Some symbols used in computer science should have a simpler definition.
Consider the equivalence relation $(0, a \ne 0, \infty) \sim (<, =, >)$ on $L = \lim\limits_{n \to \infty} \frac{f(n)}{g(n)} \in \{0, a, \infty\}.$ We define $(o, O, \Theta, \Omega, \omega) \sim (<, \le, =, \ge, >)$ where $f(n) = X(g(n))$ and $X \in (o, O, \Theta, \Omega, \omega).$
I'm hoping that someone can clean this up. Right now, the only flaw is that the alternative definition might be hard to understand unless you already know the standard definition.