(written by lawrence krubner, however indented passages are often quotes). You can contact lawrence at:

I’ve always known what this word meant yet I don’t think I could have come up with so clear an example:

A simple illustration, when considering a function f(n), is when there is a need to describe its properties as n becomes very large. Thus, if f(n) = n2+3n, the term 3n becomes insignificant compared to n2, when n is very large. The function f(n) is said to be “asymptotically equivalent to n2 as n → ∞”, and this is written symbolically as f(n) ~ n2.