 More formally, if denotes the set of all options and denotes the set of "satisficing" options, then selecting a satisficing solution (an element of ) is equivalent to the following optimization problem

where denotes the Indicator function of , that is

A solution to this optimization problem is optimal if, and only if, it is a satisficing option (an element of ).Thus, from a decision theory point of view, the distinction between "optimizing" and "satisficing" is essentially a stylistic issue (that can nevertheless be very important in certain applications) rather than a substantive issue.What is important to determine is should be optimized and should be satisficed.