----- Original Message ----- From: "Julia Thompson" <[EMAIL PROTECTED]> To: "Killer Bs Discussion" <[email protected]> Sent: Friday, September 29, 2006 5:34 PM Subject: Re: Infinities large and small (was Re: The Assumption Re: 9/11conspiracies)
> Nick Arnett wrote: >> On 9/28/06, Ronn!Blankenship <[EMAIL PROTECTED]> >> wrote: >> >>> >>> Isn't "a little infinite" a contradiction, like "a little bit . . >>> . "? >> >> >> No... some infinities are smaller than others, as is easily >> demonstrated. >> >> There are an infinite number of even numbers and an infinite number >> of odd >> numbers. Those two infinities are the same size. However, there >> are an >> infinite number of even AND odd numbers and that infinity is twice >> as big as >> the first two. > > No, it's the SAME SIZE as each of the first two. THAT'S the one > that took me a week or two to wrap my head around. :) > Heh.....that depends on which mathematician you talk to. The Dedekind Infinite is not the only view floating around. It seems to me that this is an attempt to give infinity the same standing as zero. frex: 1/2 times zero = zero is equivalent to saying 1/2 times infinity = infinity. And that is roughly like saying 1/zero = infinity and that is a pretty neat bit of mathematical philosophy. But for me the concept breaks down when considered with practicality in mind. I find the statement 1/infinity = infinity to be nonsensical since one is infinitely small and the other infinitely large and for me the implication is that all non-zero values = infinity and that is profoundly untrue. I would propose that 1/infinity is "approaching zero" or "roughly equivalent to" zero, but never exactly zero. Infinity as a value has little value.<G> I can hold out my hand and say I have zero apples in it or I could have one apple to show you. Zero has almost the same quantifiability as any natural number, but the same cannot be said for infinity. Infinity has never been shown to exist in nature. (And all the physics in the world cannot produce infinite anything since the entire universe would be overwhelmed by any introduction of the infinite into the universe.) Infinity is simply a concept, and like other concepts is malleable and subject to fads. xponent Less Than Infinite, More Than Zero Maru rob _______________________________________________ http://www.mccmedia.com/mailman/listinfo/brin-l
