User talk:Zhengyitian147

Halting problem proof
Hello,

I like to make a note on your edit on the Halting problem page. The proof you provided seemed to me to contain an error, not to mention many grammatical errors. For the sake of less ambiguity and being more technical from a mathematical perspective, I refined your submission to the following:

Another proof
We proceed with reductio ad absurdum. Suppose that such program exists that it can solve the halting problem. We shall call this program {halt}. More specifically, given a program {p} with the input {in} it can decide whether it will halt or not. Therefore, we can write a second program that behaves as follows:


 * If {p} halts with the input {in}, then the new program does not halt.


 * If {p} does not halt with the input {in}, then the new program halts.

Basically, the new program, which we shall call {r_halt}, behaves similarly to the negation of {halt}. Suppose now, that {r_halt} is ran with itself as the input. If it halts, then it must not halt. If it does not halt, then it must halt. We have reached a contradiction, which proves our assumption wrong and therefore, no such program such as {halt} exists.

The mistake I spotted was that the {r_halt} program which is fed as the input to {r_halt}, lacks a proper input itself, meaning that the situation you describe cannot happen, meaning that the proof is faulty. Please correct me if I'm mistaken. :) --C-M12000 (talk) 20:12, 6 January 2018 (UTC)