Let's restate the Zeno argument as follows.
(1) At time t2 Achilles reaches a point where the tortoise was at t1, at t3 he reaches the point where the tortoise was at t2, at t4 he reaches the point where the tortoise was at t3, and so on.
(2) Achilles will not reach the tortoise before the sequence outlined in (1) above is completed,
(3) The sequence is never completed.
(4) Achilles will never reach the tortoise.
Unlike the IEP version I referenced below, the conclusion appears to follow logically from the premisses. Furthermore, it does not rely on assumptions like 'cannot do infinitely many things in a finite time'. It relies simply on the definition of an infinite sequence as one which is endless, not terminated, not completed.
Well it appears valid, but is it? More tomorrow, and comments welcome.