 Recursive functions are abstract relations defined on natural numbers. In principle they can be defined without any reference to space and time. Such functions must be distinguished from the operations that we use to compute them. These operations mainly depend on the type of symbolic representations that we choose for them. We can represent the number seven as unary number \(|||||||\), binary number 111, Roman number VII, or Arabic number 7 and depending on our choice other types of sequential symbol manipulation can be used to compute the addition two plus five is seven, which can be represented as:   \[ \begin{align} || + ||||| &amp; = ||||||| \\ 10 + 101 &amp;  = 111 \\ \textrm{II} + \textrm{V} &amp; = \textrm{VII}\\ 2 + 5 &amp;= 7 \\ \end{align} \]     Consequently we can read these four sentences as four statements of the same mathematical truth, or as statements specifying the results of four different operations. 