In mathematics, an empty or nullary function, is a function whose domain is the empty set. For each set A, there is exactly one such empty function Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... Graph of example function, The mathematical concept of a function expresses the intuitive idea of deterministic dependence between two quantities, one of which is viewed as primary (the independent variable, argument of the function, or its input) and the other as secondary (the value of the function, or output). A... In mathematics, the domain of a function is the set of all input values to the function. ... The empty set is the set containing no elements. ... In mathematics, a set can be thought of as any collection of distinct objects considered as a whole. ...

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This includes every constant formula c; but the range of the empty function is not {c} but instead is the empty set. In mathematics and the mathematical sciences, a constant is a fixed, but possibly unspecified, value. ...

Most authors will not care, when defining the term “constant function” precisely, whether or not the empty function qualifies, and will use whatever definition is most convenient. Sometimes, however, it is best not to consider the empty function to be constant, and a definition that makes reference to the range is preferable in those situations. This is much along the same lines of not considering an empty topological space to be connected, or not considering the trivial group to be simple. In mathematics a constant function is a function whose values do not vary and thus are constant. ... Topological spaces are structures that allow one to formalize concepts such as convergence, connectedness and continuity. ... In topology and related branches of mathematics, a topological space X is said to be disconnected if it is the union of two disjoint nonempty open sets. ... The following list in mathematics contains the finite groups of small order up to group isomorphism. ... In mathematics, a simple group is a group which is not the trivial group and whose only normal subgroups are the trivial group and the group itself. ...