>>11287876we say that the function v(n) is in the class O(f(n)) (which is written v(n) = O(f(n)) even though it really should be but CS "theorists" are hacks) IF:
f(n) grows "as fast as" v(n) as n gets large, or more rigorously, there is a constant c for which |v(n)| is bounded by c|f(n)| for all n beyond some starting point.
so again, think of this as "v(n) is less than or equal to f(n)," not in terms of absolute size but in terms of growth rate.
example: 2n + 5 = O(n), since we can pick c = 3 and n_0 = 10 and then |2n + 5| < 3|n| whenever n >= 10.
another example: 100n^3 = O(n^4) since we can pick c = 1 and n_0 = 100, and we always have |100n^3| < 1|n^4| when n > 100.
