7 base units are defined in physics and other units are derived from these units.
When we say "3 kg of apples", we mention its mass and mass is a base unit.
But for "3 apples", what is its unit? Is this what unitless is?
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Yes, "3 apples" is a value of a dimensionless (unitless) quantity, the number of apples. Quite generally, quantities that are either integer, or very special if they are integer, are unitless.
All 7 base units of the SI system, or any product of their powers (derived units), has the property that it measures an intrinsically continuous quantity such that there is no a priori preferred normalization (i.e. unit) that everyone in the whole Universe would be likely to use.
answered Jun 28, 2014 at 20:27
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1$\begingroup$ The SI unit of amount is the mole so he could have 0.5E-23 moles of apples $\endgroup$ Commented Jun 28, 2014 at 22:07
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$\begingroup$ Thanks but I don't understand what you mean by "a priori preferred normalization" ? $\endgroup$ Commented Jun 29, 2014 at 3:53
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$\begingroup$ Good point, Martin. If an apple is interpreted as a large molecule, indeed, SI has another crazy unit for the number. ;-) user: I mean a choice of the coefficient that everyone without any cultural baggage would consider superior. Like counting apples as 1,2,3. This is very different from 1 meter, 2 meters, 3 meters because others may equally well prefer 1 feet, 2 feet, 3 feet which is something else. $\endgroup$ Commented Jun 29, 2014 at 4:37