Quantity: Number, or
If you check 'number' in this
Dictionary, you'll find 'quantity' - which is on purpose, to indicate
that we have here a very fundamental concept. And it would seem as if
human beings all start from an intuitive assumption of the natural
or counting numbers, and have to surrect their understanding of
number and quantity on its foundations (moving to fractions, rational
numbers, roots, real numbers etc.)
There are various generalizations of the natural numbers that go
beyond what non-mathematical people would consider numbers naturally.
Two examples of somewhat special numbers are complex numbers or
quaternions; an example of something that is in quite a few
respects like a number - can be summed, multiplied, divided - but is
more complicated are matrices.
Similarly, the entities that make up the stock of higher mathematics,
such as integrals and differentials, are quantities that
carry more assumptions and subtleties with them than mere natural
numbers can account for.
And there are special problems relating to quantities of various
kinds when these enter into or are used for measurements, and there are
related problems of scales of measurement, that are often defined by
reference to the sort of mathematical operations that can be used with
the quantities considered, and that may be quite subtle.