Cantor set V

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"An elementary example (due to Feng-Gao) of an R.E. set over [the real numbers] which is not decidable is the complement of the Cantor Middle [T]hird set in the unit interval. The demonstration is via [a] "machine" (and the fact the Cantor Middle [T]hird set is an uncountable totally disconnected set)."

--from the paper cited in commentary to Cantor set III.

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