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.

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KEY

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

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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.

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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:

NUMBER WORDS AND NUMBER SYMBOLS
A cultural History of Numbers
Dover Republication, 1992

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