1 (number)

1 (one; /ˈwʌn/ or UK /ˈwɒn/, also called unit, unity, and (multiplicative) identity), is a number, a numeral, and the name of the glyph representing that number. It represents a single entity, the unit of counting or measurement. For example, a line segment of unit length is a line segment of length 1.

As a number

One, sometimes referred to as unity, is the integer before two and after zero. One is the first non-zero number in the natural numbers as well as the first odd number in the natural numbers.

Any number multiplied by one is that number, as one is the identity for multiplication. As a result, one is its own factorial, its own square, its own cube, and so on. One is also the result of the empty product, as any number multiplied by one is itself. It is also the only natural number that is neither composite nor prime with respect to division, but instead considered a unit.

As a digit

The glyph used today in the Western world to represent the number 1, a vertical line, often with a serif at the top and sometimes a short horizontal line at the bottom, traces its roots back to the Indians, who wrote 1 as a horizontal line, much like the Chinese character 一. The Gupta wrote it as a curved line, and the Nagari sometimes added a small circle on the left (rotated a quarter turn to the right, this 9-look-alike became the present day numeral 1 in the Gujarati and Punjabi scripts). The Nepali also rotated it to the right but kept the circle small. This eventually became the top serif in the modern numeral, but the occasional short horizontal line at the bottom probably originates from similarity with the Roman numeral I. In some countries, the little serif at the top is sometimes extended into a long upstroke, sometimes as long as the vertical line, which can lead to confusion with the glyph for seven in other countries. Where the 1 is written with a long upstroke, the number 7 has a horizontal stroke through the vertical line.

−1

In mathematics, −1 is the additive inverse of 1, that is, the number that when added to 1 gives the additive identity element, 0. It is the negative integer greater than negative two (−2) and less than 0.

Negative one bears relation to Euler's identity since e^πi = −1.

In software development, −1 is a common initial value for integers and is also used to show that a variable contains no useful information.

Negative one has some similar but slightly different properties to positive one.

Algebraic properties

Multiplying a number by −1 is equivalent to changing the sign on the number. This can be proved using the distributive law and the axiom that 1 is the multiplicative identity: for x real, we have

where we used the fact that any real x times 0 equals 0, implied by cancellation from the equation

In other words,

so (−1) · x is the arithmetic inverse of x, or −x.

Square of −1

The square of −1, i.e. −1 multiplied by −1, equals 1. As a consequence, a product of two negative real numbers is positive.

Number (magazine)

Number is the leading Japanese sports magazine published on every Thursday by Bungeishunju. The official name is Sports Graphic Number. Though the circulation once hit 47 million, it is now around 10 million.

The first issue, released in April 1980, drew attention by the piece Enatsu's 21 balls (江夏の21球, Enatsu no 21 kyu). Yet the magazine failed to return a profit for the next 10 years. Today however, the magazine is one of the most profitable publications of Bungeishunju. The success of the magazine also led other rival publishers to launch sports magazines, though they tend to be less successful.

References

Personal Communications Services area codes

Area codes 500, 533, 544, 566 and 577 are non-geographic area codes reserved for personal communications services. The 500 code was authorized by the United States Federal Communications Commission, and introduced into the North American Numbering Plan in 1995.

In 1995 AT&T introduced a "follow-me" service under the brand name of AT&T True Connections using the 500 area code. It was designed to replace the AT&T EasyReach 700 service. Other local exchange carriers and interexchange carriers introduced similar competitive services.

AT&T True Connections service was not well received. Companies, hotels, and others with PBX equipment continued to block the dialing of 500 because it was a caller-paid number. Phone-sex services also began using the 500 prefix and forwarding the calls to various foreign countries.

The 500 prefix is still registered to a variety of phone companies, and is being used for non-geographic services including dial-up modem access.

Non-geographic telephone numbers in the United Kingdom

A non-geographic number is a type of telephone number that is not linked to any specific locality. Such numbers are an alternative to the traditional 'landline' numbers that are assigned geographically using a system of location-specific area codes. Non-geographic numbers are used for various reasons, from providing flexible routeing of incoming phone calls to generating revenue for paid-for services.

Functionality

Non-geographic numbers were introduced to offer services that were historically unavailable on standard landline phone numbers, particularly in terms of call routeing and special charging arrangements. Advertised benefits of non-geographic numbers include: