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Single Idea 10856

[from 'Paradoxes of the Infinite' by Bernard Bolzano, in 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.