On 5/27/2011 10:13 AM, Daniel C. wrote: > On Fri, May 27, 2011 at 10:02 AM, Lonnie Olson<[email protected]> wrote: >> If the Universe is infinite how could it be expanding. An object of >> infinite size is already at maximum, and can therefore not expand any >> larger. An object that is expanding is getting larger, therefore is >> not yet at infinite size. Based on the evidence that the Universe is >> expanding, I think the Universe is not infinite by reason of this >> logic. > Some infinities are larger than others. Consider the set of all > numbers between 0 and 1 - there are an infinite number of them. (0.1, > 0.01, etc.) The set of all numbers between 0 and 2 (or, for that > matter, 0 and 1.1) is also infinite, but it's a larger set than the > set of numbers between 0 and 1. It is in fact possible for something > that is infinite to become larger, while still being infinite. > > -Dan > > /* > PLUG: http://plug.org, #utah on irc.freenode.net > Unsubscribe: http://plug.org/mailman/options/plug > Don't fear the penguin. > */ > i think what Dan is trying to say is that there is not more numbers between 0-1 and 0-2. Infinity = infinity regardless of the rate at which it is reached but if you were to take the sum of all numbers from 1 to 1/(infinity^2) you would end up with a discrete value. In fact any power of the denominator 2 greater than the numerator always will. For example the sum of the limit 1/(n^2) as n-> infinity = (pie^2)/6 however the sum of the limit of 1/n as n-> infinity = infinity albeit extremely slowly. in both cases we have an infinite number of values being added together, but the final results are radically different.
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