This is fine as a beginner rule of thumb but it shouldn't be regarded as a universal truth about recursion. Its also possible for a simple evaluation without recursion to happen at infinity rather than at zero. In practice this usually means picking a large value of the input as a cut off point to apply an approximation or return a standard value instead.
For example, take an implementation of exp(x). The exponential function is defined as the sum to infinity of (x^n)/n!. This could be implemented recursively as exp(x,n) = 1+(x/n)exp(x,n+1). The challenge is to figure out the value (or criteria) for what value of n to cut this infinite evaluation short. Well, once n is larger than x all future terms will be multiplied by a factor less than 1. So pick some proportionality constant k such that if x is k times smaller than n (that is, x * k < n) then the remainder is presumed negligible and the function returns 1.
Another really nice example I know involves finding the resistance across a simple but infinitely repeating circuit. At very large n, there are so many resistors in the way that the contribution of the remaining circuit connected in parallel is basically nothing. So pick whatever value of net resistance R_N for an arbitrary cut off point N, then recursively find the net resistance in the circuit up to point N-1 connected in parallel with everything remaining in the circuit after point N.
There are other cases I can think of where the base case is actually the function converging (or becoming linear) for large rather than small inputs. And still other cases I know of where the function has more than one input argument, and thus it might make sense to increase the size in one input to reduce it in another etc.
For example, take an implementation of exp(x). The exponential function is defined as the sum to infinity of (x^n)/n!. This could be implemented recursively as exp(x,n) = 1+(x/n)exp(x,n+1). The challenge is to figure out the value (or criteria) for what value of n to cut this infinite evaluation short. Well, once n is larger than x all future terms will be multiplied by a factor less than 1. So pick some proportionality constant k such that if x is k times smaller than n (that is, x * k < n) then the remainder is presumed negligible and the function returns 1.
Another really nice example I know involves finding the resistance across a simple but infinitely repeating circuit. At very large n, there are so many resistors in the way that the contribution of the remaining circuit connected in parallel is basically nothing. So pick whatever value of net resistance R_N for an arbitrary cut off point N, then recursively find the net resistance in the circuit up to point N-1 connected in parallel with everything remaining in the circuit after point N.
There are other cases I can think of where the base case is actually the function converging (or becoming linear) for large rather than small inputs. And still other cases I know of where the function has more than one input argument, and thus it might make sense to increase the size in one input to reduce it in another etc.