Rice theorem Example from (https://www.cs.rice.edu/~nakhleh/COMP481/final_review_sp06_sol.pdf)

Question

L={<M>: M is a TM that accepts all even numbers } Why it is not recursively enumerable language???

Comments

Actually there are infinite number of even numbers. So, yes cases of this language  form a loop. This language produce loop in 'yes' cases of the language, so we can say yes case is not satisfied here.That is why it is non R.E.

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"So, yes cases of this language  form a loop" Can you please elaborate this line  a bit more  

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@srestha
So do you want to say that complement of halting problem(i.e given an input w whether the Turing machine will go into an infinite loop or not) which is completely undecidable can be reduced to this given problem????

Which will make this problem undecidable.

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but we have enumeration method for this .According to that it must be recursive enumerable

 akb1115  srestha