book[cormen - solution 2nd edition] solution to problem 3-3

Question

Prove that : log*(log n) = log*n -1.

Comments

what does * mean

---

Don't know exactly.May be wild card for any number.I found it in "cormen solution second edition" in a solution to problem 3.3

---

log*n means we take log to n until we gate negative no.  then no. of total iteration is output.

Answer 1

The iterated logarithm of n, written log* n (usually read "log star"), is the number of times the logarithm function must be iteratively applied before the result is less than or equal to 1.

In the question log*(log n) = log*n -1 if we are taking log then we are reducing the one count.

So in the result we have to subtract 1.

if the case is log*(log(log( n))) = log*n -2.

so by resoning we can prove this.