Have you looked at the definitions of big-O, big-Omega, small-omega notation?
You will find them here (about three quarters of the way down the page).
RonL
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