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]