What is well-defined?

  • (adj): Accurately stated or described.
    Example: "A set of well-defined values"
    Synonyms: clear
    See also — Additional definitions below

Well-defined

In mathematics, a function is well-defined if it gives the same result when the form (the way in which it is presented) but not the value of an input is changed. For example, a function that is well-defined will take the same value when 0.5 is the input as it does when 1/2 is the input. An example of a "function" that is not well-defined is "f(x) = the first digit that appears in x". For this function, f(0.5) = 0 but f(1/2) = 1. A "function" such as this would not be considered a function at all, since a function must have exactly one output for a given input.

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More definitions of "well-defined":

  • (adj): Having a clean and distinct outline as if precisely cut along the edges.
    Example: "Well-defined features"
    Synonyms: chiseled