Prove that the big-O relationship is transitive - Prove that the big-O relationship is transitive (give a direct proof). That is, if f(n), g(n) and h(n) are positive-valued functions:
if f(n) is Ο(g(n)) and g(n) is Ο(h(n)) then f (n) is ...
Proof by Contradiction - Prove the following fact (give a proof by contradiction):
There do not exist constants N > 0 and C > 0 such that ∀n ≥ N ,n^2 ≤ C*n
Big O Problem - Show that if:
T(1) = a
T(n) = T(n-1) + n^k, for n > 1
then T(n) is O(n^(k+1)). You may assume k>=0. Also, show that this is the tightest simple big-oh upper bound, that is, that T(n) is not O ...