In 4—9, express each statement using -, O-, or -notation.
6. for every integer . (Use −notation.)
The statement using -notation.
Let f and g be real-valued functions defined on the same set of nonnegative integers, with for every integer , where r is a positive real number. Then f is of order g, written f ( n ) is ( g ( n )) ( f of n is big-Theta of g of n ), if and only if, there exist positive real numbers A, B and such that
for every integer .
Consider the statement, “ for every integer
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