Let a, b ∈ R and a < b.

Then (note the usage of simple and square brackets carefully)

(i) (a, b) = {x ∈ R / a < x < b} is called open interval of a and b.

(ii) [a, b] = {x ∈ R / a ≤ x ≤ b} is called closed interval of a and b.

(iii) (a, b] = {x ∈ R / a < x ≤ b} is called left open, right closed interval of a and b.

(iv) [ a, b) = {x ∈ R / a ≤ x < b} is called left closed, right open interval of a and b.

(v) (a, ∞) = {x ∈ R / x > a}

(vi) [a, ∞) = {x ∈ R / x ≥ a}

(vii) (– ∞, a) = {x ∈ R / x < a}

(viii) (– ∞, a ] = {x ∈ R / x ≤ a}

(ix) (– a, a) = {x ∈ R / |x| < a}

(x) [– a, a] = {x ∈ R / |x| ≤ a}

(xi) (– ∞, a)⋃(b, ∞) = {x ∈ R / x < a (or) x > b}

(xii) (– ∞, a ]⋃[ b, ∞) = {x ∈ R / x ≤ a (or) x ≥ b}

(xiii) (– ∞, – a)⋃(a, ∞) = {x ∈ R / x < – a (or) x > a} (or) {x ∈ R / |x| > a}

(xiv) (– ∞, – a ]⋃[ a, ∞) = {x ∈ R / x ≤ – a (or) x ≥ a} (or) {x ∈ R / |x| ≥ a}