Part 5/9:
Mathematicians don’t invent rules arbitrarily. Instead, they derive them from foundational axioms designed for consistency. The existence of negative numbers to "undo" positive numbers, combined with distributivity and the properties of zero and addition, drives the conclusion that:
Negative times a negative must be positive to maintain logical consistency within the system.
If this weren't true, contradictions would arise—such as certain equations having multiple inconsistent answers, or fundamental properties failing. In essence, the rule is not an arbitrary choice; it emerges naturally from the structure of mathematics when these axioms are in place.