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Stephen Wolfram's A New Kind of Science | Online

Notes

Chapter 10:Processes of Perception and Analysis

Section 11:Traditional Mathematics and Mathematical Formulas


Primitive [Boolean] functions

There are several possible choices of primitive functions that can be combined to represent any Boolean function. In DNFAnd,Or andNot are used.Nand = Not[And[##]] & alone is also sufficient, as shown on page619 and further discussed on page807. (It is indicated by in the main text.) The functionsAnd,Xor andNot are equivalent toTimes,Plus and1 - # & for variables modulo 2, and in this case algebraic functions likePolynomialReduce can be used for minimization. (See also page1102.)

Further development:— The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics (2022)

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