On Sat, Jun 02, 2001 at 08:03:04PM -0500, David VanHorn wrote: > At 07:39 PM 6/2/01 -0500, michael brown wrote: > >---- Original Message ----- > >From: "Thomas McGahee" > >To: > >Sent: Saturday, June 02, 2001 11:19 AM > >Subject: Re: [OT]: Brain Burp Rounding?? > > > > > > > Sigh.... I did not say .99999 I said .99999 REPEATING. > > > As in **forever**. > > > > > > Do not get confused between the VALUE of a number and its > > > representation. Whether you like it or not, mathematically the mumber > > > 1 exactly equals .9 repeating. > > hold on jack.. > > That's as nonsensical as saying that 2=3 for large values of 2. > > I have a problem with that. > > 0.99(followed by any finite or infinite number of nines) is by definition, > not equal to 1.0 > > The value of 0.99(inf..) is less than 1.0 by an infinitely small (but > non-zero) amount. Dave, You need some infinity training. Let's try a few examples: 1) What's the largest integer? 2) What's the value of 1/0? 2A) What's the value of 1/infinity? 3) What's the smallest real number larger than 0? (BTW that's the answer to your question above) 4) Pick any two real numbers. How many real numbers are between the two? 5) What's the last digit of PI? It's a simple mathematical fact that once you start dealing with infinity the rules change. You find your difference above in the same place as the largest integer and the smallest number bigger than 0. The answer is infinity and 0. The last one sounds incongruous, but true. That's the nature of infinity. 1/infinity doesn't approch zero. It doesn't approximate zero. It isn't infinitely close to zero. IT IS ZERO! EXACTLY ZERO! There is no difference between 1 and .9 (repeating). Not in infantisimal difference. No difference. They are the same number. Of course any attempt to make an infinite value finite make it lose it's infiniteness. All of this fuss is over trying to attribute infinity to an approximation. We use approximations to gain understanding in our little finite minds! But you have to cross over and realize that once something is defined as infinite, it is no longer an approximation of anything. It's exact. And the math that works on infinity fails once you express finiteness on it. The best treatment on the subject I ever read was Issac Asimov's "Asimov on Numbers". He has several essay's on the nature of infinity. Just remember that whenever you're having an infinity discussion, that you must bring the largest integer to the table. Once you know that integer, the rest is easy. BAJ -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.