A subset I of ℝ is an interval if whenever x < y < z and x ∈ I, z ∈ I, then y ∈ I.

A bounded interval on the real line is a subset of ℝ defined in terms of end‐points a and b. Since each end‐point may or may not belong to the subset, there are four types of bounded interval:

1. (i) the closed interval {x | x∈ℝ and a ≤ x ≤ b}, denoted by [a, b],

2. (ii) the open interval {x | x∈ℝ and a<x<b}, denoted by (a, b),

3. (iii) the interval {x | x∈ℝ and a ≤ x<b}, denoted by [a, b),

4. (iv) the interval {x | x∈ℝ and a<x ≤ b}, denoted by (a, b].

There are also four types of unbounded interval:

1. (v) {x | x∈ℝ and a ≤ x}, denoted by [a, ∞),

2. (vi) {x | x∈ℝ and a<x}, denoted by (a, ∞),

3. (vii) {x | x∈ℝ and x ≤ a}, denoted by (−∞, a],

4. (viii) {x | x∈ℝ and x<a}, denoted by (−∞, a).

Here ∞ (read as ‘infinity’) and −∞ (read as ‘minus infinity’) are not real numbers, but the use of these symbols provides a convenient notation.