All the functions below are functions from Z>⁰ = {x € Z : x > 0} to R≥º = {x € R : x ≥ 0}. Prove the following statements. 1. f = O(g) if and only if g = : N(f). 2. If f₁ = N(9₁) and f2 = N(92) then f1f2 = N(9192). 3. If f = O(g) and g = O(h) then f = 0(h). This is known as transitivity. It is similar to the fact that if x ≤y and y≤z then x < 2.

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