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 Posted: Mon Sep 11, 2006 4:43 pm
Ok the underlying question here is, will achilles ever overtake the turtle.
Ok, Achilles and a turtle are racing. Achilles being the nice guy he is, lets the turtle have a 100m lead. The turtle moves at 10meters/minute and Achilles moves at 10x the turtles speed. But the turtle moves at 1/10 his original speed every minute. This race goes theoretically on forever.
So
T= 100 + 10 + 1 + .1 + .01 + .001 And so on.
A= 0 + 100 + 10 + 1 + .1 + .01 +.001 and so on.
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My opinion ( please do not read unless you have absolutely no opinion otherwise, we want to see what you think out of logic and personal inspiration)
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Ok, what I think is that he will not ever over take it. He will always be a place counter behind the turtle. Because 111.11111~ /=/ 111.111111~ -1
But inversely it can be argued that T=111.111111~= 111. 1/9
And because it goes on forever A=111.111111111~= 111. 1/9
So then they would be equal 111.1/9=111.1/9 A=T and if achilles is 10x so out of logic it passes it.
But as I said I want your opinion, not mine.
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Posted: Mon Sep 11, 2006 10:45 pm
Calculus says that Zeno's paradoxes aren't paradoxes.
I think there's already a discussion somewhere about subtracting 1 off the end of an infinite string in which the verdict there (as it is everywhere else in mathematics) is that it's a meaningless operation. 111.11111~ = 111.1111~-1 as that last -1 doesn't mean anything. Infinity - 1 = infinity, so an infinite string of 1s is the same as an infinite-1 string of 1s.
Also, if you're still checking the thread in the sci-tech forum, there's a wikipedia link that mentions some philosophical objections to the calculus answer, stating that because Achilles would have had to complete an infinite sequence of operations, he couldn't overtake the tortoise. That is complete bulllshit (see calculus), and is one of the many reasons that I despise "philosophers". Never trust a "philosopher" to deal with mathematics.
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Posted: Tue Sep 12, 2006 4:13 am
Haha ya, this was also tying off the ends of an experiment I had. Also I wanted to see what people thought of the problem. I posted my thinking in the ED main forum.
What I was testing was how answers were given in the
A) Math/Physic Guild answers were undicisive because almost no one answered.
B) In Sci/Tech (people do this all the time) to prove someone wrong or right, they do not argue, the do not discuss, they do not even talk. All they do is post links and hope that it supports thier idea.
C) In the main forum, people discuss it, prove it themselves and try to teach others how it is done.
WINNER OF MOST HELPFUL ISSSSS....
C
followed by
A
lastly and the one that should be blown to tiny pieces
B
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Posted: Wed Sep 13, 2006 11:49 pm
Yeah, well, this guild is slow. And you'd be amazed (and slightly disturbed) how many mathematical proofs are nothing but lists of references with little bits of algebra in between, so a list of links in place of arguments is par for the course.
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Posted: Fri Sep 15, 2006 5:00 pm
Layra-chan Yeah, well, this guild is slow. And you'd be amazed (and slightly disturbed) how many mathematical proofs are nothing but lists of references with little bits of algebra in between, so a list of links in place of arguments is par for the course. The old joke about the mathmatician, the physicist and the fire? Though, ED:S&T is beyond a joke.
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Posted: Tue Sep 19, 2006 6:01 am
what main forum, you mean the ED?
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Posted: Tue Sep 19, 2006 1:18 pm
poweroutage what main forum, you mean the ED? That's what I would think. I mean, if he asked in the CB…
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