Perturbing All Points in R^d into a General Position

We prove that there is a way to move each point in less than a prescribed amount, so that no two points are moved to the same point, and the resulting set of points are in a general position (i.e. no three points are in a line, no four points are in a plane, andContinue reading “Perturbing All Points in R^d into a General Position”

Borel’s Proof of the Heine-Borel Theorem

We present a polished version of Borel’s proof based on Cantor’s theory of sets. More specifically, we use transfinite recursion and the fact that any strictly decreasing sequence in a well-ordered set is finite in length.