Two functions f(x) and g(x) are asymptotically equal if f(x)/g(x) has limit 1 as x tends to ∞, written f(x) ∼ g(x). For example (x + 1)³(x + 2)⁴ ∼ x⁷. Being asymptotically equal implies something about the relative size of two functions and does not imply they are approximately equal; in the example, the difference between (x + 1)³(x + 2)⁴ and x⁷ becomes arbitrarily large as x increases. See big o notation, little o notation.