Reaalnumber

Reaalnumber is not a standard term in mathematics. In most sources, the real numbers are referred to as the real number system, denoted by R. If the form “reaalnumber” appears, it is typically a misspelling or a transliteration variant in non-English texts, and it refers to the same concept as a real number rather than to a distinct entity.

The real numbers form a complete, ordered field that contains all rational numbers (integers and fractions) and all irrational numbers (such as sqrt(2) or pi). They can be represented as points on the real number line and support the usual arithmetic operations: addition, subtraction, multiplication, and division by nonzero numbers. Real numbers can be described by decimal expansions, where every real number has at least one decimal representation; some numbers have two (for example, 0.999... equals 1).

Key properties of the real numbers include the density of the rational numbers—between any two real numbers there is a rational—and completeness: every nonempty set of real numbers that is bounded above has a least upper bound. They also form an ordered, archimedean, and complete field, which underpins many concepts in analysis and topology.

Applications of real numbers are widespread in science and engineering. They provide the foundation for measuring continuous quantities such as length, time, temperature, and velocity, and they underpin the formal development of calculus and real analysis. The standard term is “real number”; “reaalnumber” is typically a typographical or transliteration variant rather than a separate mathematical object.