Stephen Kleene notes that any of the six inequality restrictions on the range of the variable "y" is permitted, i.e. "y" < "z", "y" ≤ "z", "w" < "y" < "z", "w" < "y" ≤ "z", "w" ≤ "y" < "z" and "w" ≤ "y" ≤ "z". "When the indicated range contains no "y" such that R("y") "true", the value of the "μ"y"" expression is the cardinal number of the range" (p. 226); this is why the default ""z"" appears in the definition above. As shown below, the bounded μ-operator "μ"y""y"<"z"" is defined in terms of two primitive recursive functions called the finite sum Σ and finite product Π, a predicate function that "does the test" and a representing function that converts {t, f} to {"0", "1"}.