It matters where u truncate things at....................to begin with.........pi, e, the square root of 2............are both irrational............and endless.........the dec. expansion goes on to infinity...........so u HAVE to truncate them at one point or another....................or u can spend........forever writing in their dec expansions....................I have better things to do..............than write out millions of digits, FOREVER.....................

I remember a British mathematican/physicst.........who had a fantastic memory......................if u told him a date in the 1800s.........he could tell what day of the week that day fell on...........this was recently....................he had such a great memory.........that they challenged him.............to learn an entire language in a week.....................they picked Icelandic...........a very complicated language........................he actually did learn Icelandic in just a week.........not the entire language............but enough to have good grammar and a good vocabulary.........spoken..................some Icelandic men tested him.....they all said that the guy actually did learn Icelandic...........he said he had a near perfect memory after a seizure.................and the reason he didn't go the beach............was that every time he did.............he began to count the grains of sand...............and in his words..........he said there were just too many grains of sand to count..............................I would rather find an easier way to compute the primes...........than to run through a number..........with millions of numbers in it................talk about time consuming.................


He entered the initial condition 0.506 from the printout instead of entering the full precision 0.506127 value. The result was a completely different weather scenario.^[7]
Lorenz wrote:

"At one point I decided to repeat some of the computations in order to examine what was happening in greater detail. I stopped the computer, typed in a line of numbers that it had printed out a while earlier, and set it running again. I went down the hall for a cup of coffee and returned after about an hour, during which time the computer had simulated about two months of weather. The numbers being printed were nothing like the old ones. I immediately suspected a weak vacuum tube or some other computer trouble, which was not uncommon, but before calling for service I decided to see just where the mistake had occurred, knowing that this could speed up the servicing process. Instead of a sudden break, I found that the new values at first repeated the old ones, but soon afterward differed by one and then several units in the last decimal place, and then began to differ in the next to the last place and then in the place before that. In fact, the differences more or less steadily doubled in size every four days or so, until all resemblance with the original output disappeared somewhere in the second month. This was enough to tell me what had happened: the numbers that I had typed in were not the exact original numbers, but were the rounded-off values that had appeared in the original printout. The initial round-off errors were the culprits; they were steadily amplifying until they dominated the solution." (E. N. Lorenz, The Essence of Chaos, U. Washington Press, Seattle (1993), page 134)^[8]