"In the paradox of Achilles and the tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 meters, for example. Supposing that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 meters, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 meters. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles arrives somewhere the tortoise has been, he still has some distance to go before he can even reach the tortoise.[11]"

https://en.wikipedia.org/wiki/Zeno%27s_ ... ow_paradox

The paradox is that while the runner will always catch up to the start point of the tortoise, and the tortoise always moves a fraction of its previous distance resulting in a continual "change" in the movements of the runner and the tortoise even though the distance will always be equal.

The turtle may move 1/2 then 1/4 then 1/8 then 1/16 then 1/32 etc. but the movements are a continual progression to zero where the movements themselves are in a continual set of changes. So while the runner never catches up to the tortoise through a series of fractals, where each linear distance effectively becomes a fractal (as well as each line existing as a strict point necessitating the "point" existing as a fractal), the linear distance is continually "moving" through a process of recursion/replication.

Zeno's paraodoxes observe a simultaneous degree of movement and no-movement, and Zeno's Paradoxes contradict themselves.

## The Paradox of Zeno's Paradox (Runner and Tortoise)

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