Zeno’s paradoxes

several arguments proposed by Greek philosopher Zeno of Elea (early 5th century bce) against the ideas of plurality and motion. Individuals making a trip must first go halfway to their destination, then cover half of the remaining distance, then half again, in an indefinite sequence of such steps that appears impossible to complete. Alternatively, if Achilles gives a tortoise a head start in a race and attempts to catch up, he must first run to where the tortoise was, then to where it has moved to, and so on for an infinite sequence of such moves, seemingly never catching up with the tortoise.