1: One Without Another:
The first of a series of videos in which we look at some very foundational (or anti-foundational) issues in mathematics and reality.
Norman Wildberger has made a comprehensive playlist of videos that present a heap of well-informed topics in mathematics. He is adamant that the widespread faith in the existence of the real numbers (the continuum considered as numerical) is misplaced. I share his view. The following three videos provide some of his arguments in a form suited to a general public with curiosity about mathematics:
Video 115: The mostly absent theory of real numbers ( • The mostly absent theory of real numbers|R... )
Video 116: Difficulties with Dedekind cuts ( • Difficulties with Dedekind cuts | Real num... )
Video 117: The continuum, Zeno's paradox, and the price we pay for coordinates ( • The continuum, Zeno's paradox and the pric... )