“interval”的概念、定义、习题解题方法及翻译-数学辞典

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:

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

(ii) the open interval {x | x∈R and a

(iii) the interval {x | x∈R and a ≤ x

(iv) the interval {x | x∈R and a

There are also four types of unbounded interval:

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

(vi) {x | x∈R and a

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

(viii) {x | x∈R and x

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