1

Suppose you have two unary operators $!$ being the factorial and $\partial_1$ being the partial derivative of a function w.r.t. its first parameter.

$$ n!m $$ $$ f \partial_1 g $$

The $!$ operator operates on an argument on its left side ($n$), whereas $\partial_1$ operates on its right side ($g$). Associativity comes to mind but it doesn't quite capture the property. What do we call the differing properties of both operators?

  • We call them left and right operators. I can never remember which one is which though. (Is $!$ a right operator because it stands to the right of $n$, or is it a left operator because it affects whatever is on the left of it? I can never keep that straight.) – Arthur Nov 04 '16 at 22:24
  • @Arthur: I've never heard of "left and right operators". "Prefix" and "postfix" is the standard terminology. – Rob Arthan Nov 04 '16 at 22:28
  • @RobArthan I'm an algebraist, we talk about left right multiplication all the time, and we often think about the application of a unary operator as multiplication (at least if it's nice enough). Granted, I have never heard about the factorial referred to as such, but the differential operators are certainly common enough. – Arthur Nov 04 '16 at 22:34
  • @Arthur: sure, but when you are talking about a group or a ring acting on the left or the right of a set or a module, you don't talk about "left operators" or "right operators" but rather "left action" or "right action" or "left multiplication" or "right multiplication". – Rob Arthan Nov 04 '16 at 22:50

1 Answers1

1

In $n!$, $!$ is called a postfix operator. $\partial_1$ in $\partial_1 g$ is called a prefix operator.

Rob Arthan
  • 48,577