Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a unit of measurement.
Some quantities are such by their inner nature (as number), while others function as states (properties, dimensions, attributes) of things such as heavy and light, long and short, broad and narrow, small and great, or much and little.
Under the name of multitude comes what is discontinuous and discrete and divisible ultimately into indivisibles, such as: army, fleet, flock, government, company, party, people, mess (military), chorus, crowd, and number; all which are cases of collective nouns.
In science, quantitative structure is the subject of empirical investigation and cannot be assumed to exist a priori for any given property.
The linear continuum represents the prototype of continuous quantitative structure as characterized by Hölder (1901) (translated in Michell & Ernst, 1996).
A fundamental feature of any type of quantity is that the relationships of equality or inequality can in principle be stated in comparisons between particular magnitudes, unlike quality, which is marked by likeness, similarity and difference, diversity.
A further generalization is given by the theory of conjoint measurement, independently developed by French economist Gérard Debreu (1960) and by the American mathematical psychologist R. Duncan Luce and statistician John Tukey (1964).
The essential part of mathematical quantities consists of having a collection of variables, each assuming a set of values.
Setting the units of measurement, physics covers such fundamental quantities as space (length, breadth, and depth) and time, mass and force, temperature, energy, and quanta.
The word ‘number’ belongs to a noun of multitude standing either for a single entity or for the individuals making the whole.
[5] Radians serve as dimensionless units for angular measurements, derived from the universal ratio of 2π times the radius of a circle being equal to its circumference.