Aucbonyx.242 net.general utcsrgv!utzoo!decvax!duke!chico!harpo!mhtsa!ihnss!ucbvax!ARPAVAX:Onyx:jmrubin Mon Jan 25 17:42:44 1982 Factorial Query (repl. to mhtsa!research!sjb) Let n be identified with the set of all non-negative integers less than n. For example, 4 = { 0, 1, 2, 3 }. (definition due to Von Neuman) Then, n! is the size of the set of permutations of n. ( A permutation of a set, A, is a 1-1 function from A onto A.) 0 is the same, in this scheme, as the empty set. Therefore, 0! is the size of the set of permutations of the empty set. There is precisely one permutation of the empty set, the empty function. Therefore, the size of the set is 1. Joel Rubin ----------------------------------------------------------------- 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.