more from Bernard Bolzano

Single Idea 10856

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

Full Idea

A truly infinite quantity (for example, the length of a straight line, unbounded in either direction) does not by any means need to be a variable.

Gist of Idea

A truly infinite quantity does not need to be a variable

Source

Bernard Bolzano (Paradoxes of the Infinite [1846]), quoted by Brian Clegg - Infinity: Quest to Think the Unthinkable 10

Book Reference

Clegg,Brian: 'Infinity' [Robinson 2003], p.131


A Reaction

This is an important idea, followed up by Cantor, which relegated to the sidelines the view of infinity as simply something that could increase without limit. Personally I like the old view, but there is something mathematically stable about infinity.