This is true, thanks. As the other answer said, in this field we say given any machine M, "M2 simulates M" if M2 computes the same function as M i.e. given any

This is true, thanks. As the other answer said, in this field we say given any machine M, "M2 simulates M" if M2 computes the same function as M i.e. given any input i, iff M(i) halts then M2(i) halts and M(i) == M2(i) otherwise they both loop. This can also be called "compiling" informaly: given any Turing machine, you can "compile" it to C (i.e. constructing a C program that simulates M) which means C is Turing-complete. Note that this is a very handwavy definition. The "types" of input, output, and what it means to "compute" will depend on your language, semantics and encoding. (E.g. for lambda calcus "compute" means appying reduction rules until the machine halts, if ever)