végtelen

Végtelen is a Hungarian term meaning infinite or endless. In everyday Hungarian usage, it describes something without an end. In mathematics, végtelen denotes the concept of quantities or processes that are not bounded. The standard symbol associated with infinity is the lemniscate ∞, popularized in the 17th century by John Wallis.

Mathematics treats infinity as a concept rather than a number. There are two broad ideas: potential infinity, a process that can continue without bound, and actual infinity, a completed infinite total. Infinity appears in limits, where a function's value grows without bound, and in infinite series, where an infinite sequence of terms may converge to a finite sum or diverge.

Infinite sets are classified by cardinality. The set of natural numbers is countably infinite, while the set of real numbers is uncountably infinite. Cantor’s theory showed that some infinities are larger than others, introducing cardinal numbers such as aleph-null. Ordinals extend the notion of order into the infinite, allowing a rigorous treatment of infinite sequences and processes.

Philosophically, infinity has long been debated, appearing in paradoxes and theories about the nature of the universe, time, and mathematics. In Hungarian contexts, végtelen appears in common mathematical terms such as végtelenség (infinity), végtelen sorozat (infinite series), and végtelen sor (infinite sequence).