Very cool! I don't entirely understand some of the operations, but for what I do understand its pretty neat.

I wish in classes we were introduced to a notion of arithmetic on intervals as it comes up. Like in basic statistics with confidence intervals there's ±, as well as in the quadratic equation. It found some what dissatisfying we couldn't chain the resulting a series of operations and instead repeat the operations for the 2 seperate values of the ±. I get a teacher would rather not get hung up on this because they want to bring it back to the application generally, like solving a more complicated equation or hypothesis testing in basic stats. I just wish they hinted at the idea we can do arithmetic on these kinds of things more generally.

I realise what you've got here is well beyond this, but seeing this was some level of validation that treating the interval as a piece of data with its own behaviour of certain operations does make some sense.