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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2004-05-26 16:04 -0700 (pdt) by orcmid