more from A.George / D.J.Velleman

Single Idea 10102

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number]

Full Idea

In defining the integers in set theory, our definition will be motivated by thinking of the integers as answers to subtraction problems involving natural numbers.

Gist of Idea

The integers are answers to subtraction problems involving natural numbers


A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.63

A Reaction

Typical of how all of the families of numbers came into existence; they are 'invented' so that we can have answers to problems, even if we can't interpret the answers. It it is money, we may say the minus-number is a 'debt', but is it? Cf Idea 10106.

Related Idea

Idea 10106 Rational numbers give answers to division problems with integers [George/Velleman]