Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
A Finite Hierarchy of the Recursively Enumerable Real Numbers
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
The closure properties on real numbers under limits and computable operators
Theoretical Computer Science
Closure Properties of Real Number Classes under Limits and Computable Operators
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
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A real number x is called binary enumerable, if there is an effective way to enumerate all "1"-positions in the binary expansion of x. If at most k corrections for any position are allowed in the above enumerations, then x is called binary k-enumerable. Furthermore, if the number of the corrections is bounded by some computable function, then x is called binary ω-enumerable. This paper discusses some basic properties of binary enumerable real numbers. Especially, we show that there are two binary enumerable real numbers x and y such that their difference x - y is not binary ω-enumerable (in fact we have shown that it is even of no "ω-r.e. Turing degree").