Post #2021678
2026-04-27 20:04 UTC
@robinhouston @christianp Now I'm curious whether https://oeis.org/A019440 is well-ordered and if so what its order type is
Replies (1)
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@robinhouston@mathstodon.xyz 2026-04-27 20:26
@11011110 JDH considered this question in https://www.infinitelymore.xyz/p/the-book-of-numbers?hide_intro_popup=true, initially for the standard US number words, but (perhaps wisely, but a little disappointingly) only worked out the answer for a simpler system in which each digit is named in turn, like reading a telephone number. He concludes that the order type of the natural numbers in the alphabetical telephone number system is \(\mathbb{N}\cdot(1+\mathbb{Q})+1\)