Re: Co-re set with no infinite r.e. subset

From: r.e.s. (r.s_at_ZZmindspring.com)
Date: 09/07/04


Date: Tue, 07 Sep 2004 18:18:10 GMT


"Daryl McCullough" <daryl@atc-nycorp.com> wrote ...
> Is there an easy example of an infinite set of naturals that has no
> infinite
> r.e. subset? It would be better if it were co-r.e., but any example would
> be nice. Thanks.

The set of indices of the TMs that do not halt on a blank tape?

--r.e.s.



Relevant Pages

  • Re: Is one-to-one mapping valid for comparing infinite-sized sets?
    ... What is *Cantor's* definition of an infinite set? ... injection from it to one of its proper subsets. ... natural n such that the set of naturals less than n surjects onto it). ...
    (sci.math)
  • Re: Extrapolating linear ratios
    ... A quality is the ratio of two quantities like "number of primes per ... the proof is that an infinite set consists of finite ... The set of all even numbers consists of finite numbers only. ... Now, let's apply this to the specific case E = the set of even naturals, ...
    (sci.logic)
  • Re: Cantors circular "proof" that evens = integers
    ... Set N is an infinite set containing all the natural numbers (for these ... EVERY "proof" that I have seen that claims to prove that this is an inherent property of infinite sets simply ADDS this belief as a new axiom, ... I am NOT CLAIMING that infinite sets of the naturals have a similar structure, but I AM claiming that no one has PROVEN that there is some INHERENT feature about the infinite set of naturals that prevents the existence of sets N1 and N2 with properties similar to what I have just described for the line segments and. ... People don't just say that we have added an AXIOM that states that N and a proper subset of N are equinumerous; they claim that this is an INHERENT FEATURE of infinite sets. ...
    (sci.logic)
  • Re: infinity
    ... >>> naturals, it is the completed, total, entire, unexpandable set of all ... there is no contradiction in mappings involving all elements of ... >> Yes, you idiot, in the infinite set, it does, dumbell. ... There is a natural that maps to any idnetified set, ...
    (sci.math)
  • Re: Orlow cardinality question
    ... >> can't have a finite set without a largest member. ... I have proven thrice that the infinite set must ... Einstein said the moon is made of cheese. ... >> Is N+1 a member of the set of naturals? ...
    (sci.math)