It's not an equality relationship. If it was an equality relationship it would be transitive. But as your parent points out, you have n=O(n^2), n^2=O(n^2) but not n=n^2, so transitivity doesn't hold.

Another way to see that the relationship can't be equality: the left hand side is a function, the right hand side is a set of functions. Two things from different classes can't be equal.

The relationship is simply set membership.