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The empty set is an $n$-ary relation for every $n$, right?

How should we call a pair $(n;r)$ consisting of some number $n$ and an $n$-ary relation $r$?

To specify $n$ is necessary only when $r$ is empty, but because there are no reason for $r$ not to be empty, I need to specify $n$ explicitly.

Any term describing this situation?

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    I've found the terms "figure" and "ground" in http://en.wikipedia.org/wiki/Theory_of_relations but Wikipedia here seems to use a non-standard terminology.2012-03-26
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    The empty set is a relation if and only if your definition of a relation is one that the empty set satisfies vacuously.2012-03-26

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