Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. The target space into which a function maps elements of its domain. It always contains the range of the function, but can be larger than the range if the function is not surjective.
Etymologies
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Examples

For example, if a unary function is considered as a set of ordered pairs, then the domain and codomain are given by the first and second projections, respectively.

Combinatory terms are thought of as functions, and functions are thought to have a domain (a set of possible inputs) and a codomain (a set of possible outputs).

Category theory, where functions are components of categories (without a set theoretic reduction assumed), retains the notions of a domain and a codomain; moreover, every function has a unique domain and codomain.

Functions that have the same domain and codomain may be quite different, however, by abstraction, they are of the same sort or type.

The probability that all n values are in the lower q fraction of the codomain is p = qn.
How do evolutionary processes create information?  The Panda's Thumb

It bears mention that one of them has only the worst codomain value in its range, and another has only the best codomain value in its range.
How do evolutionary processes create information?  The Panda's Thumb

It is astonishing that in 99.99% of trials a value better than 99.999% of those in the codomain is obtained with fewer than one million evaluations.
How do evolutionary processes create information?  The Panda's Thumb

The probability that all n values are in the lower q fraction of the codomain is p = qn
How do evolutionary processes create information?  The Panda's Thumb

In the case that the original function is onetoone, the inverse mapping will also be a function with the domain and codomain interchanged.

Of course it's the "referential transparency": A 'function' is an special kind of relation which assigns values of a domainset to values of a result  ( 'codomain') set.
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