How do you proof that:
1. Show that f(n) is O(g(n)) if and only if g(n) is
2. Show that is
3. is
I am really confused on doing this, can someone help me
hmm..so I guess I did this wrong. why is f(n) < c * g(n) and g(n) < c * f(n) implies an existence? can you explain this a bit further?? does this mean by the definition that f(n) < c * g(n) and g(n) < c * f(n) gives the right condition for c and to be true, which is c > 0 and n>n0?
Assume f(n) is O(g(n) then prove this implies that g(n) is ( . This is proving the "only if" part.
Then assume g(n) is ( then prove this implies that f(n) is O(g(n). This is the "if" part.
Together they prove that f(n) is O(g(n) if and only if g(n) is (
(Both of these are implicit in what we discussed in the earlier posts)
RonL