Single Idea 14149

[catalogued under 5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox]

Full Idea

When the Achilles Paradox is translated into arithmetical language, it is seen to be concerned with the one-one correlation of two infinite classes.

Gist of Idea

The Achilles Paradox concerns the one-one correlation of infinite classes

Source

Bertrand Russell (The Principles of Mathematics [1903], §321)

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.350


A Reaction

Dedekind's view of infinity (Idea 9826) shows why this results in a horrible tangle.

Related Idea

Idea 9826 A system S is said to be infinite when it is similar to a proper part of itself [Dedekind]