I emailed John Conway about this very thing over ten years ago. His response (paraphrasing) was along the lines of RP’s comment; if you treat 1/up as a formal entity nothing breaks, but there wasn’t more to the theory than that. I do not have an account, and I don’t have the email still, so I neither want nor expect the bounty. One other detail I remember is that he represented 1/up with the Roman numeral I.
Jeffrey
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