Intervals as Subsets of R
Intervals as subsets of R
Closed intervals
Let a and b be two given real numbers such that a < b. Then the set of all real numbers x such that a ≤ x ≤ b is called a closed interval and is denoted by [a, b] .
Thus, [a, b] = { x : x ∈ R, a ≤ x ≤ b} .
Open intervals
If a and b are two real numbers such that a < b, then the set of all real numbers x satisfying a x b is called an open interval and is denoted by (a, b) or ]a, b[ .
Thus, (a,b) = (x: x ∈ R, a < x < b).
Semi-Open or Semi-Closed intervals
If a and b are two real numbers such that a < b, then the sets (a, b] = { x : x ∈ R, a < x ≤ b} and [a, b)={ x 😡 ∈ R, a ≤ x < b are known as semi-open or semi-closed intervals . (a, b] and [a , b) are also denoted by ]a, b] and [a, b[ respectively.
