The Nature of Numbers

For interest's sake we discuss different types of numbers: ordinals, cardinals as well as measures, and just names.

The first is a count in order as in a sequence. They are called ordinals: first, second, third ... 25'th  ... 100'th and on. For instance competition places, then as first, gold medal, or then silver and bronze and a list of contenders.

Cardinals give an amount, how many elements a set has. How many fingers have I? What was your score on the exam paper, in cents, how much exactly is in my wallet?

In both above kinds the numbers are distinct, discrete, consisting of positive integers each member is alone and isolated. It gets very interesting when you are working with very large sets, and very surprisingly infinitely many levels of such different infinities exist.

In turn, measures consist as a continuum. There are non-distinct (non-discrete) types of amounts, real numbers that are called measures. Like the distance from here to Cape Town in meters or water in the sea in liters. Or my weight in kg's. In principle your units may theoretically be subdivided indefinitely and in theory until infinitesimal.

Finally then are numbers that have no significance in themselves and are simply names, figures like on a car's number plate and existing of decimal digits without further meaning. Or my passport number. Or the result on casting a dice.

However strictly speaking a given number often belongs to more than one of these kinds. It depends on the context.

Of course more familiar, from a technical viewpoint you have positive and negative integers, rationals, real numbers and complex numbers. This is a different classification.