Can exact real arithmetic, interval analysis or other approach in numerical computation help remove inequalities and unify left and right residuals in non-idempotent (linear) residuated lattices by making boundaries explicit instead of talking about max and min divisors?

[u/revannld]

I hope that question makes sense. I just don't like inequalities nor the unnaturality of working with left and right residuals (talking about "max and min divisors") that rarely coincide with rational arithmetic's exact division nor with the natural interpretation of inverses in numerical mathematics, thus I would like more explicit boundaries (thus the result of a division maybe being a set or interval including max and min divisors) in division.

(Mind that I have no experience in numerical computation, I am trying to make sense of computable, numerical and interval analysis works and transport their results to residuated lattices but that's somewhat hard for me)

[u/humbleElitist_]

Can you elaborate a bit on your question please? Or some links to some context about such left and right residuals?

[u/mousse312]

What do you mean when you say something like "the result of division being a set with Max and min"?