Final answer:
In mathematics or logic, a disagreement operator, if similar to a negation operator, would not break down when iterated but may result in oscillating truth values. In programming, recursive application might cause a stack overflow if it exceeds stack size. The concept of an operator breaking down is more relevant to computation than pure logic.
Step-by-step explanation:
It seems like you are interested in the concept of an operator, which could be mathematical or logical, and what would happen if it were applied repeatedly. In mathematics or logic, a disagreement operator isn't a standard term, but if we consider it akin to a negation operator, it's clear that too much iteration wouldn't necessarily 'break' the operator but might lead to an oscillating pattern. For instance, repeatedly applying the negation operator to a statement in logic flips the truth value back and forth between true and false.
However, the consequences of iterating an operator heavily depend on the rules defined for its application. In computation and programming, recursively applying an operation can lead to a 'stack overflow' if the computation exceeds the maximum stack size, essentially 'breaking down' the process. But in pure mathematical logic, iterative application of an operator like negation simply results in one of a limited number of possible states (true or false, in the case of negation), without causing any breakdown.