The paper introduces a distinction between true metric and parametric quantities, units and dimensions. It claims in its first part that these distinctions shed important light both on the base quantity amount of substance and VIM's definitions of kind of quantity and quantity dimension. The second part is devoted to the unit one, and it claims that this unit must be regarded as a parametric unit, but also that it is not as needed as has been thought. The third part takes for granted that both the mole and the unit one are parametric units, and it argues that, for pedagogical reasons, the mole should be exchanged for the unit one, and the parametric quantity amount of substance be renamed as 'elementary entities'.
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