constructing the rationals
Summary
The rational numbers can be constructed from the integers.
Context
This concept has the prerequisites:
- equivalence relations (The rational numbers are defined as equivalence relations.)
- order relations (One needs to define an ordering on the rationals.)
- constructing the integers (The rationals are constructed from the integers.)
- fields (One must show the rational satisfy the field axioms.)
Goals
- Construct the rational numbers from the integers
- Define addition, multiplication, additive and multiplicative inverses, and the comparison operators
- Show that these definitions satisfy the field axioms
Core resources (read/watch one of the following)
-Paid-
→ Elements of Set Theory
An introductory textbook on axiomatic set theory.
Location:
Chapter 5, "Construction of the real numbers," subsection "Rational numbers," pages 101-111
See also
-No Additional Notes-