Full Idea
Frege fixed on construing real numbers as ratios of quantities (in agreement with Newton).
Gist of Idea
Real numbers are ratios of quantities
Source
report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Michael Dummett - Frege philosophy of mathematics Ch.20
Book Reference
Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.261
A Reaction
If 3/4 is the same real number as 6/8, which is the correct ratio? Why doesn't the square root of 9/16 also express it? Why should irrationals be so utterly different from rationals? In what sense are they both 'numbers'?