12-13-2003, 08:39 PM
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#186
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FFR Music Producers

Join Date: Oct 2003
Location: My lair
Posts: 163
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I'd just like to say something about the first quote. I still think it's very cool, and very interesting, but flawed in my opinion.
Okay, so there are infinite planets. Only some of them are inhabited. There would be some fraction of inhabited vs. uninhabited planets. It doesnt matter how small this fraction is (like 1/1000000000000000000000000), but any fraction of infinity is still infinity, meaning there would be an infinite population.
This goes back to a discussion we had in AP Calculus.
Let's say on a line graph.
There are points plotted on 1, 2, and 3
There are an infinite amount of points that you could place between 1 and 2 (like 1.1, 1.01, 1.001, etc.). This is also true with 2 to 3 (2.01, 2.001, etc.)
But what about from 1 to 3? There still is an infinite amount of points you could place in there, but isnt there more that you could place than in the smaller increments? After all, it goes from 1 all the way to 3
In other words, could one infinity be larger than another?
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