If x and y are two numbers in a set, then any number between x and y also belongs to this set. For example, a set of real numbers satisfying 0 ≤ x ≤ 1 is an interval, which contains all real numbers between 0, 1 and 0 to 1. Other examples include real number sets and negative real number sets.
Interval plays an important role in integral theory, because as the simplest set of real numbers, it is easy to define their length or measure. Then we can extend the concept of measure and derive Borel measure and Lebesgue measure. Interval is also the core concept of interval arithmetic.
Interval arithmetic is a numerical analysis method used to calculate rounding error. The concept of interval can also be extended to any subset S of totally ordered set T, so that if both X and Y belong to S, and X
Interval introduction
The image of interval under continuous function is also interval, which is another expression of intermediate value theorem. The intersection of any set of intervals is still an interval. The union of two intervals is an interval if and only if their intersection is not empty, or the endpoint not included in one interval happens to be the endpoint included in another interval.