mathematical/logical/mekso ternary operator: μ (mu) operator: outputs the most extreme extended-natural number that satisfies relationship/predicate A, where extremeness is bounded by B and of a version determined by C; error output is -1

A is a proposition; it will be a function of at least one variable. The output of this function will cause A to evaluate to true if plugged in as the primary (first) argument of A, except in the Error Case that is described later. C can only be -1 or 1; if C = 1, then extremeness here is defined as "least"; if C = -1, then extremeness here is defined as "greatest". If C = 1, then B is an upperbound; if C = -1, then B is a lowerbound. The contextless default value of C is 1. The contextless default value of B is sgn(C)*infinity (countable, in a sense). The output may be equal to B. The output belongs to the set of all positive integers united with the set of 0 and sgn(C)*infinity. Error Case: If no such number exists, the output is -1. Use A in order to restrict outputs from being pathological for your purposes. Example: Let C = 1 and suppose that there exists a number that satisfies A and is one of the following values: 0, a positive integer, (countable) infinity. Then the output of this function (id est: μ(A, B, 1); where "μ" represents the mu operator) is the least such number that is less than or equal to B. Note that in this example, the contextless default value of B is (countable) infinity.