( a , b ) = ] a , b [ = { x ∈ R ∣ a < x < b } , [ a , b ) = [ a , b [ = { x ∈ R ∣ a ≤ x < b } , ( a , b ] = ] a , b ] = { x ∈ R ∣ a < x ≤ b } , [ a , b ] = [ a , b ] = { x ∈ R ∣ a ≤ x ≤ b } . {\displaystyle {\begin{aligned}{\color {RedOrange}(}a,b{\color {RedOrange})}={\mathopen {\color {RedOrange}]}}a,b{\mathclose {\color {RedOrange}[}}&=\{x\in \mathbb {R} \mid a{\color {RedOrange}<}x{\color {RedOrange}<}b\},\\{}{\color {OliveGreen}[}a,b{\color {RedOrange})}={\mathopen {\color {OliveGreen}[}}a,b{\mathclose {\color {RedOrange}[}}&=\{x\in \mathbb {R} \mid a{\color {OliveGreen}\leq }x{\color {RedOrange}<}b\},\\{}{\color {RedOrange}(}a,b{\color {OliveGreen}]}={\mathopen {\color {RedOrange}]}}a,b{\mathclose {\color {OliveGreen}]}}&=\{x\in \mathbb {R} \mid a{\color {RedOrange}<}x{\color {OliveGreen}\leq }b\},\\{}{\color {OliveGreen}[}a,b{\color {OliveGreen}]}={\mathopen {\color {OliveGreen}[}}a,b{\mathclose {\color {OliveGreen}]}}&=\{x\in \mathbb {R} \mid a{\color {OliveGreen}\leq }x{\color {OliveGreen}\leq }b\}.\end{aligned}}}