03-10-2009, 05:57 PM
airhornahole Wrote:From the discussion, some people would say that difference between 0.999.... and 1 is so small it can be ignored.
Let me ask this question.
If you had a $15 million boat, would you rather miss an iceberg by the difference between the two or by ignoring it, sink your boat?
It may be infinitesimally (sp?) small, but the difference is still there.
No there is no difference, that's kind of the point. .999... keeps going to infinity. If there is an unimaginably small distance between the boat and the iceberg, because that difference goes to infinity, there is a distance that is always smaller so at no point can you make a distinction between when the iceberg and boat are touching or when they are not. When you stop and acknowledge any distance between the boat and the iceberg, you aren't considering the fact that you are dealing with infinity.