I'm not a mathematician, I barely passed GCSE Maths so the post below is written as I thought it.
Imagine Turing Machine h
h takes an input program, and determines if it halts or not
now imagine a second turning machine h+
h+ takes an input program, feed it into h, if h outputs that the program halts, enter a loop if h outputs that the program does not halt, h+ then halts
because feeding h+ into h will cause h to not work, this is the halting problem
now imagine a machine g g takes an input program, and outputs if it halts, does not halt, or contains a machine similar to g
now imagine a machine g+ g+ takes an input program and feeds it into g. if g outputs that the program halts, g+ outputs an infinite loop. g outputs that the program loops, g+ halts. however, if g outputs that the program contains a machine similar g, g+ has to either halt, or loop Imagine two derivatives of g+, g1+ halts and g2+ loops when their internal g outputs that the program contains g.
feeding g1+ into g will cause g to output that the program halts feeding g2+ into g will cause g to output that the program loops
so what happens if we feed h into g? as h is similar to g it will output that it is similar what happens if we feed h+ into g? as the h in h+ is similar to g, it will output the same as above.
Is there a theoretical Turing machine, that when fed into g would not satisfy the halting problem? A tl;dr in layman terms would be appriciated thanks, -Rob