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Show that the set of incompressible strings contains no infinite subset that is Turing - recognizable. Proof: Assume to the contrary that an infinite set

Show that the set of incompressible strings contains no infinite subset that is Turing-recognizable. Proof: Assume to the contrary that an infinite set of incompressible strings is Turing-recognizable. Then we can construct TM M which on input n finds a string of length n which is incompressible and outputs it. However, for large n, that gives a short description of the incompressible string, a contradiction.
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