Zeno's paradoxes#Achilles and the tortoise

As a paradox of Achilles and the tortoise is a refers to one of several known fallacies that are the ancient Greek philosopher Zeno of Elea attributed ( more qv). It attempts to show that a fast runner like Achilles could never catch a tortoise in a race when he grant her a head start. The course of the argument is as follows:

Before Achilles can overtake the tortoise, he must first obtain their lead. In the time that it needs for the turtle but has gained a new, albeit smaller tab, the Achilles also to go and get. Is he succeeded that the turtle has turn a - way won Tab, and so on - even smaller. The edge that has the turtle will becoming smaller and smaller, but nevertheless always remain a projection, so that the faster runner of the turtle, although more and more approaches, but they never catch up, and thus could not overtake.

In fact, a Faster is a slower one but always ask, if he has only enough time for it. This is proportional to the projection and inversely proportional to the velocity difference of the two runners or with a constant ratio, is inversely proportional to the two speeds. [Note 1]

Zeno's fallacy is based on two errors:

There are different views about what Zeno wanted to show his " paradoxes ". It is often believed that they should support the Eleatic thesis (see Parmenides of Elea ), according to which there is no multiplicity, but only one immutable and indestructible whole give in reality and that the everyday perception of diversity and movement is mere appearance. It is certain, however, that this ancient consideration for conceptualization of infinity has contributed and is still used as a teaching example.

The paradox is delivered directly, but can be found in Aristotle's Physics and Simplicius ' commentary on it.

Related paradoxes that are attributed to Zenon, are the division of paradox and Arrow 's paradox. Content not related to the Zeno paradox is one of Lewis Carroll in his short dialogue What the Tortoise Said to Achilles (What the tortoise said Achilles ) imagined argument with which he addresses the difference between object and metalinguistic implication and occasionally as Carroll Paradox is called.