I think the point is that it is _finite_. if you allow infinite expressions then the basic monomial basis or quotients thereof are “even simpler”
replyIt’s only finite by putting the infinite series into an operation.
replyAnd 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.
well, the statement is: is there a single operation, built from elementary operations, such that all _other_ elementary operations have finite representations.
replythis 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!