sokaságok

Sokaságok is the plural form of sokaság, a Hungarian term used in mathematics and related fields to denote a collection or group of objects. The word generally refers to a whole made up of individual elements that are considered together, without prescribing a particular formal structure.

In mathematical usage, sokaság is a flexible notion and is often used interchangeably with gyűjtemény or halmaz, depending on the author. However, halmaz has a precise formal meaning in set theory: a collection with distinct elements where order does not matter and repetition is not allowed. Because sokaság can be used more loosely, some authors employ it to encompass collections that may admit repetition (multisets) or carry extra structure, whereas others reserve sokaság for a broader, less formal concept.

Sokaságok can be finite or infinite. Examples include the sokaság of natural numbers as an infinite collection, or a finite sokaság such as {1, 2, 3}. The term is also common in applied contexts: a sokaság of observations in statistics, a sokaság of functions or sequences in analysis, or a sokaság of geometric objects in geometry.

In Hungarian discourse, sokaság is a general descriptive term for a grouping of items, while halmaz and gyűjtemény refer to more specific mathematical notions. The exact meaning of sokaság depends on context and author, but it remains a prevalent way to express the idea of a collection of objects considered as a unit.