Style guide for asymptotic notation

Question

There are two widely accepted forms of asymptotic notation:

1. $f(n) = O(g(n))$
2. $f(n) ∈ O(g(n))$

1 seems to be more widely used, but implies a symmetry between the two sides that just isn't there. 2 is less confusing in that way, but is less used.

Are there any commonly used mathematical style guides that recommend one over the other? Or at least ones that say something on the matter?

Answer 1

There is no commonly used mathematical style guide that provides a recommendation. But sometimes one of the great tells us reasons for his preferences. An interesting paper of this kind is Big Omicron and Big Omega and Big Theta by D.E. Knuth from 1976.