>>16836768
My thoughts are that we could define an absorptive inverse. In this case, I use the term indeterminate to refer to it, but a less ambiguous term might be "semivalued"
Effectively, I see it still as acting as an absorptive notion. eg:
[math]1 \div 0 = semivalue[/math]
[math]1 + semivalue = semivalue[/math]
This can hold trivially for any operation, any function, unless defined otherwise. Not sure where and when you'd want to do that, maybe for boolean operations so we don't have to change logics? That would also imply you can assign identities to semivalues, even if they're absorptive.
[math]1 \div 0 \neq 2 \div 0[/math]
My question is, why didn't we just do this?
"Undefined" makes sense for this example:
[math]24.1.2 [[/math]
But re-using defined/undefined as a fence against some of the weirder behaviors of algebra doesn't just seem sub-optimal, but inherently wrong. Division by zero is left undefined for completely different reasons than the above. The inability to formulate and represent that difference in a concrete, unambiguous manner would mean a strengthening of the formal system.
