On Infinity

The conclusion does not follow from the premises. If there are an infinite number of planets, and if not all of them are inhabited, then there may be an infinite number of inhabited planets or just a finite number.There are an infinite number of natural numbers. Not all of them are greater than 10. In fact, only a finite number are less than 10.There are an infinite number of natural numbers. Not all of then are even. In fact, an infinite number of them are odd.Hope that helps.

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Actually, if their god makes better pancakes, I'm totally switching sides. -- Charley the Australopithecine

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And, if I'm not mistaken, you're a mathematician.

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Heh. A failed mathematician. But better than some of your teachers, it would seem:

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x=0.999...
10x=9.999...
9x=9
x=1

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This is a correct calculation, however the second and third steps do need to be justified. But all this needs to be done using limits; do you remember your calculus? Just nod your head as if you do and we'll proceed.First, we have to figure out what 0.999999... even means. Here is what it means:We have a sequence of numbers:
0.9
0.99
0.999
0.9999
...0.999999... just means the limit of that sequence of numbers. What is the limit? Well, if 1 - 0.999999... = 0, then the limit must be 1. In fact, this is just what it means (the definition) of the limit being equal to 1.So:
1-0.9=0.1
1-0.99=0.01
1-0.999=0.001
1-0.9999=0.0001
...Clearly (meaning that it looks obvious and I don't think anyone wants to see an epsilon-delta proof) the limit really is 0.Hence, 0.999999... = 1.Does that clear anything up?-The whole problem is the idea of infinity. Infinity can get really weird. Look up the Hotel Infinity when you get the chance. (Cool story, even if it doesn't even get to the weirdness of uncountably infinite!)

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Actually, if their god makes better pancakes, I'm totally switching sides. -- Charley the Australopithecine

Be careful, IaJ. Several of us have advanced degrees in mathematics, and others are pretty knowledgeable in this area, too. If you want to learn what "infinity" means, then we can teach you. However, if you insist that you know what you are talking about (and I assure you that you don't), then you are going to get spanked as badly as you are being spanked by Brian and arachnophilia in the archaeology threads.

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I've done everything the Bible says, even the stuff that contradicts the other stuff! -- Ned Flanders