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Big-O Notation

For functions f(n) and g(n), we say that "f(n) is Big-O of g(n)" if

There exists a constant c > 0 there exists a constant n0 such that
for all n ≥ n0, 0 ≤ f(n) ≤ c * g(n)

We write f(n) = O(g(n)), but the "=" is not the usual meaning.

The intention is to allow us to say

Technically, 101,000,000*n is O(n), but programs with that running time is still very slow.