The real numbers provide a simple example: Each real number is uniquely defined, and collectively they form an algebraic
field under the operations of addition and multiplication. The identity elements for addition (“zero”) and multiplication
(“one”) are uniquely fixed, and all rational numbers may be generated from them by iterating the operations of addition,
multiplication and their inverses subtraction and division. Real numbers may then be defined by Dedekind cuts between sets of
rational numbers.