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Recursion is the process of repeating items in a self-similar way. For instance, when the surfaces of two mirrors are exactly parallel with each other, the nested images that occur are a form of infinite recursion. The term has a variety of meanings specific to a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics and computer science, in which it refers to a method of defining functions in which the function being defined is applied within its own definition. Specifically, this defines an infinite number of instances (function values), using a finite expression that for some instances may refer to other instances, but in such a way that no loop or infinite chain of references can occur. The term is also used more generally to describe a process of repeating objects in a self-similar way. ==Formal definitions== In mathematics and computer science, a class of objects or methods exhibit recursive behavior when they can be defined by two properties: # A simple base case (or cases)—a terminating scenario that does not use recursion to produce an answer # A set of rules that reduce all other cases toward the base case For example, the following is a recursive definition of a person's ancestors: *One's parents are one's ancestors (''base case''). *The ancestors of one's ancestors are also one's ancestors (''recursion step''). The Fibonacci sequence is a classic example of recursion: Many mathematical axioms are based upon recursive rules. For example, the formal definition of the natural numbers by the Peano axioms can be described as: ''0 is a natural number, and each natural number has a successor, which is also a natural number.'' By this base case and recursive rule, one can generate the set of all natural numbers. Recursively defined mathematical objects include functions, sets, and especially fractals. There are various more tongue-in-cheek "definitions" of recursion; see recursive humor. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Recursion」の詳細全文を読む スポンサード リンク
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