Chapter 12: The Principle of Computational Equivalence

Section 9: Implications for Mathematics and Its Foundations

[Axioms for] real analysis

The axiom given is Dedekind's axiom of continuity, which expresses the connectedness of the set of real numbers. Together with set theory it allows standard results about calculus to be derived. But as well as ordinary real numbers, these axioms allow non-standard analysis with constructs such as explicit infinitesimals (see page 1172).

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