multiplicitásokkal

Multiplicitásokkal is a Hungarian term that translates to "with multiplicities" in English. It is primarily used in mathematics, particularly in algebra and combinatorics, to describe how many times a particular element or factor appears in a given set or structure.

For instance, when factoring a polynomial, a root might have a multiplicity greater than one. If a polynomial has a root 'r' with a multiplicity of 2, it means that '(x-r)' appears twice as a factor. This concept is crucial for understanding the structure of polynomial roots and their behavior.

In set theory, multiplicity is used to describe multisets, which are collections where elements can appear more than once. Unlike a standard set where each element is unique, a multiset allows for repeated elements, and the multiplicity of an element indicates how many times it is present in the multiset.

Combinatorics also utilizes the idea of multiplicity when counting arrangements or selections. For example, when considering permutations with repetitions, the multiplicity of each distinct element dictates the number of unique arrangements possible. The term "multiplicitásokkal" therefore signifies that such repetitions or repeated occurrences are being accounted for in a mathematical context.