 If the relation \(R\) is between persons \( x \) and \( y \) when \( x \) is the father of \( y \) then the function will take an individual \(y \) as argument to the value \(x \) as their father. For instance, if \(xRy\) is the relation ‘ \(x\) is father of \(y\)’, then R‘\(y\) is the function which maps \(y\) to the father of \(y\) (if he exists). Note that here the left argument \(x\) corresponds to the value of the function, whereas the right argument \(y\) of R is the argument, or input, to the function R‘\(y\). Likewise if \(xSy\) is the relation of a number to its successor, \(n\) to \(n + 1\), then S‘\(y\) would be the argument of the function which maps \(y\) to the number that it succeeds, rather than expressing the “successor function ” which maps a number to its successor. This is the reverse of the order that is now commonly used when relating functions and relations. Nowadays we reduce functions to a binary relation between the argument in the first place and value in the second place. This may lead to some confusion in the definitions of notions such as the domain and range of a relation below. 