Reálne

Reálne is a word used in Slovak and Czech with several related senses. As an adjective and adverb, it means real, actual, genuine, or feasible, describing something that exists in reality or corresponds to facts rather than to theory or appearance. In everyday language it is used to emphasize practicality or authenticity: for example, "reálne problémy" (real problems), "reálna situácia" (the real situation), or "reálna cena" (the current price). The term can also replace "skutočný" in many contexts, though nuances may differ by dialect.

In mathematics, Slovak and Czech speakers use "reálne čísla" or "reálné čísla" to denote the real numbers. This is the set of numbers that can be placed on the number line: all rational numbers (fractions) and all irrational numbers such as √2 or π. Real numbers form a complete ordered field and are uncountable; they provide the foundation for calculus and real analysis. The symbol most often used is R. The concept was developed in the 19th century by mathematicians including Bolzano, Cantor, and Dedekind, to give a rigorous underpinning to limits, continuity, and real-valued functions.

Outside mathematics, the sense of reálne as "real" or "actual" remains central to distinguishing fact from hypothesis, possibility, or appearance in Slovak and Czech.