Zeno's Paradox (continued)

While browsing through this section for the first time, I came across the "Zeno's Paradox" thread (Space, Time, & Stephen Hawking Jive). The thread is interesting, but seems to veer away from the core of the "paradox."

The reason you never get to Point B is that the situation is described in a way that doesn't allow enough time to elapse for you to get there. Consider an example, where the distance from A to B is 1.0 mile and you are moving at the leisurely pace of 1 mile per hour:

First you go 1/2 mile in 1/2 hour; then 1/4 mile in 1/4 hour; then 1/8 mile in 1/8 hour; etc., etc. The reason you never reach B is that when the situation is described this way, an hour never elapses. The sum:

(1/2 hr + 1/4 hr +1/8 hr +.....)

converges to 1.0 hours, but doesn't get there in a finite number of increasingly small steps. So the seeming paradox arises because the construct assumes (implicitly) that 1.0 hr never passes. Zeno's Paradox boils down to saying (staying with this specific example) that if you're moving at a constant rate of 1.0 mph, you won't cover 1.0 mile unless you allow 1.0 hr to elapse.

Looking at it this way seems to make it less paradoxical.

[thrillhouse7]

I like this answer but not smart enough to vouch for it or go against it. Thanks though. And somebody smarter than me, add something to thiss

[MelchyBeau]

what it is saying is that

Sum(1/(2^n)) < 1 from i=1 to infinity.

The proof is a fairly easy one to do. I'll leave it to your enjoyment to figure out.

Melch