The Avogadro number is an integer multiple of the number “1”

In early civilizations, the question ‘‘how much is there?’’ could be related to a number of cattle, soldiers, days, or denarii (a denarius is a Roman silver coin current 187 B.C.–274 A.D.). It gave rise to the development of a numbering system 1, 2, 3, ... enabling to quantitatively express a number of things (generically called entities). Counting them by means of numbers is a very old way of obtaining an answer to the question ‘‘how much is there?’’ It also gave rise to special names for defined numbers such as a dozen (for 12) or a gross (for 144, i.e. 12 dozens). However, counting of things is only related to discrete entities since a fraction-of-entity is not meaningful nor even possible (that would destroy the very concept of discrete entity). The unit for measuring such numbers is quite simple: it is (the natural number) 1. Contrary to the requirement that results of measurements are expressed as a number times a stated unit [1], the unit is not written after the number in the case of counting because adding ‘‘times 1’’ after a number, is somewhat superfluous. [Numbers are termed ‘‘natural’’ when fractions are not possible and ‘‘real’’ when fractions are possible such as in 17.52 m] Numbers used in counting are independent of the nature of the entities. The quantity involved is ‘‘number of entities’’ which ‘‘can be regarded as a base quantity in any system of units’’ according to entry 1.4 NOTE 3 in [2]. Their measurement unit is one, symbol 1 ‘‘which can be regarded as a base unit in any system of units’’ according to entry 1.10 NOTE 3 in [2]. According to another usage, the term used to designate a quantity (‘‘number of entities’’) must not be used in naming the unit. Twenty-first century analytical sciences make it possible that (very) small numbers of atoms and molecules can be counted in, e.g. a measurement of a few hundreds of atoms or molecules by isotope dilution mass spectrometry. Single electron tunnelling has been achieved and opens the possibility of counting single electrons. The number of particles in a specified volume of laboratory air in ‘‘clean’’ laboratories’’ for (ultra-) trace analysis, serves to express the quality of the laboratory air is, e.g. ‘‘class 100’’ when the air contains 100 or less than 100 particles of less than 0.5 lm per cubic foot (a US standard in the field). The simplest and most convenient unit to express such measurement results is (the natural number) 1. As the number of entities measured in analytical work becomes larger, counting of discrete entities comes with a significant measurement uncertainty (a rate of 10 s can be achieved by modern ion counters with an acceptably small counting uncertainty such as ffiffiffiffiffiffiffiffiffiffiffi