Posted 31 July 2007
This section has five 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, I
just give you some of their basic properties. Those collections of properties
form a partial specification of each kind of number. In proofs involving these
number systems, math texts rarely mention explicitly the definition of the
system; instead, the proofs are based on known properties of the system.
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.