Definitions
An infinite set can also be ordered cyclically. Important examples of infinite cycles include the unit circle, S1, and the rational numbers, Q. The basic idea is the same: we arrange elements of the set around a circle. However, in the infinite case we cannot use the immediate successor relation; instead we use a ternary relation denoting that elements a, b, c occur after each other (not necessarily immediately) as we go around the circle.
By currying the arguments of the ternary relation, one can think of a cyclic order as a one-parameter family of binary order relations, called cuts, or as a two-parameter family of subsets of K, called intervals.
Read more about this topic: Cyclic Order
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