Illustrate the intervals in mathematics

Carrier set of a Range of T is the set of all sets of values v ∈ T such that for some start value s ∈ T and end value e ∈ T, either s ≤ v and v ≤ e (the inclusive ranges), or s ≤ v and v < s (the exclusive ranges), plus empty set. For instance, carrier set of the Range of Integer is the set of all sequences of contiguous integers. Carrier set of the Range of Real is the set of all sets of real number greater than or equal to a given number and either less than or equal to another, or less than another. These sets are known as intervals in mathematics.