Asymptotic Relations and Notation

Big O: g(n) &lt;= O(f(n)) iff there exist positive constants c and n 0 such that 0 &lt;= g(n) &lt;= cf(n) for all n &gt;= n 0 " g is asymptotically bounded above by f "
Big Omega: g(n) &gt;= &Omega;(f(n)) iff there exist positive constants c and n 0 such that 0 &lt;= cf(n) &lt;= g(n) for all n &gt;= n 0 " g is asymptotically bounded below by f "
Big Theta: g(n) = &Theta;(f(n)) iff there exist positive constants c 1 , c 2 , and n 0 such that 0 &lt;= c 1 f(n) &lt;= g(n) &lt;= c 2 f(n) for all n &gt;= n 0 " g is asymptotically bounded above and below by f "

Asymptotic Relations and Notation

Big O:
g(n) <= O(f(n)) iff there exist positive constants c and n₀ such that 0 <= g(n) <= cf(n) for all n >= n₀
"g is asymptotically bounded above by f "

Big Omega:
g(n) >= Ω(f(n)) iff there exist positive constants c and n₀ such that 0 <= cf(n) <= g(n) for all n >= n₀
"g is asymptotically bounded below by f "

Big Theta:
g(n) = Θ(f(n)) iff there exist positive constants c₁, c₂, and n₀ such that 0 <= c₁f(n) <= g(n) <= c₂f(n) for all n >= n₀
"g is asymptotically bounded above and below by f "

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