back to ideas for this text


Single Idea 11042

[from 'Categories' by Aristotle, in 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers ]

Full Idea

A line is a continuous quantity. For it is possible to find a common boundary at which its parts join together, a point.

Gist of Idea

Parts of a line join at a point, so it is continuous

Source

Aristotle (Categories [c.331 BCE], 04b33)

Book Reference

Aristotle: 'Categories and De Interpretatione', ed/tr. Ackrill,J.R. [OUP 1963], p.13


A Reaction

This appears to be the essential concept of a Dedekind cut. It seems to be an open question whether a cut defines a unique number, but a boundary seems to be intrinsically unique. Aristotle wins again.