In system operations it is commonly assumed that arbitrary changes to a system can be reversed or `rolled back', when errors of judgement and procedure occur. We point out that this view is flawed and provide an alternative approach to determining the outcome of changes. Convergent operators are fixed-point generators that stem from the basic properties of multiplication by zero. They are capable of yielding a repeated and predictable outcome even in an incompletely specified or `open' system. We formulate such `convergent operators' for configuration change in the language of groups and rings and show that, in this form, the problem of convergent reversibility becomes equivalent to the `division by zero' problem. Hence, we discuss how recent work by Bergstra and Tucker on zero-totalised fields helps to clear up long-standing confusion about the options for `rollback' in change management.