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.

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- November 28th 2009, 02:05 AMnesibessProve problem
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. - November 28th 2009, 02:52 AMtonio
- November 28th 2009, 05:02 AMnesibess
- November 28th 2009, 05:42 AMHallsofIvy
What is the definition of "O(f)"?

- November 28th 2009, 06:19 AMtonio
- November 28th 2009, 06:44 AMemakarov
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. - November 28th 2009, 06:56 AMnesibess
If I am wrong, Please tell me.

My solution is:

a) => f(n)<C.g(n) if n=even 2<C.3 OR if n=odd 1<C.4

b) => g(n)<C.f(n) if n=even 3<C.2 OR if n=odd 4<C.2

is it correct? or I don't know anything this topic is hard for me (Crying) Please help me - November 28th 2009, 07:33 AMtonio