abstractmath.org 2.0
help with abstract math

Produced by Charles Wells     Revised 2017-02-16
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# NUMBERS

This section has four chapters that briefly describe the basic types of numbers used in math:

You will be familiar with most of what is talked about here, but some of the details may surprise you. I have concentrated on the properties that cause trouble to people new to abstract math.

I don't define the types of numbers discussed here. In proofs involving these number systems, math texts rarely explicitly mention the definition of the system; instead, the proofs are based on known properties of the system. For each system of numbers, this chapter gives a collection of properties of the system, emphasizing the properties that beginning abstractmath students may not be familiar with. Those collections of properties form a partial specification of each kind of number.

The definition of integer, real number, etc, may be stated explicitly in the beginning of books on real analysis or foundations of math. The Seton Hall analysis site and Wikipedia are good online sources for the definitions and some of their properties.