BIG O NOATION - PLEASE EXPLAIN

Let f(n) and g (m) be positive valued increasing functions of n. Using the definition of Big-0, prove that: If f (n) epsilon O (g(m)) and g(n) epsilon O(h (m)) then f(m) E O(h(m)). The definition of f(m) epsilon O(g(n)) says that we can find constants C_1 and k_1 such that whenever n > k_1. Similarly, the definition of g(n) epsilon O(h(n) says that we can find constants C_2 and k_2 such that whenever n > k_2. We can show that f(n) epsilon O(h(n)) by finding constants C_3 and k_3 such that whenever n > k_3. Let C_3 = and let k_3 =. This works because