I am defining the relation $\sim$ to be
$$ f \sim g \Longleftrightarrow \lim_{n \to \infty} \frac f g = 1 $$
In my paper, I am asserting that if $f \sim f_0$, then
$$ f + g \sim f_0 + g\\ fg \sim f_0{g}\\ \frac f g \sim \frac {f_0} g $$
Basically, it works like an algebraic equation: you can add, multiply, or divide both sides by the same quantity. Is there a name for this type of relation?
I'm asking this because I'm trying to write a terse description of this in a header, but the best that comes to mind is "Both Sides of a $\sim$ Relation may be Added, Multiplied, or Divided by the Same Quantity". I need to write something like "$\sim$ is an ___ Relation".
edit: I decided to put "$\sim$ Relations can be Algebraically Manipulated" for the header. Does that sound appropriate?