"Counting" may seem like a simple topic, but there's more to
it than you might think.
The Peano Postulates --
Proving the properties of natural numbers using the Peano Postulates, which
have been formulated so that zero is not included in the set of natural
numbers. (There's quite a debate about this
Zero a Natural Number? -- a discussion of the fact that some authors
include zero, and others do not.
Introduction to Counting -- explains what
mathematicians mean by "counting" -- that is, putting sets in
Construction -- Construction of sets
of numbers, starting with the original Peano Axioms, formulated so that zero is
included in the set of natural numbers.
Set Theory -- an introduction to sets, including
examples of some standard sets.
Counting Ordered Pairs of
Integers -- An explanation of the "square spiral" that puts the
set of natural numbers in one-to-one correspondence with the set of rational
Counting the number of times Friday
the 13th occurs.
Counting the number of
partitions of n into
powers of two such that no power is used more than twice.