Ahocsb.108 net.space utcsrgv!utzoo!decvax!duke!chico!harpo!npois!houxi!hocsb!bsm Wed Mar 3 10:44:35 1982 Reply To FUNCTIONAL INFINITY Several years ago (nowhere near infinity) I was discussing a similar idea with a friend. We never thought to consider the vector implications, thus our idea diverged somewhat from yours. This infinity was a general range of values (or distances) that could not be represented by our usual numerical system. It might be visualized as moving the decimal point to the left by some reference distance (10 ** 1000), the result being that all usual numbers now (almost) equal zero and all the infinity numbers are now scaled down to the usual numbers. This visualization is poor because these numbers of infinity can still be represented by the usual number system. It would be a significant step if someone could develop a math system for dealing with such numbers. I beleive this has already been done by Isaac Newton around 1675 and possibly Archimedes before Christ. Calculus always deals with numbers that are to small to be represented by the usual numerical system, these numbers being called DELTA's. In many Calculus derivations, reciprocals of Delta's arise and must be eliminated by inversion. These reciprocals of Delta's are FUNCTIONAL INFINITIES. Unfortunately, the Calculus always eliminates them to obtain a result. What is needed is a way of directly dealing with them, or treating them as "ANTI-DELTA's". (This would be distinct from Antiderivative or Integral) L'Hopital's Rule is a nice start, but it only evaluates points on a function, and what we need are functions whose values are infinite everywhere. I enjoyed your vector description of infinity, but I disagree on a major concept. If the infinite position was at a distance relatively infinite from all other positions. , then there would be only one direction. This would be from the infinite position toward all the other positions. Although this puts a kink in some of your observations, it could have some astounding uses. By introducing infinity to a 3 dimensional system, it reduces the system to one dimension. ......but maybe this observation is incorrect......? I would appreciate any re-replies or additional information. Sorry for being so wordy. yours till the end of time, Bryan Moffitt ----------------------------------------------------------------- gopher://quux.org/ conversion by John Goerzen of http://communication.ucsd.edu/A-News/ This Usenet Oldnews Archive article may be copied and distributed freely, provided: 1. There is no money collected for the text(s) of the articles. 2. The following notice remains appended to each copy: The Usenet Oldnews Archive: Compilation Copyright (C) 1981, 1996 Bruce Jones, Henry Spencer, David Wiseman.