1 (number)

The one (1) is a natural number between zero and two. It is odd, a square and a cube number.

Mathematical properties

The number 1 is not prime, but dividing each natural number. It is often taken to be the smallest natural number (but some authors include the natural numbers from zero ). Your prime factorization is the empty product with 0 factors, which is defined as having the value 1. The 1 is often referred to as one of the five most important constants of Analysis (besides 0, π, e, and i). The Euler's identity

Establishes a simple relation between these mathematical constants.

The 1 is also used in other meanings in mathematics, such as a neutral element for multiplication in a ring, called the identity element. In these systems, different rules can apply, so 1 1 has different meanings and can yield different results. With 1 are in linear algebra and vectors, and one Einsmatrizen whose elements are all equal to the identity element, and refers to the identity map.

Importance in the computer science

In computer science, the one thing is very important as it is, together with the zero part of the binary system. It stands in the machine language for " On" (On) and recover in programming languages ​​as the data type boolean variable ( 1 = true = true, 0 = false = false).

In data modeling are clarified and described to each other (especially in the Entity -Relationship Model ), in which relationships and frequencies of entities, plays the " to - one " relationship an important role, since it determines the uniqueness of an assignment. For example, is the entity " vehicle " for entity "owner" in "N -to-1 " relationship: An owner can have several motor vehicles, but every car must have exactly one owner.


Symbol 1

The symbol 1 is used as digit of the value system. Is the number 1 alone, so it means after the usual interpretation of the number one. In particular, the 1 is the largest number in the binary system.

In Germany, the number 1 is handwritten drawn mainly in two moves: A vertical line and a smaller slash. In other countries such as England, however, only a vertical line is drawn. The German spelling with two strokes is therefore often mistakenly read in England than 7. When writing Roman numerals and often binary numbers is the one drawn in Germany as a stand alone line.

Recurring decimal

The number one has in addition to the usual letters than 1 a periodic Dezimalbruchdarstellung as.

This statement can be proved in various ways, for example by the following:

Reduction to a known infinite decimal fraction

This proof is widely used - but there is this to consider:

Array of real numbers

Equality is a consequence of the fact that two real numbers x and y are different only if there is a real number Z, which is located between them, for the thus x

Limit of a sequence of numbers

Is the limit of the sequence of numbers The general term of this sequence. The difference between and is. For every little one finds a n for all. So by the definition of the limit.

Geometric series

For the periodic Dezimalbruchdarstellung

This is an infinite geometric series of the form. Such series are convergent and have the value. With and yields the sum value as.

Other important systems

In other value systems delivers the highest point of the particular system in place of the number 9. In the binary system is thus equal to 1, in hexadecimal 0, FFF ... etc.

Other number fonts

The roman numeral one is I. In the Hebrew Scriptures, the letter Aleph ( א ) has the numerical value of one, in the Arabic script its equivalent, the Alif ( ا ). The Arabic characters for the fuel is 1; in Bengali, the number 1 is also written in Devanagari 1 in Malayalam and one in Chinese一.

Other meanings

  • The fuel used in many countries as a school grade and under, including Germany and Austria for " very good", but referred to in Switzerland, the worst grade.
  • In the symbolism of numbers, the 1 is often used as a symbol for everything the beginning or God (see Chinese numerology ).
  • The Sch ᵉ ma Yisroel is the oldest expression of Jewish self- understanding and includes the unity and Oneness of God ( Adonai Adonai echad = ( is ) one). The Shema expression includes the monotheistic essence of Judaism and the central context of the Torah, in which the core message of the charity is embedded:


Words that express a uniqueness, often begin with the Greek prefix mono, about monocle or monographs, or is derived from the Latin singularis or solus as singular or solo.

Words that express a uniformity are often derived from the Latin unus: Union or uniform. Even words represent the uniqueness, such as Unique, plain ... are derived from the Latin unus.

Where reference is made to the rank or sequence reference, the Latin root prim - used, such as Primus or prime.