Yes you're right. I should have said "it's impossible to create a program that, in general, for all input programs, determines whether it halts or not (in finit

Yes you're right. I should have said "it's impossible to create a program that, in general, for all input programs, determines whether it halts or not (in finite time)." The whole of mathematics and computer science is, in some sense, analyzing those programs which we can prove to halt.