Let's say I start out at one end of a football field and begin walking toward the other end zone. When I reach the 50, it would be accurate to say that I have halved my original distance from the end zone. When I reach the 25, it would be accurate to say I've halved that remaining distance, and when I'm 12 and a half yards away, it would be accurate to say that I've halved that remaining distance. So one accurate description of my approach would be "continuously halving remaining distances from the end zone."
We know from mathematics that a number can be infinitely halved and will never reach zero because there will always be some infintesimal fraction remaining. Nevertheless, I will eventually find myself in the end zone, having not only reached zero, but surpassed it.
Is it actually inaccurate to describe me as halving the distances, and, if so, why does this seemingly incontrovertible description fail? Or is it that something I do not understand happens when I get there
2006-08-13
16:53:25
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18 answers
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asked by
Matt F
1
in
Physics