The extremes of an interval refer to the two boundary points that define its limits. An interval is a subset of the real number line between two values, denoted by square brackets [a, b] or parentheses (a, b), where "a" represents the lower extreme and "b" represents the upper extreme. This concept is integral in mathematics, especially in the field of analysis and calculus.
The lower extreme of an interval is the smallest value within the set, and it is inclusive when using square brackets. However, when using parentheses, the lower extreme is excluded. The upper extreme, on the other hand, is the largest value in the interval, which is inclusive when using square brackets but excluded when using parentheses.
Understanding the extremes of an interval is crucial in various mathematical applications, such as calculating the range, finding critical points, or determining convergence and divergence of sequences and series. In the context of functions, the extremes of an interval help establish the domain and range.
In summary, the extremes of an interval serve as the boundaries that define the range of values within a subset of the real number line. They provide important information for mathematical analysis, calculation, and establishing the domain and range of functions.
