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A unit-entity UX [x] of elementary entity type X is a single countable object (X = molecules, cells, organisms, particles, parties) or a single countable event (X = beats, collisions, emissions, decays, celestial cycles, instances, occurences, parties). "An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles" (Bureau International des Poids et Mesures 2019).

If an object is defined as an assembly of particles (a party of two, a molecule as the assembly of a stoichiometric number of atoms), then the entity is the assembly but not the assembled particle. A number of defined elementary units UX is a count, NX = N·UX [x], where N is only a number and as such N is dimensionless. The elementary unit UX has the dimension U of the count NX. The elementary unit UX has the same unit [x] as the count NX, or more accurately it gives the count the defining 'counting-unit' [x]. From the definition of count as the number (N) of elementary units (U) of entity type X, it follows that count divided by elementary unit is simply a number, N = NX·UX-1. The unit uN of a count can neither be the entity X nor a number. The elementary entity type X defines the identity X of the elementary unit UX with the unit 'counting-unit' with symbol [x]. Since a count NX is the number of unit-entities, the unit-entity UX is not a count (UX; it is not identical with N·UX).

Abbreviation: UX [x]

Reference: BEC2020.1 doi10.26124bec2020-0001.v1

Communicated by Gnaiger Erich (2020-05-20) last update 2020-07-06
in: Anastrophe XX Entity X and the elementary unit x of A X-mass Carol

Elementary entity-type, unit-entity, and elementary unit

In Euclid's Elements (Book VII) a "unit" is defined as 'a single individual thing'. Take 'individual thing' as equal to elementary entity. Then we see in Euclid's definition a kaleidoscopic imaging of Number, Unit, Count, Entity — NUCE (in nuce), which remains a CASE to this day (CASE represents the Counting-Assembling-Sorting Experience).
Entity-type X is distinguished from unit-entity UX. Dual-message code may lead to misunderstanding depending on context. For example, X = ce in 'cell mass' is normally understood as meaning "the mass of all entities of entity-type ce in a sample", mce [kg]. In contrast, X = body in the context of body mass and body mass index (BMI) is used in dual-message code, mbody. Body mass with dual-message code means the mass of all entities of entity-type human body, mbody [kg], divided by the number of bodies, Nbody, which leads to the explicit canonical expression MUbody = mbody·Nbody-1.
  • Colour code: Colour red may be used in X, indicating that the term entity or symbol X are used in dual-message code, meaning both entity-type and unit-entity. When specifying "single entity X" it is sufficiently clear that X is used in dual-message mode, and the term "number of X" is equally clear to meaning "number of unit-entities X", NX = N·UX-1. Similarly, in the term "O2 flow per cell" IO2/ce" it is sufficiently clear that ce is used in in dual-message code.

Base quantities and count

Quantity Symbol for quantity Q Symbol for dimension Name of SI unit Symbol for SI unit uQ [*]
length l L meter m
mass m M kilogram kg
time t T second s
electric current I I ampere A
thermodynamic temperature T Θ kelvin K
amount of substance *,§ nX = NX·NA-1 N mole mol
count *,$ NX X elementary unit x
unit-entity *,$ UX U elementary unit x
charge *,€ QX = NX·zX·e I·T coulomb C = A·s
luminous intensity Iv J candela cd
[*] »SI base units, except for the canonical 'elementary unit' [x]. The following footnotes are canonical comments.
* For the quantities n, N, U, and Q, the entity-type X of the unit-entity U has to be specified in the text and indicated by a subscript: nO2; Nce; QX.
§ Amount nX is an elementary quantity, converting the elementary unit [x] into moles [mol] using the Avogadro constant, NA.
$ Count NX equals the number of unit-entities UX. In the SI, the quantity 'count' is explicitly considered as an exception: "Each of the seven base quantities used in the SI is regarded as having its own dimension. .. All other quantities, with the exception of counts, are derived quantities" (Bureau International des Poids et Mesures 2019 The International System of Units (SI)). A unit-entity UX is not a count (UX is not a number of UX). NX has the dimension X of a count and UX has the dimension U of a unit-entity, and both quantities have the same unit, the 'elementary unit' [x].
Charge is a derived SI quantity. Charge is an elementary quantity, converting the elementary unit [x] into coulombs [C] using the elementary charge, e, or converting moles [mol] into coulombs [C] using the Faraday constant, F. zX is the charge number of entity X, which is a constant for any defined entity X. QX = nX·zX·F


Bioblast linkReferenceYear
Gnaiger Erich (2020) A X-mass Carol. Body Mass Excess and mitObesity. MitoFit Preprint Arch 2020.4.v0.
Gnaiger Erich et al ― MitoEAGLE Task Group (2020) Mitochondrial physiology. Bioenerg Commun 2020.1. doi:10.26124/bec:2020-0001.v1.2020


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Bioblast links: SI base units - >>>>>>> - Click on [Expand] or [Collapse] - >>>>>>>
Entity, count, and number, and SI base quantities / SI base units
Quantity name Symbol Unit name Symbol Comment
unit-entity UX elementary unit [x] UX, UB; [x] not in SI
count NX elementary unit [x] NX, NB; [x] not in SI
number N - dimensionless = NX·UX-1
amount of substance nB mole [mol] nX, nB
electric current I ampere [A] A = C·s-1
time t second [s]
length l meter [m] SI: metre
mass m kilogram [kg]
thermodynamic temperature T kelvin [K]
luminous intensity IV candela [cd]
Fundamental relationships
» Avogadro constant
» Boltzmann constant
» elementary charge
» Faraday constant
» gas constant
SI and related concepts
» International System of Units
» International Union of Pure and Applied Chemistry, IUPAC
» entity
» quantity
» dimension
» format
» motive unit

MitoPedia concepts: Ergodynamics