What kind of mathematical entities can have $arity = 0$ without being a constant ?
Or there is a concept that generalize the concept of constant and I can't see it ?
Background: I am having some troubles in grasping the real meaning of an operator when dealing with linear algebra and matrices; the so called identities like $0$ for algebraic sum and $1$ for the multiplication, can be seen as an operator? Which means that the identity matrix is an operator of arity $0$, which means that an identity matrix can be generalized as a matrix $M$, $n \times n$ wide where all cells are 0 except the ones at the coordinates $i,j$ where $i=j=n$? So the identity matrix operator is basically an infinite matrix?