# number

Auxiliary unit of measure | |
---|---|

Unit name | number |

Unit symbol | none |

Formula symbol | , |

Type | Counting measure |

definition |

The **number** is a physical quantity or a calculated value, as a measure of how many objects a set consists of. It is determined by counting . It is an indication of the quantity .

A **countable quantity** (see countability ) is a physical quantity for which a number can be determined as a measure. The *true value* can only be measured exactly with such quantities . The precondition of countability means that the quantity can only assume integer values greater than or equal to 0, i.e. only has natural numbers as values.

Due to the fixed zero point and the unchangeable unit, the number is absolutely scaled . The stochastic term synonymous with number is absolute frequency . The designation absolute frequency, like the designation number, can be applied to physical objects, events of a random experiment or characteristics of characteristics.

## Mathematical basics

Every finite set has a *number of elements* that can be given by a natural number . Counting combinatorics deals with the calculation of such numbers .

There are different approaches in mathematics to extend this concept to infinite sets. One possibility is the *cardinality* , which is no longer expressed with natural numbers, but with infinite cardinal numbers . *Measure theory* , which generally deals with the assignment of numerical values to mathematical structures, offers another approach .

## Measurement technology: Counting measures and counting units (units of measure)

In the SI system of units, no unit of measurement is assigned to the physical quantity *number* as a *quantity of the dimension number* , the addition of an *auxiliary word* , for example “piece”, “unit [s]”, “pair”, “sentence” or the designation of the objects / subjects counted (such as 12 trees) is however tolerated.

- To
*measure the number,*see the sections*Counting*in the article Measuring device and*Analog and digital measurement*in the article Measurement .

There are different *counting measures* and *counting units (units of measure)* , exactly *measuring units of the number* :

- for piece goods one speaks of
*number*of*pieces*, auxiliary unit of measure is*piece*(piece, piece) - In actinometry (radiation measurement)
*particles are common*in the sense of a number of events - particle numbers for amounts of substance are given in the SI-conforming unit mol . - the book of printing (1 book = 24 or 25 sheets (the sheet is one piece))

Other auxiliary *units of* measurement are words that are called *counting* words *(numerical classifiers)* for more specific objects to be counted:

- Typical counting measures next to the
*single item*are the pair , the dozen and the bulk for basic units larger than one. - in the case of persons:
*man*or*head*for the*team*,*Pax*for passengers.

Other old units of measurement can be found under *Old Counting Measures* .

A principle similar to the counting measure is the *place value system* of number systems , which converts units of the order of magnitude (10 ^{0} , 10 ^{1} …) into a positioning within the number (digit 1, digit 2).

## Number density

The size *number **density is* closely related to the size *number* . The number density is equal to the number of objects contained in a space divided by the volume of the space

- .

The spatial area should be chosen so large that it contains a sufficient number of objects and so small that the particle density does not depend on the shape and volume of the spatial area.

The SI unit of number density is m ^{−3} , but the unit cm ^{−3 is} often used.

## Web links

**Wiktionary: number**- explanations of meanings, word origins, synonyms, translations

**Wiktionary: Category: Number classifier**-

**explanations of**meanings, word origins, synonyms, translations