- Ku, Yin Bon (Albert)
Given a certain set of real numbers . Suppose for any two real numbers in , , , and (if is non-zero) are also in , we say that is a field. Addition, subtraction, multiplication and division are collectively called rational operations. Examples
- The set of all rational numbers is obviously a field.
- The set of all constructible numbers is also field because we have already shown that addition, subtraction, multiplication and division can be done by Euclidean constructions, which implies that if and are two constructible numbers, , , and (if is non-zero) are also constructible numbers.