The NSTP Theoretical Resolution of Zeno's Paradoxes
Zeno of Elea's (b.490 BC) arguments against motion precipitated
a crisis in Greek thought. All of these, concerning motion, have
had a profound influence on the development of mathematics. They
are described in Aristotle's great work 'Physics' and are
presented as four arguments in the form of paradoxes, stated
below :
1. The Racecourse or Dichotomy Paradox -
There is no motion because that which is moved must arrive at
the middle of its course before it arrives at the end. In order
to traverse a line segment it's necessary to reach the halfway
point, but this requires first reaching the quarter - way point,
which first requires reaching the eighth - way point, and so on
without end. Hence motion can never begin.
This problem isn't alleviated by the well - known infinite sum