Question

the number (b-a) is called the length of any of the intervals (a,b) ,[a.b],[a,b) or (a,b).
What is meant by it

Answer 1

Step-by-step explanation:

By an interval we mean a subset I of R such that

(i) for every a, b ∈ I with a < b, (a, b) ⊆ I and

(ii) there exists x ∈ I and ε > 0 such that (x − ε, x + ε) ⊆ I.

Thus, intervals are of the forms

(a, b), [a, b), (a, b], [a, b] for a, b ∈ R with a < b.

The intervals (a, b), [a, b), (a, b], [a, b] are bounded

intervals with endpoints a and b. Length of an interval I is denoted by `L(I). For a bounded interval I

of end points a, b, L`(I) is defined as b − a.