Page "Binary relation" Paragraph 11

A special case of this difference in points of view applies to the notion of function.

Many authors insist on distinguishing between a function's codomain and its range.

Thus, a single " rule ," like mapping every real number x to x < sup > 2 </ sup >, can lead to distinct functions and, depending on whether the images under that rule are understood to be reals or, more restrictively, non-negative reals.

But others view functions as simply sets of ordered pairs with unique first components.

This difference in perspectives does raise some nontrivial issues.

As an example, the former camp considers surjectivity — or being onto — as a property of functions, while the latter sees it as a relationship that functions may bear to sets.