The numbers package provides a tower of numeric types that are all implementations of numbers.Number. Additionally, the fractions and decimal modules provide extension numeric types: fractions.Fraction and decimal.Decimal. These definitions roughly parallel the mathematical thought on the various classes of numbers. An article available at http://en.wikipedia.org/wiki/Number_theory contains numerous links to in-depth explanations; for example, An Introduction to the Theory of Numbers.
The essential question is how well computers can implement the underlying mathematical abstractions. To be more specific, we want to be sure that anything that is computable in the abstract world of mathematics can be computed (or approximated) using a concrete computer. This is why the question of computability is so important. The idea behind a Turing complete programming language...
