Reading a text on computability by a guy called Cutland, and he basically asserts the following, which is suppose to be a proof by recursion that x ∸ 1 is a computable function:
(1) 0 ∸ 1 = 0
(2) (x+1) ∸ 1 = x; by recursion
So my question is: how on earth is this a proof of x ∸ 1 being computable? I just don't see how, say, 3 ∸ 1 = 2 can be derived from 0 ∸ 1 = 0? What I mean is, (1) isn't included in the expression on the right hand side of the equation in (2), so in what sense is this a recursive definition?