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
 

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