Definition:Ordered Tuple/Empty

Definition

Let $S$ be a set.

The empty ordered tuple on $S$ is the empty mapping:

$\O \to S$

from the empty set $\O$ to $S$.

It is justified to call this an ordered tuple because the "first $0$ non-zero natural numbers" form the empty set:

$\N^*_0 = \O$

Also see

• Definition:Empty Mapping

• Results about ordered tuples can be found here.