I heard a great explanation of this once. You get to the next factorial by multiplying by the next number in the series. That is what LM's n! = n(n-1)! means.
1! = 1
2! = 1!*2 = 1*2 = 2
3! = 2!*3 = 2*3 = 6
4! = 3!*4 = 6*4 = 24
5! = 4!*5 = 24*5 = 120
6! = 5!*6 = 120*6 = 720
It thus follows that you get to the previous factorial by a division process, so n! = (n+1)! / (n+1)
5! = 6!/6 = 720/6 = 120
4! = 5!/5 = 120/5 = 24
3! = 4!/4 = 24/4 = 6
2! = 3!/3 = 6/3 = 2
1! = 2!/2 = 2/2 = 1
ergo...
0! = 1!/1 = 1/1 = 1
The same argument works for n0 = 1
Cool!
1! = 1
2! = 1!*2 = 1*2 = 2
3! = 2!*3 = 2*3 = 6
4! = 3!*4 = 6*4 = 24
5! = 4!*5 = 24*5 = 120
6! = 5!*6 = 120*6 = 720
It thus follows that you get to the previous factorial by a division process, so n! = (n+1)! / (n+1)
5! = 6!/6 = 720/6 = 120
4! = 5!/5 = 120/5 = 24
3! = 4!/4 = 24/4 = 6
2! = 3!/3 = 6/3 = 2
1! = 2!/2 = 2/2 = 1
ergo...
0! = 1!/1 = 1/1 = 1
The same argument works for n0 = 1
Cool!
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