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How do I prove that Language L_{1}[tex]\in[/tex] R?

L_{1}={<M>|L(M)[tex]\in[/tex]RE}

( M is a turning machine, <M> is machine's encoding)

I have the answer but i don't understand it!

The answer goes like this (sorry for loose translation):

Because of the fact that L(M)[tex]\in[/tex]RE, L_{1}contains all the encodings of the turning machine.

We can build turning machine M that decides L_{1}language:

On a given input string X we check if it's comprise an encoding of some machine, if it's M stops.

First of all I don't understand the conclusion that "L_{1}contains all the encodings of the turning machine"

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# Question abot Recursive\Recursively Enumerable Languages

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