> Would the proof completely fall apart if the algorithm could update itself to handle the new information? The only thing stopping it is that in the formulatio

> Would the proof completely fall apart if the algorithm could update itself to handle the new information? The only thing stopping it is that in the formulation of the problem, the algorithm is assumed to not be able to change with new information (ie it's not an "online" algorithm). First an online algorithm is an algorithm that process a stream instead of the full input. It's not because it changes. Regarding the halting problem, lets assume that you give me a program can change itself and you claim solves the halting problem. Use Turings proof on that and it proves that you have not solved the halting problem for all inputs, because it just gave you one that it produced the wrong answer for.