Formally, a $k$-place relation\index{relation $k$-place} on a set $X$ is just a subset of $X^k$, {\em i.e.\/} the collection of sequences of length $k$ of elements of $X$ for which the relation is true.} Finally, $=$\index{$=$} is a special binary relation\index{relation binary} symbol intended to represent equality\index{equality}. \begin{exmp} \label{e:lannt} Since the logical symbols are always the same, first-order languages are usually defined by specifying the non-logical symbols.

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