Naming and Ordering Natural Numbers (Mathematics Foundations 188)
Associate Professor of Mathematics
This lecture systematically defines natural numbers as primitive expressions, examining their nomenclature and organization. It delineates the distinction between cardinal and ordinal number usage and introduces the successor operation for natural number ordering.
Now that we have a clear idea of what a (primitive) natural number is, how should we name them? And how should we organize them? And how do we use them, or perhaps what uses for them do we have in mind?
In this video we give a simplified system for naming natural numbers (Nat) which is really more or less the only one possible, except for a choice of word: mark/stroke/unit/something/one. We show how to count using Nat, and discuss the differences between cardinal and ordinal usage of numbers. And we introduce the idea of the natural ordering of primitive natural numbers, with the successor operation. It is important to remind people that we are dealing with objects here of a particularly simple and immediate nature: they are expressions of exactly the following form: