Hopefully this question is not a duplicate.
How do I show the problem below is decidable by describing a Turing machine?
Input: Turing machine M
Question: Are there infinitely many Turing machines that all recognize L(M)?
I know a language is decidable if there exists a Turing machine that halts on all inputs when running on that language, where it accepts if a string is in the language and rejects otherwise.
Now I know that a Turing machine can simulate the behavior of another turing machine, so in theory a turing machine, say T, CAN simulate the behavior of M, therefore accepting the language of M.
Wouldn't it then be possible if I argue that there can exist an infinite amount of turing machines that all simulate the behaviour of M, and as a result accept L(M)?
Or is what I'm proposing not doing its job of showing the problem is decidable?