big-Theta notation

1. Show that big-Theta notation (Θ) defines an equivalence relation on the set of functions.

2. Give the best lower bound that you can for the following code fragment, as a function of the initial value of n.

while (n > 1)

   if (ODD(n))

     n = 3 * n + 1;

else

     n = n / 2;

Do you think that the upper bound is likely to be the same as the answer you gave for the lower bound?

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