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Friday, December 16, 2011

Fearless Symmetry 4/24: Modular Arithmetic

I read the fourth chapter of Fearless Symmetry.

Part 1: Algebraic Preliminaries

Chapter 4: Modular Arithmetic

Chapter 4 is all about modular arithmetic.

Considering the goal of the book somewhere fields have to be introduced and in this chapter we find the first definition of a field.

Definition: A field is a number system where we can divide by anything nonzero.

Anything more precise would scare off the laymen casual reader for who the book is intended. I kind of like the definition myself. '... where you can divide anything by nonzero'.

Modular arithmetic is introduced as clock arithmetic of course with examples like: "Today is Tue. What day is it in 25 days?" or "The analog clock shows 8. What time will it show in 33 hours?"

Also, the extremely important concept of an equivalence relation is defined. There is much more about modular arithmetic in the book, of course.

To be continued with 5. Complex Numbers

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