Awatmath.1602 net.general utcsrgv!utzoo!decvax!watmath!mabgarstin Wed Jan 27 20:55:16 1982 more boring factorials, be forewarned This a simple relation to discovered in grade 10 and was published in a nation-wide high school math rag to which I cannot remember the name. In my notation the > sign between lines means to take the difference of the two numbers to which the arms of the > sign point back to. i.e. 10 >14 means 24-10=14 24 Sorry but this is the best way I pass this thing through the net. Lets start off with powers of 3. 0**3= 0 > 1 1**3= 1 >6 > 7 >6 2**3= 8 >12 >19 >6 3**3= 27 >18 >37 >6 4**3= 64 >24 >61 5**3=125 | | etc. As you can that after THREE rounds of subtractions we got the number 6 or 3!. Lets try some others. 0**2= 0 >1 1**2= 1 >2 >3 2**2= 4 >2 >5 3**2= 9 >2 >7 4**2=16 | etc. With the power of 2 we 2 or 2! after only 2 rounds of subtraction. 0**1=0 >1 1**1=1 >1 2**1=2 >1 3**1=3 etc. And with the power of 1 we get what we expect. Now lets try it for the power of 0. 0**0=???? Welllll,...lets skip this particular value for now (Murphy's fudge factor or Honsberger realignment procedure, something like that). 1**0=1 2**0=1 3**0=1 etc. Well now, with the power of 0 we 1 after 0 rounds of subtractions. Therefore 0! must equal 1 in order to satisfy this relation. (typo above, should be '...of 0 we GET 1...'). Try it out for powers of 4 and 5 if you have some time to waste like me. You'll find things get strange when you hit powers of 7. For some reason you have to take 8 rounds of subtraction to get 7! instead of 7. I haven't figured that one out yet. Any memos, tips or other related ditties please mail to: watmath!mabgarstin or watarts!mab MAB Garstin at the Univ. of Waterloo ----------------------------------------------------------------- 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.