 The factorial function is definable from the predecessor function plus from multiplication, and it is useful e.g., in combinatorics. The factorial function (denoted by \(\,!\,\)) is recursively definable by the equation \(\,!\, m=Zm(\textsf{V}(\textsf{KI})\textsf{I})(\cdot m(\,!  \,(Pm)))\), that may be read as “if \(m\) is \(0\), then \(\,!\, m=1\), otherwise \(\,!\, m\) equals to \(m\) multiplied by the factorial of \(m-1\).”