(UTC)

Any line segment can be divided continuously ad infinitum.
At all times, with each division, the length of each part shortens by a half,
while at the same time, the number of parts multiplies by two.
So, how can an infinite number of parts
make up a finite whole? Because for every division, the lengths
of the parts are reducing as fast as the number of parts are increasing.   

There is not enough in sources for Zeno's writings to fully justify saying that Zeno ever actually claimed that the sum of an infinite number of numbers is infinite - though he has been interpreted that way by some. What is clear is that he thinks a task with an infinite number of steps cannot be completed.   01:03, 10 August 2012