[SideQuark]

It’s only finite by putting the infinite series into an operation.

And the basic monomial basis is not a single binary operation capable of reproducing the set of basic arithmetic ops. If you want trivial and basic, pick Peano postulates. But that’s not what this thread was about.

[LolWolf]

well, the statement is: is there a single operation, built from elementary operations, such that all _other_ elementary operations have finite representations.

this preprint answers that in the affirmative

otoh, (x, y) -> 1/(x-y) does not answer this question at all. you can argue that the preprint does so "via the infinite series in an operation" (which I have no idea what that means; surely if exp(x) qualifies then so must 1/(x-y) if we pick a monomial basis?) but ¯\_(ツ)_/¯

now, do I think that this is groundbreaking magical research (as I'm currently seeing on twitter) no... But it's neat!