Yeah, agreed :) I mentioned ω−1 existing as a surreal in the original comment, though more in passing than epsilon. I guess the name Norklet more than anything made me think to mention epsilon--it has a kinda infinitesimal ring to it. But agreed that ω−1 is a way better analog.
This is great! It reminds me a bit of ordinal arithmetic, in which addition is non-commutative. The ordinal numbers begin with all infinitely many natural numbers, followed by the first infinite ordinal, ω. The next ordinal is ω+1, which is greater than ω. But 1+ω is just ω.
Subtraction isn't canonically defined for the ordinals, so ω−1 isn't a thing, but there's an extension of the ordinal numbers called the surreal numbers where it does exist. Sadly addition is defined differently on the surreals, and here it is commutative. ω×−1=−ω does exist though, and as with Norahats ω×−1×−1×−1 does equal ω.
The surreals also contain the infinitesimal number ϵ, which is greater than zero but less than any real number. it's defined as the number between 0 on the left and all members of the infinite sequence 1,12,14,18,… on the right. Not exactly Norklet (ω−1≠ϵ), but not too far away: ω−1=1ω=ϵ :)
(h/t Alex_Altair, whose recent venture into this area caused me to have any information whatsoever about it in my head)