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Talk:Quantities, symbols, and units

From Bioblast
Since units are of such fundamental importance for consistency of meaning, it should not be surprising that one of the biggest areas of confusion is the application of the quantity 'count', as a consequence of the lack of an explicit unit in the International System of Units (SI). In the SI the quantity 'count' is given the unit 1, which is not written. Then the units of extensive quantities amount of B nB [mol], electric charge Q [C], mass of sample s ms [kg], volume of B VB [m3] or [L] are not different from the units of these quantities expressed per count. Quantity per count means quantity of X per single X. The term 'single X refers to a count NX with a value of NX = 1 in the SI format (but NX = 1 x in the explicit format). Since the SI gives identical units to the extensive quantities and the 'per count quantities', a check for consistency is impossible on the basis of units. Compare the extensive quantity electric charge Q [C] with QB in the equation defining the charge number of B, zB,
Eq. 3: zB = QB·e-1
In the SI, elementary charge e has the unit coulomb [C]. However, e does not have the dimension of electric charge, but electric charge per count (unit [C·x-1] in the explicit system). The dimension of QB cannot be deduced from the units in the SI: Quantities relating to counting .. are just numbers (Bureau International des Poids et Mesures 2019 The International System of Units (SI) p. 151). As a consequence of the quantity 'count' given the meaning of 'just numbers' in the SI, count has neither a unit nor a dimension in the SI. Q and QB have the same SI units but different dimensions, both with equally negative consequences. In the explicit system, the meaning of QB [C·x-1] is signalled in the units: it is a count-specific ('per count') quantity in contrast the extensive quantity Q [C]. Neither the name 'elementary charge' nor the SI unit [C] reveal the important meaning of this quantity, which is a universal constant declared by the SI on 2019-05-20. Add to 'elementary charge' the term 'per proton' and the counting unit [x] to the message, then the meaning is immediately clear — 'elementary' means 'per count:
Term Symbol and definition Unit
electric charge Qel = Iel·t [C] = [A·s]
elementary charge (per proton) e = Qel·NH+-1 [C·x-1]
elementary charge per substance B QB = Qel·NB-1 [C·x-1]
count of protons NH+ = Qel·e-1 [x]
count of substance B NB = Qel·QB-1 [x]
charge number per count of protons, elementary charge number of H+ zH+ = QH+·e-1 = 1 nondimensional
charge number per count B, elementary charge number of B zB = QB·e-1 = NH+·NB-1 nondimensional