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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 Ref
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]
| 5109 | The fast runner must always reach the point from which the slower runner started [Zeno of Elea, by Aristotle] |
| 1507 | We don't have time for infinite quantity, but we do for infinite divisibility, because time is also divisible [Aristotle on Zeno of Elea] |
| 21585 | The tortoise won't win, because infinite instants don't compose an infinitely long time [Russell] |
| 7557 | To solve Zeno's paradox, reject the axiom that the whole has more terms than the parts [Russell] |
| 14149 | The Achilles Paradox concerns the one-one correlation of infinite classes [Russell] |
| 21690 | Whenever the pursuer reaches the spot where the pursuer has been, the pursued has moved on [Quine] |
| 8075 | Space and time are atomic in the arrow, and divisible in the tortoise [Devlin] |
| 4229 | An infinite series of tasks can't be completed because it has no last member [Lowe] |
| 20457 | Zeno assumes collecting an infinity of things makes an infinite thing [Rovelli] |