What’s interesting about “If and only If” statements is they’re bi-directional. It’s a very stringent requirement. It’s also odd because In non-math contexts, “if and only if” is usually quite rare as most conditional situations in life and physics are unbalanced and don’t play by IFF. Too many variables outside of the math lab. So I think it makes math definitions kind of unique in that way. People that expect LAW for example to behave like math definitions are surprised that no, law is full of holes and contradictions. It kind of has to be that way.

It’s also odd because In non-math contexts, “if and only if” is usually quite rare as most conditional situations in life and physics are unbalanced and don’t play by IFF. Too many variables outside of the math lab.

So I think it makes math definitions kind of unique in that way. People that expect LAW for example to behave like math definitions are surprised that no, law is full of holes and contradictions. It kind of has to be that way.