# Formal definition of cyclic order

I want to say the nodes $0,1,2 \ldots n-1$ are in cyclic order and want to express that in terms of mathematical notation. Say $0 \prec_c 1$, $1 \prec_c 2$, $n-1 \prec_c 0$ etc.

What will be the formal definition of cyclic ordering? How do I define the cyclic order $\prec_c$ in a formal way.

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Following Wikipedia, define your order rather as a ternary "betweenness" relation. Or say that a cyclic order of a set $S$ of $n$ elements is a transitive operation of a cyclic group $\mathbb Z/n\mathbb Z$ on $S$ (with $x\prec_c y\iff 1+x = y$).