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Single Idea 8738

[catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite]

Full Idea

Euclid's Postulate 2 says the geometer can 'produce a finite straight line continuously in a straight line'.

Gist of Idea

Postulate 2 says a line can be extended continuously


report of Euclid (Elements of Geometry [c.290 BCE]) by Stewart Shapiro - Thinking About Mathematics 4.2

Book Reference

Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.87

A Reaction

The point being that this takes infinity for granted, especially if you start counting how many points there are on the line. The Einstein idea that it might eventually come round and hit you on the back of the head would have charmed Euclid.