[ a , b ]{ x ∈ R ∣ a ≤ x ≤ b } , ( − ∞ , b ]{ x ∈ R ∣ x ≤ b } , [ a , + ∞ )
[ a , b ][ a , b ]{ x ∈ R | a ≤ x ≤ b } .
\;[a,b]&=\{x\in \mathbb {R} \mid a\leq x\leq b\},\\\left(-\infty ,b\right]&=\{x\in \mathbb {R} \mid x\leq b\},\\\left[a,+\infty \right)&=\{x\in \mathbb {R} \mid a\leq x\},\\(-\infty ,+\infty )&=\mathbb {R} ,\\\left[a,a\right]&=\{a\}.\end{aligned}}} The closed intervals are those intervals that are closed sets for the usual topology on the real numbers.
(a,b)={\mathopen {]}}a,b{\mathclose {[}}&=\{x\in \mathbb {R} \,|\,a<x<b\},\\{}[a,b)={\mathopen {[}}a,b{\mathclose {[}}&=\{x\in \mathbb {R} \,|\,a\leq x<b\},\\{}(a,b]={\mathopen {]}}a,b{\mathclose {]}}&=\{x\in \mathbb {R} \,|\,a<x\leq b\},\\{}[a,b]={\mathopen {[}}a,b{\mathclose {]}}&=\{x\in \mathbb {R} \,|\,a\leq x\leq b\}.\end{aligned}}} Perhatikan bahwa (a, a), [a, a), dan (a, a] melambangkan himpunan kosong, sedangkan [a, a] melanmbangkan himpunan {a} .
[ a , b ){ x ∈ R ∣ a ≤ x < b } . \left(a,b\right]&=\{x\in \mathbb {R} \mid a<x\leq b\},\\\left[a,b\right)&=\{x\in \mathbb {R} \mid a\leq x<b\}.\\\end{aligned}}} In summary, a set of the real numbers is an interval, if and only if it is an open interval, a closed interval, or a half-open interval.
(a,b)={\mathopen {]}}a,b{\mathclose {[}}&=\{x\in \mathbb {R} \,|\,a<x<b\},\\{}[a,b)={\mathopen {[}}a,b{\mathclose {[}}&=\{x\in \mathbb {R} \,|\,a\leq x<b\},\\{}(a,b]={\mathopen {]}}a,b{\mathclose {]}}&=\{x\in \mathbb {R} \,|\,a<x\leq b\},\\{}[a,b]={\mathopen {[}}a,b{\mathclose {]}}&=\{x\in \mathbb {R} \,|\,a\leq x\leq b\}.\end{aligned}}} Perhatikan bahwa (a, a), [a, a), dan (a, a] melambangkan himpunan kosong, sedangkan [a, a] melanmbangkan himpunan {a} .
Both notations are described in International standard ISO 31-11.
Kedua notasi ini dijelaskan dalam International standard ISO 31-11.
(a,b)={\mathopen {]}}a,b{\mathclose {[}}&=\{x\in \mathbb {R} \mid a<x<b\},\\[5mu][a,b)={\mathopen {[}}a,b{\mathclose {[}}&=\{x\in \mathbb {R} \mid a\leq x<b\},\\[5mu](a,b]={\mathopen {]}}a,b{\mathclose {]}}&=\{x\in \mathbb {R} \mid a<x\leq b\},\\[5mu][a,b]={\mathopen {[}}a,b{\mathclose {]}}&=\{x\in \mathbb {R} \mid a\leq x\leq b\}.\end{aligned}}} Each interval (a, a), [a, a), and (a, a] represents the empty set, whereas [a, a] denotes the singleton set {a}.
(a,b)={\mathopen {]}}a,b{\mathclose {[}}&=\{x\in \mathbb {R} \,|\,a<x<b\},\\{}[a,b)={\mathopen {[}}a,b{\mathclose {[}}&=\{x\in \mathbb {R} \,|\,a\leq x<b\},\\{}(a,b]={\mathopen {]}}a,b{\mathclose {]}}&=\{x\in \mathbb {R} \,|\,a<x\leq b\},\\{}[a,b]={\mathopen {[}}a,b{\mathclose {]}}&=\{x\in \mathbb {R} \,|\,a\leq x\leq b\}.\end{aligned}}} Perhatikan bahwa (a, a), [a, a), dan (a, a] melambangkan himpunan kosong, sedangkan [a, a] melanmbangkan himpunan {a} .
When a > b, all four notations are usually taken to represent the empty set.
Ketika a > b, maka keempat notasi ini biasanya diasumsikan melambangkan himpunan kosong.
[ a , ∞ ){ x ∈ X ∣ a ≲ x } , ,} ( − ∞ , b ){ x ∈ X ∣ x < b } , ,} ( − ∞ , b ]{ x ∈ X ∣ x ≲ b } , ,} ( − ∞ , ∞ )X , where x < y means x ≲ y ≴
{ x | x > a } } tertutup kiri: [ a , ∞ ){ x | x ≥ a } } tak berbatas kiri dan berbatas kanan: terbuka kanan: ( − ∞ , b ){ x | x < b } } tertutup kanan: ( − ∞ , b ]{ x | x ≤ b } } tak berbatas di kedua ujungnya: ( − ∞ , + ∞ )R {\displaystyle (-\infty ,+\infty )
Weisstein, Eric W. "Interval".
(Inggris) Weisstein, Eric W. "Interval".