Reciprocal function extended within reals

The Reciprocal function extended within reals is an extension to the reciprocal function denoted R+(n), in which it is like the normal reciprocal function but the reciprocal of zero is zero. The idea is that the reciprocal function cannot take zero nor return zero, so why not close the gap by making zero return zero? This extension does, however, violate the inequality R(n)n = 1.