more from Shaughan Lavine

Single Idea 15904

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts]

Full Idea

Roughly speaking, the upper and lower parts of the Dedekind cut correspond to the commensurable ratios greater than and less than a given incommensurable ratio.


'Commensurable' implies 'knowable'

Gist of Idea

The two sides of the Cut are, roughly, the bounding commensurable ratios


Shaughan Lavine (Understanding the Infinite [1994], II.6)

Book Reference

Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.38

A Reaction

Thus there is the problem of whether the contents of the gap are one unique thing, or many.