[pdurrant]

Originally Posted by HarryT

The reason for it is...

Spoiler:

...that if Achilles is running at a constant speed, and the track is extending at a linear rate (any linear rate), his progress along the track will be some divisor of the arithmetic series:

1 + 1/2 + 1/3 + 1/4 + ...

and that series, as can trivially be shown, sums to infinity:

Group the terms as:

1/2 + (1/3 + 1/4) + (1/5 + 1/6 + 1/7 + 1/8), etc, doubling the number of terms each time. Each group sums to at least 1/2, so we have an infinite number of halves, which sums to infinity.

No matter HOW fast the track stretches linearly, therefore, Achilles will reach the end.

Yes, spot on.