The results for testing numbers for divisibility in base 10 are laid out here. It appears we’ll be reaching the rational numbers at some point in the spring of 2012.
The fifteenth lesson of the Math From Scratch series, dealing with the Fundamental Theorem of Arithmetic, is available here.
The next chapter in the Math From Scratch series is available here. We can now define a division algorithm involving remainder.
We can finally define distances, which allows us to establish the number line. Those tools are presented in lesson 13: Metric Spaces Other Than Canada.
With the bases representation theorem established, we can examine the bases that are common to computer science, and how they have plagued some of the more adept Nintendo players of by generation. Lesson 12: Other Bases.
In our eleventh lesson, we can formally justify the number representation we inherited from Arab mathematicians so many centuries ago. I hope you enjoy All Your Bases Are Belong To Us.
Some regions have seen a trend towards multiplying numbers from left to right instead of right to left in recent years. An explanation of how this “works” and my own personal critique of the methods can be found here.
Our tenth lesson introduces ring theory, which allows us to define several familiar concepts: One Algebra To Rule Them All. Remember, past lessons can all be found by clicking on the “math from scratch” tag below.
Part nine of a number that I hope will be finite: Cosets and Cardinality. Remember, past lessons can all be found by clicking on the “math from scratch” tag below. Also, try as I might, I couldn’t find a natural ZZ Top reference to work into this lesson dealing with Lagrange’s Theorem. Suggestions are welcome in the space below.
Part eight of a number that just keeps getting bigger: Mappings and Functions. Remember, past lessons can all be found by clicking on the “math from scratch” tag below.