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An
-ary relation is a set
together with a set
of ordered tuples
.
Binary relations
A
binary relation or
dyadic relation is a set
together with a set
of ordered pairs
, i.e.
| {(s, s′ ) ∈ S × S | s ρS s′} |
where
.
For example, the set
together with the set
| "<S" := {(1, 2), (2, 3), (1, 3)} |
defines the binary relation
| {(s, s′ ) ∈ S × S | s <S s′} |
where
| s <S s′ := (s, s′ ) ∈ "<S" |
.
For example, the set
together with the set
| "dividesS" := {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 2), (2, 4), (2, 6), (3, 3), (3, 6), (6, 6)} |
defines the binary relation
| {(s, s′ ) ∈ S × S | s "dividesS" s′} |
where
| s "dividesS" s′ := (s, s′ ) ∈ "dividesS" |
.
Ternary relations
A
ternary relation or
triadic relation is a set
together with a set
of ordered triples
.
For example, the set
together with the set
| "betweenS" := {(1, 2, 3), (1, 2, 4), (1, 3, 4), (2, 3, 4)} |
defines the ternary relation
| {(s1, s2, s3 ) ∈ S 3 | s1 <S s2 <S s3} |
where
| s1 <S s2 <S s3 := (s1, s2, s3 ) ∈ "betweenS" |
.
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