összeghatárok

Összeghatárok is a Hungarian term formed from the words összege/n (sum) and határ (limit, boundary). It refers to the range of values that a sum can take under given constraints. The concept is used mainly in mathematical and applied contexts to describe the possible total of a set of quantities.

In mathematics, összeghatárok arise when the individual summands are restricted. If the summands a1, a2, …, an lie within known intervals, then the total S = a1 + a2 + ... + an has corresponding lower and upper bounds, called the összeghatárok of the sum. A simple rule is: if αi ≤ ai ≤ βi for all i, then ∑ αi ≤ ∑ ai ≤ ∑ βi. For example, if 0 ≤ ai ≤ 3 for i = 1, ..., n, then 0 ≤ ∑ ai ≤ 3n. This captures the worst-case or best-case totals implied by the individual constraints.

Beyond pure math, összeghatárok are used in statistics, computer science, and optimization to reason about margins, resource limits, or cumulative quantities. They help assess how large or small a total can be given known bounds on components.

Etymology and usage notes: the term is a compound noun built from összegezés (summation) and határ (boundary). In many Hungarian texts, a more common phrasing is “a sum határai” or “a összeg tartománya,” but összeghatárok may appear as shorthand in some discussions.

See also: összeg, határ, határérték, összegzés.