Nullary operation

Definition

Let $A$ be a set and let $A^0 = \set{()}$ be the set whose only element is the empty tuple $()$ . A nullary operation on $A$ is a finitary operation of arity $0$ , that is, a function $c \colon A^0 \to A$ . The element $c(()) \in A$ is the constant given by $c$ .

Remarks

The map $c \mapsto c(())$ is a bijection from the set of nullary operations on $A$ to $A$ . So a nullary operation is usually written as an element of $A$ .

Example: in $(\Z, +, 0)$ the constant $0$ is the nullary operation $c$ with $c(()) = 0$ .

Non-example: on the empty set there is no nullary operation, because a function from the one-element set $A^0$ to $\emptyset$ does not exist. This is why an algebra with a constant has a nonempty universe.

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Finitary operation concept
Nullary operation definition

Tag	`GXNE1EPK0S`
URI	`m2://GXNE1EPK0S`
Kind	definition
Writing	W0 stub
MSC	08A62, 08A02
Defines	Nullary operation
Uses	Finitary operation
Changed	2 November 2026

Nullary operation

Definition

Remarks

Reading path

Further reading

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