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Ah, What I Like To Call The Irrelavent Infinite

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Posted by Rich on February 23, 2001 20:22:35 UTC

Distances are relative, especially when including the sizes of an object. 1/2 to 1/4 to 1/8 to 1/16, etc... will lead to an insignificant number at which the rabbit will be right next to the turtle and win by just "a hare"! Ha! I bet you didn't see that coming. Luckily in my racing experiences, I haven't come into this problem of not be able to pass people because of this silly problem. The major problem with that person's reasoning is that he is taking a two vector problem and simplfying it to a single vector problem. He ignores time! He would only be allowed to use that logic if AND ONLY IF the rabbit was lessening the lead by a factor of two in equal time segments. Turtle has 10 meter lead at time 0, then 5 at time 3 secs, then 2.5 at time 6 secs, then 1.25 at time 9 secs, then .625 at time 12 secs, etc... In that case, the rabbit will never seem to catch up to the turtle. BUT!!! that isn't the case. For the rabbit if moving at a rate of 5 m/s and the turtle at 4 m/s. So through simple dynamics, the rabbit must pass the turtle because what is really happening is the opposite of what Mr. Philosophy is talking about. Rather than the distance being cut in half to infinity, the time is. Turtle with 10 meter lead at time 0, 5 meter lead at time 3 secs, 2.5 meter lead at time 4.5 secs, 1.25 meter lead at 5.75 seconds.
Philosophers love to switch situations and make the impossible seem possible and visa versa, but they are playing with the variables.
As to the irrelavent infinite, lets look at how many numbers are in between 1 and 2. There are an infinite decimals between 1 and 2. Does that mean that it is impossible to reach the number 2? NO! Why? Because that infinity is an irrelavent infinite.

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