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Numbering
There are many different numbering schemes for assigning nominal numbers to entities. These generally require an agreed set of rules, or a central coordinator. The schemes can be considered to be examples of a primary key of a database management system table, whose table definitions require a database design. In computability theory, the simplest numbering scheme is the assignment of natural numbers to a set of objects such as functions, rational numbers, graphs, or words in some formal language. A numbering can be used to transfer the idea of computability and related concepts, which are originally defined on the natural numbers using computable functions, to these different types of objects. A simple extension is to assign cardinal numbers to physical objects according to the choice of some base of reference and of measurement units for counting or measuring these objects within a given precision. In such case, numbering is a kind of classification, i.e. assigning a numeric pro ...
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North American Numbering Plan
The North American Numbering Plan (NANP) is a telephone numbering plan for twenty-five regions in twenty countries, primarily in North America and the Caribbean. This group is historically known as World Zone 1 and has the international calling code ''1''. Some North American countries, most notably Mexico, do not participate in the NANP. The NANP was originally devised in the 1940s by the American Telephone and Telegraph Company (AT&T) for the Bell System and the independent telephone operators in North America. The goal was to unify the diverse local numbering plans that had been established in the preceding decades and prepare the continent for direct-dialing of calls by customers without the involvement of telephone operators. AT&T continued to administer the numbering plan until the breakup of the Bell System, when administration was delegated to the North American Numbering Plan Administrator (NANPA), a service that has been procured from the private sector by the Fede ...
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Telephone Numbering Plan
A telephone numbering plan is a type of numbering scheme used in telecommunication to assign telephone number A telephone number is a sequence of digits assigned to a landline telephone subscriber station connected to a telephone line or to a wireless electronic telephony device, such as a radio telephone or a mobile telephone, or to other devices f ...s to subscriber telephones or other telephony endpoints. Telephone numbers are the addresses of participants in a telephone network, reachable by a system of destination code routing. Telephone numbering plans are defined in each of the administrative regions of the public switched telephone network (PSTN) and in private telephone networks. For public numbering systems, geographic location typically plays a role in the sequence of numbers assigned to each telephone subscriber. Many numbering plan administrators subdivide their territory of service into geographic regions designated by a prefix, often called an area code or ...
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Numbering (computability Theory)
In computability theory a numbering is the assignment of natural numbers to a set of objects such as functions, rational numbers, graphs, or words in some formal language. A numbering can be used to transfer the idea of computability and related concepts, which are originally defined on the natural numbers using computable functions, to these different types of objects. Common examples of numberings include Gödel numberings in first-order logic, the description numbers that arise from universal Turing machines and admissible numberings of the set of partial computable functions. Definition and examples A numbering of a set S is a surjective partial function from \mathbb to ''S'' (Ershov 1999:477). The value of a numbering ''ν'' at a number ''i'' (if defined) is often written ''ν''''i'' instead of the usual \nu(i) \!. Examples of numberings include: * The set of all finite subsets of \mathbb has a numbering \gamma , defined so that \gamma(0) = \emptyset and so that, for eac ...
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Australian Telephone Numbering Plan
The Australian telephone numbering plan describes the allocation of phone numbers in Australia. It has changed many times, the most recent major reorganisation by the Australian Communications & Media Authority taking place between 1994 and 1998. Overview For landline telephony, Australia is now geographically divided into four large areas, three of which cover more than one state and/or territory. All local telephone numbers within these four areas are of eight digits, consisting (mainly) of a four digit exchange code plus a four digit number. The national significant number consists of a single digit area code followed by the local eight digit number – a total of nine digits. Within Australia, to access the number of a landline telephone in an area other than that in which the caller is located (including callers using mobile phones), it is first necessary to dial the Australian trunk code of 0 plus the area code, followed by the local number. Thus, the full national nu ...
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French Telephone Numbering Plan
The French telephone numbering plan is used in Metropolitan France, French overseas departments and some overseas collectivities. France uses a ten-digit closed numbering plan, where the first two digits denote a geographic area, mobile or non-geographic number. * 01 * 02 Northwest France * 03 Northeast France * 04 Southeast France * 05 Southwest France * 06 Mobile phone services * 07 Mobile phone services * 08 Special phone numbers: Freephone () and shared-cost services. * 09 Non-geographic number (used by Voice over IP services) All geographic numbers are dialed in the ten-digit format, even for local calls. The international access code is the International Telecommunication Union's recommended 00. When calling France from abroad, the leading zero should be omitted: for example, to call a number in Southwest France, one would dial +33 5 xx xx xx xx. French people usually state phone numbers as a sequence of five double-digit numbers, e.g., 0x xx xx xx xx (and not, ...
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Computability Theory
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definability. In these areas, computability theory overlaps with proof theory and effective descriptive set theory. Basic questions addressed by computability theory include: * What does it mean for a function on the natural numbers to be computable? * How can noncomputable functions be classified into a hierarchy based on their level of noncomputability? Although there is considerable overlap in terms of knowledge and methods, mathematical computability theorists study the theory of relative computability, reducibility notions, and degree structures; those in the computer science field focus on the theory of subrecursive hierarchies, formal methods, and formal languages. I ...
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