.
Any player on the kicking team behind the kicker, and including the kicker, can recover the kick.
Any sound that can be sampled can be used.
Any ellipse can be obtained by rotation and translation of a canonical ellipse with the proper semi-diameters.
# 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.

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