On Infinity

I was recently reading The Restaurant at the End of the Universe by Douglas Adams, and in it I found the following passage: Now let's assume for the sake of argument that the first two sentences are correct. Is the conclusion Adams draws from these two statements correct?For simplicity, let's say there is only one uninhabited planet. That follows the premises, right? So all but one of the infinite worlds in the universe are inhabited. My question is: Is the number of inhabited worlds finite or infinite?It seems to me it must be infinite. If it's a finite number, then adding the one uninhabited planet to find the total number of planets would render a finite number, which is impossible given the premise of an infinite number of worlds.So who's right? Me or Douglas Adams?Big Bang and Cosmology? Coffee House? Somewhere else?

Good. I'm not just crazy.After discovering this thread's promotion and your and others' responses, I decided to check out what Wikipedia says about the subject. Quoting the Yajur Veda, it says: So, basically, I'm right. As you said, there could be a finite number of planets, but it's not necessarily so. Right. Because -10=, there are an infinite number of natural numbers over ten. Because /2=. I think I've got the hang of this.On a slightly related note, a friend and I were arguing over whether or not .999...=1. He contended that it didn't, while I contended that it did. I used the following proof (which he was previously familiar with): He said the problem with the proof was in the second line. His claim was that 0.999... went on till infinity, but when multiplied by ten it only went to infinity minus one, so the subtraction on the next line would leave one 9 at the end left over. But infinity minus one is still infinity, so there is no 9 left over (nor is there an end).And, if I'm not mistaken, you're a mathematician. I've been dying to hear from a reliable source. (Besides Wikipedia, I've asked two math teachers at my school, who both said .999... doesn't equal one, but I didn't bother with any proofs or challenge their answers.) Does 0.999... equal 1?

You can make anything equal anything if you use an invalid proof. Usually, this involves division by zero.

Actually I'm in calculus at the moment. I know what a limit is, at least in relation to lines and graphs, but I've never dealt much with sequences. What you're saying makes sense, but I wouldn't be able to prove it mathematically. I did, and I quite enjoyed it. Very strange.

Sounds like you were right, though, like Creavolution, I wouldn't say a line is finite on one end. It certainly has a starting point, but that doesn't make it finite. I remember someone (cavediver, I believe) called the sort of line you're describing as semi-infinite. And if you cut an infinite line in two points, you would have two semi-infinite lines and one finite line.But that's just infinite lines. Infinity itself is a whole different matter.

Ha! I should have known. Douglas Adams is a smart guy, and with as much illogic as there is in the rest of the book, it should have been obvious that it was a joke. But either way, it helped me gain a deeper understanding of the concept of infinity.

Yeah, he did. He didn't reference any specific quotes from Adams himself, but he seems rather knowledgeable on the subject, so I take his word.

The 'tweak on people's tails' did refer back to God, but only as a comparison. AZPaul3 wrote:

quote:

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Just like Ulan Colluphid’s blockbuster trilogy, “Where God Went Wrong,” “Some More of God’s Greatest Mistakes” and “Who Is This God Person, Anyway?” the “infinity” issue was a tweak on peoples’ tails.

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Emphasis mine. I think Paul was just saying, "Like the trilogy of books about God, the part on infinity was a joke."