Definition

Noun: 1. (Mathematics & Computing) A method or process where the solution to a problem depends on solutions to smaller instances of the same problem. It involves a function, procedure, or definition that refers to itself in its own definition. 2. (General) The act or process of returning or recurring; a repeated application of a rule or procedure.

Usage

The term "recursion" is primarily used in formal, technical contexts like mathematics, computer science, and logic. It describes a self-referential process. * In computer programming, a recursive function calls itself to solve a problem by breaking it down into smaller, identical sub-problems. * In mathematics, a recursive sequence defines each term using the preceding terms.

Examples

• Mathematics: "The definition of the Fibonacci sequence is a classic example of recursion, where each term is the sum of the two preceding ones."
• Computing: "To traverse a directory tree, the programmer implemented a function using recursion."
• General: "The artist's work explores the recursion of patterns within patterns."

Advanced Usage

• Recursive Definition: A definition that defines something in terms of itself, often with a base case to terminate the process.
  • Example: "The factorial function (n!) is often given by the recursive definition: n! = n * (n-1)!, with 0! = 1."
• Mutual Recursion: A situation where two or more functions or definitions call each other recursively.
  • Example: "The functions is_even() and is_odd() can be implemented using mutual recursion."
• Infinite Recursion: A faulty recursive process that lacks a terminating condition, causing it to call itself indefinitely (leading to a stack overflow in computing).
  • Example: "The program crashed due to infinite recursion."

Variants and Related Words

• Recursive (Adjective): Characterized by or using recursion.
  • Example: "A recursive algorithm is elegant but can be memory-intensive."
• Recursively (Adverb): In a recursive manner.
  • Example: "The data structure was defined recursively."
• Recur (Verb): To occur again, periodically or repeatedly. (Shares the Latin root but is a distinct, more general word).
  • Example: "The same issue seems to recur every year."

Synonyms

• Self-reference
• Iteration (Note: Iteration typically uses loops, while recursion uses function calls, but they can solve similar problems.)
• Repetition (General term, not technical)

Related Phrases & Idioms

• Recursive Acronym: An acronym where one of the letters stands for the acronym itself.
  • Example: "GNU stands for 'GNU's Not Unix', which is a recursive acronym."
• To understand recursion, one must first understand recursion: A humorous, self-referential statement that illustrates the concept.
  • Example: "The joke about recursion is itself recursive."

Noun

1. (mathematics) an expression such that each term is generated by repeating a particular mathematical operation