1. Big Omicron and big Omega and big Theta
Jiaheng Lu
Renmin University of China

2. Big Omicron
O(f(n)) denotes the set of all g(n) that there exist positive constants C and m with g(n) <= C*f(n) for all n >=m
O(f(n)) can be read as “order at most f(n)”.
E.g. g(n) = n3+n2, f(n)=n3

3. Big Omega
Ω(f(n)) denotes the set of all g(n) that there exist positive constants C and m with g(n) >= C*f(n) for all n >=m
Ω(f(n)) can be read as “order at least f(n)”.
E.g. g(n) = n3+n2, f(n)=n3

4. Big Theta
Θ(f(n)) denotes the set of all g(n) that there exist positive constants C , C’ and m with C*f(n) <= g(n) <= C’*f(n) for all n >=m
Θ(f(n)) can be read as “order exactly f(n)”.
E.g. g(n) = log10n, f(n)= log2n