# Question abot Recursive\Recursively Enumerable Languages

1. Apr 1, 2009

### 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"

2. Apr 1, 2009

### HallsofIvy

Staff Emeritus
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}" says that [itex]L_1[itex] is the set of such encodings.

3. Apr 1, 2009

### markiz

And if i was L1={<M>|L(M)$$\in$$R} ?