Hi everybody. I need a help about prove. My question is
Let f,g: Z ->R where
f(n)= {2, for n even and 1,for n odd}
g(n) ={3,for n even and 4,for n odd}
Prove or disprove each of the following
a)
b)
Thank you for your attentions.
Imagine that g(n) is your salary during the nth month and f(n) is the salary of the head of the company where you work. If f(n) is O(g(n)), then, even though your boss ma earn, say, between 2 and 100 more then you, this ratio stays within these limits as time goes. But when f(n) is not O(g(n)), it means that the ratio increases indefinitely with time. It does not have to increase monotonically. Say, for n=1, 2, 3, 4, 5, 6, 7, 8 ..., the ratio f(n)/g(n) can be 5, 50, 10, 60, 15, 70, 20, 80, ... etc. If this continues, this will lead to social tension, possibly strikes and all kinds of problems in the society.
In your case, since neither function grows indefinitely compared to the other, both are big-O of each other.