Reaalilukuna

Reaalilukuna is a Finnish mathematical term meaning “as a real number” and is used to indicate that a quantity is treated within the real-number system. In international notation, this system is the set of real numbers, denoted by the symbol ℝ.

Real numbers include all rational numbers (integers and fractions) and irrational numbers (non-terminating, non-repeating decimals). They can be represented on the number line and form a complete ordered field: they can be added, subtracted, multiplied, and divided (except by zero), and they obey the usual order properties.

The decimal expansions of real numbers are either terminating or infinite; rational numbers have terminating or repeating decimals, while irrational numbers have non-repeating, non-terminating decimals. Real numbers are a subset of complex numbers, with any real x corresponding to the complex number x + 0i. The completeness axiom states that every nonempty subset of real numbers that is bounded above has a least upper bound.

In practice, the phrase “reaalilukuna” is used in Finnish texts when an expression or quantity is specifically to be interpreted as a real number, rather than as a complex number or other type of quantity. See also Real numbers, Real analysis, Complex numbers.