Definition

Noun: - The number of arguments that a function can take: In logic, mathematics, and computer science, "arity" refers to the fixed number of arguments or operands that a function, operation, or relation requires. A function's arity defines its input structure.

Usage

• "Arity" is a technical term used primarily in formal contexts such as programming, logic, and mathematics.
• It is often used with adjectives to specify the number (e.g., nullary, unary, binary, ternary, n-ary).
• Example:

Examples

• In programming:
• In logic:
• In mathematics:

Advanced Usage

• Fixed vs. Variable Arity: Some functions have fixed arity, while others, like variadic functions, can accept a variable number of arguments.
  • In some programming languages, printf is a function with variable arity.
• Adjectival Forms: The concept is commonly expressed using adjectives derived from arity.
  • Binary operations are fundamental in arithmetic. (Here, "binary" implies an arity of two).

Variants and Related Words

• Adjectival Forms:
  • Nullary (adj): Having an arity of zero; taking no arguments.

    • A nullary function is often a constant.
  • Unary (adj): Having an arity of one.

    • The unary minus operator changes the sign of a number.
  • Binary (adj): Having an arity of two.

    • Addition is a binary operation.
  • Ternary (adj): Having an arity of three.
  • N-ary or Multary (adj): Having an arity of 'n' or multiple arguments.

Synonyms

• Argument count: (Informal) The number of arguments.
• Adicity: A synonymous term used especially in logic and philosophy.
• Degree: Sometimes used interchangeably, particularly for predicates in logic (e.g., the degree of a relation).

Related Terms and Concepts

• Function Signature: A broader concept that includes the arity along with the types of arguments and return value.
• Parameter: The variable listed in the function definition that receives the argument.
• Operand: An object of a mathematical or logical operation, the quantity of which is defined by the operator's arity.

Noun

1. the number of arguments that a function can take