Määritelmäjoukko

Määritelmäjoukko, known in English as domain, is a fundamental concept in mathematics, particularly in set theory and function theory. It represents the collection of all possible input values for which a mathematical object, such as a function, is defined. For a function f, which maps elements from a set A to a set B, the määritelmäjoukko is the set A. This means that every element within the määritelmäjoukko is a valid input for the function, and the function will produce a corresponding output in its codomain (maalijoukko).

The concept of a määritelmäjoukko is crucial for understanding the behavior and limitations of mathematical expressions. For instance, the function f(x) = 1/x has a määritelmäjoukko of all real numbers except zero, because division by zero is undefined. Similarly, the square root function g(x) = sqrt(x) has a määritelmäjoukko of all non-negative real numbers, as the square root of a negative number is not a real number. Specifying the määritelmäjoukko clarifies the context in which a mathematical object operates and prevents ambiguity. In more advanced mathematics, the concept extends to relations, mappings, and other structures where a set of allowed inputs is essential.