algorithm - 证明 f(n) + d(n)= O(g(n)+ h(n))

Question

If f(n) is Ο(g(n)) and d(n) is Ο(h(n)), then prove that f(n) + d(n)= O(g(n)+ h(n))

我在想出正式证明时遇到了麻烦。

这是我目前所拥有的:

f(n)=O(g(n)) and d(n)=O(h(n)) so, O(g(n)) + O(h(n)) = O(g(n)+ h(n))

但我不确定这个，因为它看起来很简单。

感谢任何帮助。

EDIT: i must prove this, I cant prove this by saying an example, I have to solve it as a proof by using a C constant I think or some other way..

Answer 1

正式地，通过使用 Big-O-Notation 的定义，它可以像 Hans Hyttel 那样完成 here .

证明: