I  am trying to reduce the complement of the HALTING problem (WLOG, the complement of the HALTING problem is the language of TMs that loop on some string w)to this language in order to show that it is not recognizable. Does anyone know how to do this reduction, what I come up with is:Using python-like syntax:def R(<M>,w):    def F(x):        if M(w)loops: //Run M on w            return True on every x        else            loop on every xreturn FOf course the problem here is that we can't really know when M loops on wDoes anyone know how to do this reduction, or if it is possible to prove that the language of TMs that accept every input string is unrecognizable using a reduction from a different unrecognizable language?
Is the language of Turing Machines that halt on every input recognizable?
computability;turing machines;reductions;undecidability;halting problem