Name for "relative difference"

50 Views Asked by At

If we want to express that two numbers $x, y$ are not so far away from each other absolutely we use the absolute value function $|\cdot|$ with $0 < \epsilon \ll 1$:

$$|x-y| < \epsilon$$

which is equivalent with:

$$x > y\quad\wedge\quad x-y < \epsilon$$

or

$$x < y\quad\wedge\quad y-x < \epsilon$$


What's the name (and shorthand) of the function that tells us that two numbers $x, y$ are not so far away from each other relatively:

$$x > y\quad\wedge\quad x/y < 1 + \epsilon$$

or

$$x < y\quad\wedge\quad y/x < 1 + \epsilon$$