Wednesday, July 27, 2016

MF89: Fractions and repeating decimals (English)

...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!

UPDATE 30-07-2016:

This video is an exploratory video in which we loosely introduce an interesting variant on repeating decimals: namely 10-adic numbers, or repeating reversimals (this is our own name). These are decimal-like objects whose digits carry on to the left, rather than the right, but still in a periodical fashion. Surprisingly, the arithmetic with these "repeating reversimals" parallels that of repeating decimals...