Definition: Interval
Let be a set with a total order and a strict total order .
Every pair with defines:
- an open interval as the set ;
- a half-open interval as the set ;
- a half-open interval as the set
- a closed interval as the set .
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Definition: Interval
Let S be a set with a total order ≤ and a strict total order <.
Every pair a,b∈S with a<b defines:
- an open interval (a;b) as the set {x∈S∣a<x<b};
- a half-open interval (a;b] as the set {x∈S∣a<x≤b};
- a half-open interval [a;b) as the set {x∈S∣a≤x<b}
- a closed interval [a;b] as the set {x∈S∣a≤x≤b}.