# Name for “relative difference”

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

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

• Note that your notion of "relatively" close translates into an absolute value statement by taking logarithms. I don't know of any special terminology for this, though. – Lee Mosher Jun 17 '14 at 15:34
• How about the percent difference (or percent error) between $x$ and $y$ is small? – Dave L. Renfro Jun 17 '14 at 15:38
• @Lee: You are right. Maybe |log(x) - log(y)| should do it. (While it's a little more hand-writing than |x-y|. My suggestion would be |x/y|.) – Hans-Peter Stricker Jun 17 '14 at 15:40