aribitrary

Arbitrary refers to something that is based on random choice or personal whim, rather than any reason or system. It signifies a lack of underlying logic or predetermined structure. In mathematics, an arbitrary element is one that is chosen without any specific properties, allowing for the generalization of theorems and proofs. For example, when proving a theorem about all numbers, one might select an arbitrary number 'x' to represent any possible number.

In computer science, an arbitrary precision arithmetic system allows calculations with numbers of virtually unlimited size, without the usual limitations imposed by fixed-size data types. This means computations can be performed on numbers far exceeding what standard integer or floating-point types can represent. The term can also describe an arbitrary file format, which is a format that has not been standardized and may be specific to a particular application or developer.

In everyday language, an arbitrary decision might be one that seems to have no good reason behind it, or is made without consultation. It implies a freedom from constraint or external influence in the decision-making process.