We introduce some basic orientation towards the difficulties with real numbers. In particular the differences between computable and uncomputable irrational numbers is significant. Then we discuss the relation between fractions and repeating decimals, giving the algorithms for converting back and forth, familiar from high school. The operations of addition and multiplication for repeating decimals are more subtle, and involve some lovely number theoretical aspects.The current theory of `real numbers' is logically deeply flawed. Essentially this theory is awol---everyone refers to it, but no one can tell us where it it is actually written down properly and completely. We are moving here towards the realization that mathematics is really about rational numbers, and theories that can be built from them in a finite and completely precise way. Hello future mathematics!
Does mathematics make logical sense? No, it does not. Foundational issues have been finessed by modern mathematicians, and this series aims to turn things around. And it will have interesting things to say also about mathematics education---especially at the primary and high school level. The plan is to start right from the beginning, and to define all the really important concepts of basic mathematics without any waffling or appeals to authority. Roughly we discuss first arithmetic, then geometry, then algebra, then analysis, then set theory. This course is aimed for a general audience, interested in mathematics, or willing to learn.