Határrök

Határrök is a term that appears in some Hungarian mathematical texts to denote a limiting value—the value that a sequence, function, or process approaches under a limiting operation. In standard Hungarian mathematical vocabulary, the more common and widely accepted term for this concept is határérték, or simply the limit. As a result, határrök is often described as a variant or regional usage rather than a universally established technical term.

Usage and interpretation in texts that employ határrök are similar to those of határérték. If a sequence (a_n) converges to L, then L can be described as the határrök of the sequence. Likewise, if a function f(x) has a limit L as x approaches a, then L is the határrök of f at a. The exact phrasing may vary by author, but the underlying concept remains the same: a value that the object in question tends toward under a limit process.

Examples help illustrate the idea. For the sequence a_n = 1/n, the határrök is 0. For a function with lim_{x→a} f(x) = L, the határrök at a is L. These examples align with the broader notion of limits used in calculus and analysis.

Relation to terminology. Határrök is typically viewed as a synonym or variant of határérték in discussions of limits, convergence, and continuity. In contemporary standard texts, határérték is preferred, and határrök may be encountered primarily in older literature or in specific regional publications.

See also: határérték, limit, convergence, sequence, function.