At 10:25 +1300 3/17/10, Martin D Kealey wrote: >On Mon, 15 Mar 2010, Mark J. Reed wrote: >> > Anything that can be made into a list is discrete. >> >> Not quite, since you can create lists whose members belong to >> continuous sets, e.g. real numbers. Anything that naturally forms a >> list, maybe. > >A discrete non-finite set is isomorphic to the set of integers. > >This implies that you can pick an ordering, although perhaps not one that is >computational useful. E.g. rational numbers can be mapped onto integers by >laying them out in a 2D array, much like Gauß's complex integers, and then >walking diagonally in one quadrant. If you have more than one quadrant, take >them in turns. Extends to 3D and higher in a logic fashion. > aleph 0.
In the world of real (pun intended) computers there is no continuous set of real numbers. Microsoft Excel users are regularly reminded of that when they report bugs that are nothing more than the impossibility of representing 0.1 (10) as an IEEE float. Perhaps everything is discrete in the set of things that perl is expected to deal with. -- --> If you are presented a number as a percentage, and you do not clearly understand the numerator and the denominator involved, you are surely being lied to. <--
