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
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