I think your confusion here is between "is there such $f$", and actually finding $f$ expicitly,

or in other words, finding the machine $M_L$ from $L$. This we do not know how to do in general

(there is also the question of how $L$ is represented). But for sure such computable $f$ exists (which

is what we need for the claim). If, on top of it, $M_L$ is provided, the construction becomes explicit.

In the class about Re-Completeness it is said that Atm is Re-Complete. here is a copy paste of the begining of the proof:

"Suppose L is in Re, and let M

My question is why is f computable? To generate it's input, f must build the coding of M_{L}. How would she do this? It is obvoius that M_{L} exists, but my question regards to the process of computing it.

Thanks,

Yoni.

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