Definition
Operator The
operator defines a function from a total function . The minimum is taken over the first argument of
.
Examples
Example
Example
The above is the predecessor function, which is undefined for
.
Example
The above is the subtraction function over
.
Example
The above is the division function over
.
Define
as: Then:
Since
is strictly increasing in for each fixed , there is at most one satisfying the equation. Therefore, The above is the partial inverse of
with respect to the first argument. For example,
is undefined for .
Examples: