The "Real" Number System

Why the Quotes?

It seems that our life in the real physical world is what produced the real numbers [_1_].

However, when we look at the finished product [_2_],
we find it to be a pure logical construct - with no real connection to the physical world.



Understanding is never immediate because it comes with use which takes time and SUBSEQUENT MATERIAL.

"In mathematics, you don't understand things. You just get used to them."
- John von Neumann


The    STARTING POINT     was found by looking back in history to the point when there were no pure, abstract, numbers: There were only one, two, and many, ATTACHED, to the things counted.


CONSEQUENTLY:    Our set of objects, the numbers, starts empty:

I like to think that the double vertical line in the 'R' represents the quotes I have put around the 'real' word.

The curly braces,   { },   are used to write down sets, and the elements of the set go between the braces.

The slashed 'o' is a symbol for the empty set.

This is a working draft for the start of my new project. It is based on [2] Introduction to Analysis, plus [1] Menninger below.

The starting point was inspired by material found in Karl Menninger's book:

A cultural History of Numbers
Dover Republication, 1992