Editing Zeno's paradoxes (section)

==== Achilles and the tortoise<!--'Achilles and the Tortoise' and 'Achilles and the tortoise' redirects here--> ====
{{Redirect|Achilles and the Tortoise}}
{{See also|Infinity#Zeno: Achilles and the tortoise|selfref=yes}}
[[File:Zeno Achilles Paradox.png|thumb|Achilles and the tortoise]]

{{ quote
| In a race, the quickest runner can never over&shy;take the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.| as recounted by [[Aristotle]], [[Physics (Aristotle)|''Physics'']] VI:9, 239b15
}}
In the paradox of '''Achilles and the tortoise'''<!--boldface per WP:R#PLA-->, [[Achilles]] is in a footrace with a tortoise. Achilles allows the tortoise a head start of 100 meters, for example. Suppose that each racer starts running at some constant speed, one faster than the other. 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 2 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. As Aristotle noted, this argument is similar to the Dichotomy.<ref>{{cite encyclopedia |last=Huggett |first=Nick |url=http://plato.stanford.edu/entries/paradox-zeno/#AchTor |title=Zeno's Paradoxes: 3.2 Achilles and the Tortoise |year=2010 |encyclopedia=[[Stanford Encyclopedia of Philosophy]] |access-date=2011-03-07 |archive-date=2022-03-01 |archive-url=https://web.archive.org/web/20220301174333/https://plato.stanford.edu/entries/paradox-zeno/#AchTor |url-status=live }}</ref> It lacks, however, the apparent conclusion of motionlessness.