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Single Idea 18253

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

Full Idea

You need a double transition, from cardinal numbes (Anzahlen) to the rational numbers, and from the latter to the real numbers generally. I wish to go straight from the cardinal numbers to the real numbers as ratios of quantities.

Gist of Idea

I wish to go straight from cardinals to reals (as ratios), leaving out the rationals

Source

Gottlob Frege (Letters to Russell [1902], 1903.05.21), quoted by Michael Dummett - Frege philosophy of mathematics 21 'Frege's'

Book Ref

Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.270


A Reaction

Note that Frege's real numbers are not quantities, but ratios of quantities. In this way the same real number can refer to lengths, masses, intensities etc.