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Full Idea
The idea that an infinite number of instants make up an infinitely long time is not true, and therefore the conclusion that Achilles will never overtake the tortoise does not follow.
Gist of Idea
The tortoise won't win, because infinite instants don't compose an infinitely long time
Source
Bertrand Russell (Our Knowledge of the External World [1914], 6)
Book Ref
Russell,Bertrand: 'Our Knowledge of the External World' [Routledge 1993], p.178
A Reaction
Aristotle spotted this, but didn't express it as clearly as Russell.