## Description

A **unit** is defined as 'a single individual thing' in Euclid's *Elements* (Book VII). This defines the elementary entity *U*_{X} of entity-type *X* (thing). The International System of Units defines the unit as 'simply a particular example of the quantity concerned which is used as a reference'. Then the *value* of a quantity *Q* is the product of a number *N* and a unit *u*_{Q}. The symbols *U*_{X} and *u*_{Q} are chosen here with *U* and *u* for 'unit': *U*_{X} is the Euclidean or entetic unit ('eunit'), and *u*_{Q} is the abstract unit ('aunit'). Subscripts *X* and *Q* for 'entity-type' and 'quantity-type' reflect perhaps even more clearly than words the contrasting meanings of the two fundamental definitions of an entetic versus abstract 'unit'. The term 'unit' with its dual meanings is used and confused in practical language and the scientific literature today. In the elementary entity *U*_{X}, the unit (the 'one') relates to the entity-type *X*, to the single individual thing (single individual or undivided; the root of the word *thing* has the meaning of 'assembly'). The quantity involved in the unit of a single thing is the *count*, *N*_{X} = *N*ยท*U*_{X} [x]. In contrast to counting, a unit *u*_{Q} is linked to the measurement of quantities *Q*_{u} = *N*ยท*u*_{Q}, such as volume, mass, energy; and these quantities โ and hence the units *u*_{Q} โ are abstracted from entity-types, pulled away from the world of real things. The new SI (2019-05-20) has completed this total abstraction of units, from the previous necessity to not only provide a quantitative definition but also a physical realization of a unit in the form of an 'artefact', such as the international prototype (IPK) for the unit kilogram. The new definitions of the base SI units are independent of any physical realization: *u*_{Q} is separate from *X*. The classical unit of Euklid is the elementary unit for counting, entirely independent of measuring. Therefore, the quantity count is unique with respect to two properties: (*1*) in contrast to all other quantities in the metric system, the count depends on quantization of entities *X*; and (*2*) in the SI, the **N**umber 1 is the **U**nit of the **C**ount of **entities** โ NUCE.

**Abbreviation:** *U*_{X} [x]; *u*_{Q}

**Reference:** Bureau International des Poids et Mesures 2019 The International System of Units (SI), MitoFit 2020.4

Communicated by Gnaiger Erich (2020-07-06) last update 2020-08-14 in: AnastropheXXEntityofXand elementary unit xX-mass Carol

**MitoPedia concepts:**
Ergodynamics