# number

Auxiliary unit of measure
Unit name number
Unit symbol none
Formula symbol ${\ displaystyle N}$, ${\ displaystyle n}$
Type Counting measure
definition ${\ displaystyle \ mathrm {1}}$

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 :

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

${\ displaystyle {\ text {number density}} = {\ frac {\ text {number of objects}} {\ text {volume}}}}$.

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.