Visszavezethetetlenséggel

Visszavezethetetlenséggel is a Hungarian term that translates to "unreducibility" or "irreducibility" in English. It is a concept that appears in various fields, including mathematics, logic, and computer science, to describe a property where something cannot be broken down into simpler components or explained by simpler principles.

In mathematics, particularly in abstract algebra, irreducible polynomials are those that cannot be factored into the product of two non-constant polynomials over a given field. This concept is fundamental in the study of field extensions and Galois theory. Similarly, irreducible representations in group theory are those that cannot be decomposed into smaller, non-trivial representations.

In logic, a set of axioms or rules might be considered irreducibly fundamental if they cannot be derived from or simplified by a smaller set of underlying principles. This relates to the search for foundational truths or minimal sets of assumptions.

In computer science, the term can refer to problems that are computationally irreducible, meaning they cannot be solved by a more efficient algorithm or reduced to a simpler known problem. The concept of NP-completeness, for example, hinges on the idea that all NP-complete problems are polynomially reducible to each other, implying a form of "connectedness" in their difficulty, but the core problems themselves might be considered irreducible in the sense that no fundamentally easier solution has been found. The idea of visszavezethetetlenséggel emphasizes a certain fundamental and indivisible nature within a given system or context.