# Divide and conquer: Why F(0) = 0?

by user10511500   Last Updated October 16, 2018 09:20 AM

I saw an example where it said F(1) =1 and F(0) = 0. (fibonacci)

Why F(1) =1 and F(0) = 0? From where does it originate?

Thanks.

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The initialization with $$F(0)=F(1)=0$$ is pretty fine. The recursion $$F(n+1) = F(n)+F(n-1)$$ for $$n\geq 1$$ gives $$F(2)=1$$, $$F(3)=2$$ and so on. This definition defines the sequence $$(F(n))_n$$ for all $$n\geq 0$$. The sequence is 0,1,1,2,3,5,8, and so on. It can also be written without the initial term: 1,1,2,3,5,8, and so on.