Brackets
Suppose we define a new �product� a*b of two numbers a and b as follows :
a*b
= ab2. Notice that this
product is not commutative:
a*b
g
b*a,
in general, since ab2
g
ba2,
in general; and
also it is not associative : That is, a*b*c
has two meanings according to where we insert brackets: (a*b)*c
= (ab2)*c
= ab2c2,
whereas a*(b*c)
= a*(bc2)
= a(bc2)2
= ab2c4. The
Problem : How
many possible meanings does �
a
*b
*c * d
* e �
have?
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