more from A.George / D.J.Velleman

Single Idea 10107

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers]

Full Idea

One reason for introducing the real numbers is to provide answers to square root problems.

Gist of Idea

Real numbers provide answers to square root problems


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

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.70

A Reaction

Presumably the other main reasons is to deal with problems of exact measurement. It is interesting that there seem to be two quite distinct reasons for introducing the reals. Cf. Ideas 10102 and 10106.

Related Ideas

Idea 10102 The integers are answers to subtraction problems involving natural numbers [George/Velleman]

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