anyways, i've been trying to understand how Cantor's Diagonalisation is used to solve the Halting Problem and from what I understand...
we design the Decider - TM, say D, so that it works by not doing f_n(n) i.e. by going into an infinite loop if f_n(n) halts, or by halting if f_n(n) doesnt. So obviously, this TM does not belong to the set of all TMs, yet at the same time, it is computing a recursive task, so it should, so this is where the contradiction arises thus the assumpting that D exists is wrong.
It seems kinda convoluted
can someone tell me if I'm on the right track and if u can, plzzzz post up a better explaination
thanks in advance
we design the Decider - TM, say D, so that it works by not doing f_n(n) i.e. by going into an infinite loop if f_n(n) halts, or by halting if f_n(n) doesnt. So obviously, this TM does not belong to the set of all TMs, yet at the same time, it is computing a recursive task, so it should, so this is where the contradiction arises thus the assumpting that D exists is wrong.
It seems kinda convoluted
can someone tell me if I'm on the right track and if u can, plzzzz post up a better explainationthanks in advance