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Define the "parallel sum" a∥b=((a*b)/(a+b) A normal sum has the associative property: a+(b+c)=(a+b)+c which justifies dropping the parentheses a+(b+c)=a+b+c
by DoctorOetker 15d ago
Define the "parallel sum"
a∥b=((a*b)/(a+b)
A normal sum has the associative property:
a+(b+c)=(a+b)+c which justifies dropping the parentheses
a+(b+c)=a+b+c=(a+b)+c
It is just an exercise for the reader that the parallel sum ∥ operation is associative:
a∥(b∥c) = (a∥b)∥c
multiplication is typically defined as repeatedly adding:
a x b = b+b+...+b+b (a times b)
similarily one can define parallel multiplication xx :
a xx b = b∥b∥...∥b∥b (a parallel-times b)
The reader can verify that 9 parallel-times size
9 xx size = size∥size∥size∥size∥size∥size∥size∥size∥size = size / 9
So I just think the Bonsai designers meant it was 9 parallel-times smaller, which checks out...
x∥x=(xx)/(x+x)= x/2
x∥x∥x =(x/2x)/(2/x+x)=(x/2)/(3/2)=x/3
x∥x∥x∥x = x/4