parillisyyttä

Parillisyyttä is the Finnish term for parity or evenness. It describes the property of being even, or more broadly the idea of symmetry between two classes. In everyday Finnish, parillisyyttä is most often discussed in connection with numbers, but the concept appears in several disciplines and contexts.

In mathematics, parity refers to whether an integer is even or odd. A number n is even if it is divisible by 2, and odd otherwise; this is often expressed as n mod 2 = 0 for even and n mod 2 = 1 for odd. Parity governs many basic rules: the sum of two even numbers is even; the sum of two odd numbers is even; the sum of an even and an odd number is odd; the product of any number of even factors is even. Parity is a useful tool in proofs and modular arithmetic, especially when working modulo 2.

Parity also appears in the study of permutations. An even permutation can be achieved by an even number of transpositions, while an odd permutation requires an odd number. The sign of a permutation, +1 for even and −1 for odd, is closely related to determinants in linear algebra.

In computer science, parity is used for simple error detection. A parity bit is added to a binary word to ensure an even or odd total number of 1s. Parity checks can detect single-bit errors, though more robust error-correcting codes are used in practice.

In physics, parity describes symmetry under spatial inversion. The parity operator flips spatial coordinates, and some interactions conserve parity while others, notably the weak interaction, do not. This has been foundational to understanding fundamental symmetries in nature.

Etymologically, parillisyyttä stems from parillinen, meaning even. The term is common in mathematical, physical, and technical Finnish, while in everyday use it often refers to the evenness of integers.