Question abot Recursive\Recursively Enumerable Languages

[markiz]

Note: If this is a wrong section please move this thread to it's appropriate section.How do I prove that language L₁$$\in$$ R?

L₁={<M>|L(M)$$\in$$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)$$\in$$RE, L₁ contains all the encodings of the turning machine.
We can build turning machine M that decides L₁ 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 "L₁ contains all the encodings of the turning machine"

 

[HallsofIvy]

First the term is "Turing machine", not "turning machine". It is named for the British mathematician, Alan Turing.

"[itex]L_1= {<M>|L(M)\in RE}" <b>says</b> that [itex]L_1$is the set of such encodings.$[/itex][/itex]

 

[markiz]

And if i was L₁={<M>|L(M)$$\in$$R} ?