Yes, but the point is, if you have an amount of memory M, there exists an amount of memory N for which there is no program that fits into M that can successfull

Yes, but the point is, if you have an amount of memory M, there exists an amount of memory N for which there is no program that fits into M that can successfully predict whether an arbitrary that fits into N will halt. No infinites required. (since your example is using two copies, you're essentially using 2M memory)