Operational quantities have been derived from the norm of operators between Banach spaces. For example, given an operator \(T\) between Banach spaces \(X\) and \(Y\), \(\text{in}(T)\) is defined as the infimum of the operator norms of \(TJ_ M\) over all infinite dimensional closed subspaces \(M\), where \(J_ M\) denotes the injection of the subspace \(M\) into \(X\). This has in turn been used to characterize upper semi-Fredholm operators. In an effort to generalize this type of construction, the author considers the abstract setting of maps from a set \(X\) with two orders related by certain properties. This is called a biordered space. If an initial map is bounded and monotone, then it is established that only three different new maps can be derived using the infimum and supremum.