vahemikud

Vahemikud, or intervals in English, are fundamental concepts in mathematics used to describe sets of real numbers. They represent a continuous portion of the number line. There are several types of intervals, distinguished by whether the endpoints are included or excluded.

An open interval, denoted as (a, b), includes all real numbers strictly between a and b, meaning a and b themselves are not part of the interval. A closed interval, denoted as [a, b], includes all real numbers between a and b, as well as the endpoints a and b.

Half-open or half-closed intervals combine these notations. A left-open, right-closed interval is written as (a, b] and includes all numbers greater than a and less than or equal to b. Conversely, a left-closed, right-open interval is written as [a, b) and includes all numbers greater than or equal to a and less than b.

Intervals can also be unbounded. A ray extending infinitely to the right and including its starting point is written as [a, ∞). If the starting point is excluded, it's written as (a, ∞). Similarly, an interval extending infinitely to the left and including its starting point is written as (-∞, a]. If the starting point is excluded, it's written as (-∞, a). The entire set of real numbers is represented by the unbounded interval (-∞, ∞).

Understanding intervals is crucial for various mathematical topics, including calculus, inequalities, and function domains. They provide a precise way to define and work with continuous sets of numbers.