Brackets
Suppose we define a new “product” a*b of two numbers a and b as follows :
a*b
= ab^{2}. Notice that this
product is not commutative:
a*b
g
b*a,
in general, since ab^{2}
g
ba^{2},
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
= (ab^{2})*c
= ab^{2}c^{2},
whereas a*(b*c)
= a*(bc^{2})
= a(bc^{2})^{2}
= ab^{2}c^{4}. The
Problem : How
many possible meanings does “
a
*b
*c * d
* e “
have?
Open the File as a Word Document

Send site mail to admin@1000problems.org
or personal comments direct to sdakeyne@psc.ac.uk with
questions or comments about this web site. 