Discrete Math: Let f1, f2, g1, g2 be functions from the set N of natural numbers such that g1(n) 0 and g2(n) 0 hold for all n 0. Let f1(n) = O(g1(n)) and f2(n) = O(g2(n)). Use the definition of Big O to prove that f1(n)f2(n) = O(g1(n)g2(n))

Question

Discrete Math: Let f1, f2, g1, g2 be functions from the set N of natural numbers such that g1(n) > 0 and g2(n) > 0 hold for all n > 0. Let f1(n) = O(g1(n)) and f2(n) = O(g2(n)). Use the definition of Big O to prove that f1(n)f2(n) = O(g1(n)g2(n))

anonymous · Answer

we have seen your post, it's just 1 question away do not repost it so often

anonymous · Answer

I'm sorry, I will delete the last post.

anonymous · Answer

f1(n) = O(g1(n) .. this means that for all n > N1 f1(n) < g1(n) f2(n) = Og(2(n).. this means that for all n>N2 f2(n) < g2(n) take x = max(N1,N2) then f1(n) < g1(n) for all n>x and f2(n) < g2(n) for all n > x hence multiplying both f1(n)*f2(n) < g1(n)g2(n) for all n > x hence f1(n)f2(n) = O(g1(n)g2(n)) .. hence proved