Intervalmerkingar

Intervalmerkingar, often translated as interval notation or interval markings, is a system used in mathematics to represent a set of real numbers that lie between two specific numbers. These numbers are called the endpoints of the interval. Interval notation provides a concise and unambiguous way to describe continuous subsets of the real number line.

There are four main types of intervals, distinguished by whether the endpoints are included in the set. Open intervals exclude the endpoints. They are denoted using parentheses, for example, (a, b) represents all real numbers x such that a < x < b. Closed intervals include the endpoints. They are denoted using square brackets, for example, [a, b] represents all real numbers x such that a ≤ x ≤ b. Half-open or half-closed intervals include one endpoint but exclude the other. These are denoted with a combination of parentheses and square brackets, such as (a, b] for a < x ≤ b or [a, b) for a ≤ x < b.

Intervals can also be unbounded, meaning they extend infinitely in one or both directions. Unbounded intervals are represented using the infinity symbol (∞) or negative infinity symbol (-∞). For instance, [a, ∞) represents all real numbers x such that x ≥ a, and (-∞, ∞) represents the set of all real numbers. Understanding interval notation is fundamental for various mathematical concepts, including solving inequalities, defining domains and ranges of functions, and working with sets.