We begin this chapter by introducing a convenient notation that is common in some branches of mathematics for indicating a numeric interval: a comma-separated pair of values, enclosed in square brackets or parentheses, with the convention that a bracket means that the endpoint is included, and a parenthesis indicates that the endpoint is excluded. Thus, [1, 2) is the set of values x for which \( 1 \le x < 2, \) and [2, 3] is the adjacent set for which \( 1 \le x \le 2, \). Endpoint distinction is often important in numerical computation, and we use that interval notation extensively in the rest of this book.
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