Get the latest tech news
What are the real numbers, really? (2024)
The real real numbers—what are they? Must we answer?
Russell explains how one may undertake this creation process explicitly, building the real numbers as a mathematical structure that fulfills Dedekind's completeness property. Indeed, one can prove that the real numbers construed as Dedekind cuts or as equivalence classes of Cauchy sequence are complete ordered fields and thereby fulfill Hilbert's axioms. In particular, the question of whether the real numbers are categorically characterized by the property of Suslin's hypothesis is itself independent, neither provable nor refutable from the axioms of set theory.
Or read this on Hacker News
