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INTERVAL


In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set.

Open interval of extremes a and b: (a,b) = {x ∈ ℝ | a < x < b}

Closed interval of extremes a and b: [a,b] = {x ∈ ℝ | a ≤ x ≤ b}

Left-closed and right-open interval: [a,b) = {x ∈ ℝ | a ≤ x < b}

Left-open and right-closed interval: (a,b] = {x ∈ ℝ | a < x ≤ b}

(a,+∞) = {x ∈ ℝ | a < x}

[a,+∞) = {x ∈ ℝ | a ≤ x}

(-∞,b) = {x ∈ ℝ | x < b}

(-∞,b] = {x ∈ ℝ | x ≤ b}

(a,a) = {x ∈ ℝ | a < x < a} = Ø

[a,a] = {x ∈ ℝ | a ≤ x ≤ a} = {a}