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Baby Sister Numbers

Yeah, agreed :) I mentioned  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  is a way better analog.

Baby Sister Numbers

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, . The next ordinal is , which is greater than . But  is just

Subtraction isn't canonically defined for the ordinals, so  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.  does exist though, and as with Norahats  does equal .

The surreals also contain the infinitesimal number , which is greater than zero but less than any real number. it's defined as the number between  on the left and all members of the infinite sequence  on the right. Not exactly Norklet (), but not too far away:  :)

(h/t Alex_Altair, whose recent venture into this area caused me to have any information whatsoever about it in my head)