Reaalnumbreid

Reaalnumbreid, known in English as real numbers, constitute a fundamental concept in mathematics. They encompass all the rational numbers, which can be expressed as a fraction of two integers, and all the irrational numbers, which cannot be expressed in such a way. This includes numbers with decimal representations that either terminate, repeat, or go on infinitely without repeating.

The set of real numbers is often visualized as a continuous line, known as the number line, where each point on the line corresponds to a unique real number. This line extends infinitely in both positive and negative directions. The number zero is a key reference point on this line.

Real numbers are essential for measurement and describing continuous quantities in the real world. They are used extensively in calculus, algebra, geometry, and virtually all branches of mathematics and science. The properties of real numbers, such as their ordering and completeness, are crucial for developing advanced mathematical theories.

The set of real numbers is denoted by the symbol ℝ. It is a complete ordered field, meaning it possesses both ordering properties (like less than or greater than) and algebraic properties (like addition and multiplication) that allow for a robust mathematical framework.