The Axioms required to make the theoretical machinery operate are set out tersely and powerfully, so that all permissible operations within the theory can be traced rigorously back to these axioms, rules, and primitive notions.

The individual articles set the rules for current and future operations of the United States government.

While there is no generally accepted formal definition of " algorithm ," an informal definition could be " a set of rules that precisely defines a sequence of operations.

But humans can do something equally useful, in the case of certain enumerably infinite sets: They can give explicit instructions for determining the nth member of the set, for arbitrary finite n. Such instructions are to be given quite explicitly, in a form in which they could be followed by a computing machine, or by a human who is capable of carrying out only very elementary operations on symbols.

AVL trees are often compared with red-black trees because they support the same set of operations and because red-black trees also take O ( log n ) time for the basic operations.

A key point which is often overlooked is that published lower bounds for problems are often given for a model of computation that is more restricted than the set of operations that you could use in practice and therefore there are algorithms that are faster than what would naively be thought possible.

The ARIN membership elects the Board of Trustees ( BoT ), which has ultimate responsibility for the business affairs and financial health of ARIN, and manages ARIN's operations in a manner consistent with the guidance received from the Advisory Council and the goals set by the registry's members.

Typical examples of binary operations are the addition (+) and multiplication (×) of numbers and matrices as well as composition of functions on a single set.

This type of algebraic structure captures essential properties of both set operations and logic operations.

Ownership of the track and infrastructure passed to Railtrack, whilst passenger operations were franchised to individual private sector operators ( originally there were 25 franchises ) and the freight services sold outright ( six companies were set up, but five of these were sold to the same buyer ).

Axiomatic set theory was developed in response to these early attempts to study set theory, with the goal of determining precisely what operations were allowed and when.

Hardwired into a CPU's design is a list of basic operations it can perform, called an instruction set.

In many CPU designs, an instruction set will clearly differentiate between operations that load data from memory, and those that perform math.

The purpose of programming is to create a set of instructions that computers use to perform specific operations or to exhibit desired behaviors.

; The Common Type System ( CTS ): A set of data types and operations that are shared by all CTS-compliant programming languages.

A complex instruction set computer ( CISC, ) is a computer where single instructions can execute several low-level operations ( such as a load from memory, an arithmetic operation, and a memory store ) and / or are capable of multi-step operations or addressing modes within single instructions.

In the Babbage design, one iteration i. e. one full set of addition and carry operations happens once for four rotations of the crank.

Meanwhile, the arguments of the transformation group operations composition and inverse are elements of a set of bijections, A → A.

These three operations are repeated until no new states can be added to the set.

Intuitively, a field is a set F that is a commutative group with respect to two compatible operations, addition and multiplication, with " compatible " being formalized by distributivity, and the caveat that the additive identity ( 0 ) has no multiplicative inverse ( one cannot divide by 0 ).

The most common way to formalize this is by defining a field as a set together with two operations, usually called addition and multiplication, and denoted by + and ·, respectively, such that the following axioms hold ; subtraction and division are defined implicitly in terms of the inverse operations of addition and multiplication :< ref group =" note "> That is, the axiom for addition only assumes a binary operation The axiom of inverse allows one to define a unary operation that sends an element to its negative ( its additive inverse ); this is not taken as given, but is implicitly defined in terms of addition as " is the unique b such that ", " implicitly " because it is defined in terms of solving an equation — and one then defines the binary operation of subtraction, also denoted by "−", as in terms of addition and additive inverse.

the purpose of producing plays at the College is three-fold: to provide the Carleton students with the best possible opportunity for theater-going within the limits set by the maturity and experience of the performers and the theatrical facilities available ; ;

When sufficiently accurate and complete measurements are available, it will be possible to set limits on the thermal and electrical characteristics of the surface and subsurface materials of the moon.

A useful by-product of this system is that the information necessary to set the gyro drift biases is available from the currents necessary to hold the system in level.

Information is also available from this autocollimator system to set the drift bias for the Z-axis gyro.

This will be true, even without expanding the available instruction set available to the programmer.

Thus the axiom of choice is not generally available in constructive set theory.

Based on a newer, slightly more flexible, version of the Asters original Motorola MC6845 video chip, the Rockwell 6545, it worked by adding a new video mode, one with the ability to reprogram an extended, ( 2048 characters instead of 256 characters ) version of the character set, supported by an extended character memory of the video card that did not use one ( 8 bit ) byte per character, but an 11 bit " word ", so it could address each one of the available 2048 unique programmable characters.

When AA was ported to the English Electric KDF9 computer, the character set was changed to ISO and that compiler has been recovered from an old paper tape by the Edinburgh Computer History Project and is available online, as is a high-quality scan of the original Edinburgh version of the Atlas Autocode manual.

The Number Resource Policy Manual, ARIN ’ s complete set of current policies, is available at https :// www. arin. net / policy / nrpm. html.

As time progressed, most terminal programs began using the ANSI standard, but could use their native character set if it was available.

A small selection was issued on a 1971 LP and a 2-cassette set of the series ' soundtrack was made available in the late 1990s.

Series 1 was also made available as a 2-cassette set.

The set of agreements used by a partnership about the meaning of each call is referred to as a bidding system, full details of which must be made available to the opponents ; ' secret ' systems are not allowed.

The enhanced assembler's source program was then assembled by its predecessor's executable ( A1 ) into binary or decimal code to give A2, and the cycle repeated ( now with those enhancements available ), until the entire instruction set was coded, branch addresses were automatically calculated, and other conveniences ( such as conditional assembly, macros, optimisations, etc.

Ogden's word lists include only word roots, which in practice are extended with the defined set of affixes and the full set of forms allowed for any available word ( noun, pronoun, or the limited set of verbs ).

It includes 19 of the band's greatest hits and is also available in a box set with a 25 track DVD of their music videos.

The wagers, and their associated odds, that are typically available are set out in the table below.

The existing terms and structures available to them were often insufficient to express these new set of religious concepts, and taken together, these new forms of discourse led to the beginnings of Christology as an attempt to understand, explain and discuss their understanding of the nature of Christ.

A context menu offers a limited set of choices that are available in the current state, or context, of the operating system or application.

These controls are only available when a set of application programs are customized for each data entry and updating function.

The Davros Mission is an original audio adventure ( without the Doctor ) available on the Complete Davros Collection DVD box set.

Economic efficiency describes how well a system generates desired output with a given set of inputs and available technology.