Fractions and repeating decimals | Real numbers and limits Math Foundations 89 | N J Wildberger

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!

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My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger

My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.

Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics' most important subjects!

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Видео Fractions and repeating decimals | Real numbers and limits Math Foundations 89 | N J Wildberger канала Insights into Mathematics