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
nationwide 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 2410=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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