Empty: [ b , a ] = ( b , a ) = [ b , a ) = ( b , a ] = ( a , a ) = [ a , a ) = ( a , a ] = { } = ∅ {\displaystyle [b,a]=(b,a)=[b,a)=(b,a]=(a,a)=[a,a)=(a,a]=\{\}=\emptyset } Degenerate: [ a , a ] = { a } {\displaystyle [a,a]=\{a\}} Proper and bounded: Open: ( a , b ) = { x ∣ a < x < b } {\displaystyle (a,b)=\{x\mid a<x<b\}} Closed: [ a , b ] = { x ∣ a ≤ x ≤ b } {\displaystyle [a,b]=\{x\mid a\leq x\leq b\}} Left-closed, right-open: [ a , b ) = { x ∣ a ≤ x < b } {\displaystyle [a,b)=\{x\mid a\leq x<b\}} Left-open, right-closed: ( a , b ] = { x ∣ a < x ≤ b } {\displaystyle (a,b]=\{x\mid a<x\leq b\}} Left-bounded and right-unbounded: Left-open: ( a , + ∞ ) = { x ∣ x > a } {\displaystyle (a,+\infty )=\{x\mid x>a\}} Left-closed: [ a , + ∞ ) = { x ∣ x ≥ a } {\displaystyle [a,+\infty )=\{x\mid x\geq a\}} Left-unbounded and right-bounded: Right-open: ( − ∞ , b ) = { x ∣ x < b } {\displaystyle (-\infty ,b)=\{x\mid x<b\}} Right-closed: ( − ∞ , b ] = { x ∣ x ≤ b } {\displaystyle (-\infty ,b]=\{x\mid x\leq b\}} Unbounded at both ends (simultaneously open and closed): ( − ∞ , + ∞ ) = R {\displaystyle (-\infty ,+\infty )=\mathbb {R} } :