Is there a name for the function $f(a,b)=\max(a-b,0)$?

Question

Is there any conventional (standard) terminology for the function $f(a,b)=\max(a-b,0)$?

This function "caps" the value of $a-b$ with at least $0$.

Some would call $x \mapsto \max(x,0)$ a ramp. It is also the primitive of the Heaviside step. — Rodrigo de Azevedo, Sep 03 '21 at 12:14
This is called the positive part of $(a-b)$. In general $h(x)=x^+:=\max{x , 0}$. — Nap D. Lover, Sep 03 '21 at 12:18
Oh, I can't remember exactly the name but we had $a \dot- b$ notation for this function in Discrete Mathematics course. — VIVID, Sep 03 '21 at 12:20
@RodrigodeAzevedo: Thank you! This indeed seems to be the correct terminology, except for the a-b part, since the ramp function is defined to take a single input value. So I suppose diffRamp would be the most suitable answer to my question. Thanks! — bbbbbbbbb, Sep 03 '21 at 13:28
@bbbbbbbbb I would say it's the composition of scalar field $(a,b) \mapsto a - b$ and function $x \mapsto \max(x,0)$. — Rodrigo de Azevedo, Sep 03 '21 at 13:43
If $a>b$, then $f(a,b)=a-b$. Otherwise, $f(a,b)=0$ (if $a \le b$). — Geoffrey Trang, Sep 03 '21 at 14:11

score 0 · Answer 1 · answered Sep 03 '21 at 16:02

0

The standard name for this is floored subtraction.

answered Sep 03 '21 at 16:02

PMar

1 Answers1