Definition:Ordered Tuple/Empty

Definition
Let $S$ be a set.

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


 * $\varnothing \to S$

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


 * $\N^*_0 = \varnothing$

Also see

 * Definition:Empty Mapping