You've reached the **Java** section for illustration of **Peano
Numerals** (pn) as part of a treatment of **Peano Arithmetic** in
computational terms.

We manifest Peano Numbers here via Java Classes for Peano Numerals.
This exercise demonstrates how much tacit and
incidental knowledge accompanies the application of a concrete computational
system to the representation of something of a theoretical nature. Peano
Numbers were chosen because that is about as simple as it gets, it ties to a
body of mathematical-logic knowledge, and it illustrates the complex
difficulties of attaching meaning to computer programs.

The differentiation of Peano Numbers from Peano Numerals is carried out
here so that we can make it clear what it means to represent something in a way
that satisfies requirements of the Peano Arithmetic theory. We will come
to terms with whether or not it is harmless to collapse the two concepts
together, and why (not).

This material will provide an explanation of what this is all about and
how it is material to an understanding of how computers support human endeavors
(and not).

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