On Fri, May 27, 2011 at 10:13 AM, Daniel C. <[email protected]> wrote: > 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.
In your example, your use of the term infinite is in relation to the count of numbers, not the sums or values. This count is in fact infinite, no upper bound. There are no more numbers between 0 and 1 than there are between 0 and 2. This upper bound is limitless. You cannot multiply infinity by two, since infinity is already fully encompassing that result. There is no value greater than infinity. /* PLUG: http://plug.org, #utah on irc.freenode.net Unsubscribe: http://plug.org/mailman/options/plug Don't fear the penguin. */
