MATH.4:2 - Problem

An assertion that a suitable object exists can leave the receiver unable to obtain it. A recursive formula can leave a different gap: it may call itself without reaching an answer, omit a case, or return objects that fail the required property.

The mathematical task is to build the operation and its justification together. The case for a larger input must use only what the smaller-input results actually provide. Sometimes this reveals that the proposed result was too weak: the step needs an extra parameter or an auxiliary value.