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The Universe of Discourse : The road to epsilon-zero: Productive programs and well-founded orders
This installment in a series on ordinal numbers explores 'productive' programs (ones that will eventually print every item in an infinite set) and the difference between lexicographic and shortlex string ordering. It shows why lexicographic order fails to be well-founded for certain infinite string sets (no productive program can enumerate them, and some sets lack a lexicographically first element), while shortlex order (comparing by length first, then lexicographically) is always well-founded, guaranteeing a first element for any set of strings and enabling productive, decidable enumeration programs. The piece sets up a following article on shortlex order applied to sequences of ordinals.
Nguồn: https://blog.plover.com/math/ordinals/05-shortlex.html. 8 Sync News chỉ tóm tắt và dẫn link; bản quyền nội dung thuộc tác giả và nguồn gốc.
