Codomain

In Maths¹, the codomain of a function is the set to which it's output belongs. The exact set of a functions output is known as its range.

Backlinks

• A Programmers Introduction to Mathematics
  • codomain
• Topic: Maths
  • codomain
• Mathematical Functions
  • A function in mathematics¹ is a relation between a value in a domain and a value in a codomain across a range. In programming terms, this means that mathematical functions are single-arity and pure. In other words, they take a single value and, given the same value, always produce the same output.
• Range
  • In Maths¹, the range of a function is the set of all possible outputs within the Codomain. This might be smaller than the codomain itself if the function is not injective.
• A pair of types with the same cardinality will always be isomorphic
  • There will always be a way of exhaustively mapping each value of type $a$ to type $b$, injectively and surjectively when viewing the domain and the codomain as a set.
• Language: Function over a set
  • In maths, for a given function, it can be said to operate 'over' a set in the case that its domain and codomain are in the same set. For example the function $f : \\mathbb{R} \\rightarrow \\mathbb{R}$ could be said to be a function over reals.

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1. from a Programmers intro to Maths ↩↩↩