Notes

Chapter 12: The Principle of Computational Equivalence

Section 9: Implications for Mathematics and Its Foundations


Properties [of logical primitives]

Page 813 lists theorems satisfied by each function. {0, 1, 6, 7, 8, 9, 14, 15} are commutative (orderless) so that a b = b a, while {0, 6, 8, 9, 10, 12, 14, 15} are associative (flat), so that a (b c) = (a b) c. (Compare page 886.)



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From Stephen Wolfram: A New Kind of Science [citation]