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
Source
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]