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altairian · 12-14-2003, 06:00 AM

Ok time for me to throw my hat in the ring on this whole infinity bit, since I just took a course on logic and proofs and the last thing we covered was cardinality, I know a thing or two

(this will get a little technical and if you don't know anything about mathematical sets and number theory, you might not understand everything I say)
First off, what cardinality is, is basically taking 2 sets of anything and saying "these sets are the same size" or "these sets are not the same size". There are also two classifications of infinity, countably infinite and uncountably infinite. So we all know that the set of all positive integers is infinite right? But the set of all integers is countably infinite because you can count the number of elements between any two elements within the set (in other words, you know how many integers there are between, for example, 1 and 1,000,000,000,000,000,000). It's the set of positive integers that is used for cardinality comparisons in higher mathematics. The reason I'm saying all this is because the set of all planets in the universe would also be considered countably infinite...and I just think it's really interesting

For anyone wondering, the main difference between countably and uncountably infinite sets is that the countable ones we can actually kind of comprehend the size of in our minds... an uncountably infinite set is just too massive to comprehend. If you'd like an example, just think of the set of real numbers. How many real numbers are there between 0 and 1?

To answer Rage, yes one infinity can be larger than another infinity. It's weird I know, but it does make sense.

Ok, sorry about the long explanation, but it does have a real point to it, which is this... Yes the universe is infinite, so yes there is an infinite number of worlds. Since there is an infinite number of worlds, there is also an infinite number of worlds capable of sustaining life. The reason? A smaller infinity is still infinity. If you take the set of all positive even integers, it's still infinite right? Or even the set of all positive integers that are divisible by 10, or 100, or 1,000. No matter how much you tried, how long you lived, how fast you could search, you could never travel around the universe and eventually be able to say "I've visited every planet capable of sustaining life in the universe".

12-14-2003, 06:00 AM	#193
altairian FFR Player Join Date: Sep 2003 Location: Potsdam, NY Posts: 2,055	Ok time for me to throw my hat in the ring on this whole infinity bit, since I just took a course on logic and proofs and the last thing we covered was cardinality, I know a thing or two (this will get a little technical and if you don't know anything about mathematical sets and number theory, you might not understand everything I say) First off, what cardinality is, is basically taking 2 sets of anything and saying "these sets are the same size" or "these sets are not the same size". There are also two classifications of infinity, countably infinite and uncountably infinite. So we all know that the set of all positive integers is infinite right? But the set of all integers is countably infinite because you can count the number of elements between any two elements within the set (in other words, you know how many integers there are between, for example, 1 and 1,000,000,000,000,000,000). It's the set of positive integers that is used for cardinality comparisons in higher mathematics. The reason I'm saying all this is because the set of all planets in the universe would also be considered countably infinite...and I just think it's really interesting For anyone wondering, the main difference between countably and uncountably infinite sets is that the countable ones we can actually kind of comprehend the size of in our minds... an uncountably infinite set is just too massive to comprehend. If you'd like an example, just think of the set of real numbers. How many real numbers are there between 0 and 1? To answer Rage, yes one infinity can be larger than another infinity. It's weird I know, but it does make sense. Ok, sorry about the long explanation, but it does have a real point to it, which is this... Yes the universe is infinite, so yes there is an infinite number of worlds. Since there is an infinite number of worlds, there is also an infinite number of worlds capable of sustaining life. The reason? A smaller infinity is still infinity. If you take the set of all positive even integers, it's still infinite right? Or even the set of all positive integers that are divisible by 10, or 100, or 1,000. No matter how much you tried, how long you lived, how fast you could search, you could never travel around the universe and eventually be able to say "I've visited every planet capable of sustaining life in the universe".