Hi, and thanks in advance for any help.
I'm multiplying two inequalities: [math]g_1(n) ≤ ch_1(n) \text{ for all } n ≥ n_0[/math] and [math]g_2(n) ≤ c'h_2(n) \text{ for all } n ≥ n_0'[/math] where [imath]c, c', n_0, \text{ and } n_0''[/imath] are all constants.
The product of the inequalities is [math]g_1(n)g_2(n) ≤ cc'h_1(n)h_2(n)[/math] but what happens to the range? I'm thinking it's either [math]n^{2} ≥ n_0 n_0'[/math] if you just multiply the ranges, or maybe [math]n ≥ max(n_0, n_0')[/math] if you're taking where the ranges overlap.
Any help and insight into why the answer is what it is would be greatly appreciated!
Edit: It's known that [imath]n ≥ 0[/imath].
I'm multiplying two inequalities: [math]g_1(n) ≤ ch_1(n) \text{ for all } n ≥ n_0[/math] and [math]g_2(n) ≤ c'h_2(n) \text{ for all } n ≥ n_0'[/math] where [imath]c, c', n_0, \text{ and } n_0''[/imath] are all constants.
The product of the inequalities is [math]g_1(n)g_2(n) ≤ cc'h_1(n)h_2(n)[/math] but what happens to the range? I'm thinking it's either [math]n^{2} ≥ n_0 n_0'[/math] if you just multiply the ranges, or maybe [math]n ≥ max(n_0, n_0')[/math] if you're taking where the ranges overlap.
Any help and insight into why the answer is what it is would be greatly appreciated!
Edit: It's known that [imath]n ≥ 0[/imath].