In
mathematics and
physics, the term
generator or
generating set may refer to any of a number of related concepts. The underlying concept in each case is that of a smaller
set of objects, together with a set of
operations that can be applied to it, that result in the creation of a larger collection of objects, called the
generated set. The larger set is then said to be
generated by the smaller set. It is commonly the case that the generating set has a simpler set of properties than the generated set, thus making it easier to discuss and examine. It is usually the case that properties of the generating set are in some way preserved by the act of generation; likewise, the properties of the generated set are often reflected in the generating set.