 A coarse analogy with elementary arithmetic operations, perhaps, can shed some light on the situation. The addition and multiplication of natural numbers always yield a natural number. However, if division is included then it is no longer true that all numerical expressions evaluate to a natural number, since \(7/5\) is a rational number that is not a natural one, and \(n/0\) is undefined (even if \(n\) were real). That is, some numerical expressions do not evaluate to a (natural) number. Although the analogy with combinatory terms is not very tight, it is useful. For instance, \(n/0\) (assuming that the codomain of the function \(\lambda n.\,n/0\) is extended to permit \(r\) to be rational) could be implemented on a computer by a loop (that would never terminate when executed if \(n\ne0\)) which would go through an enumeration of the rational numbers trying to find an \(r\) such that \(r\cdot0=n\).