Why is the Halting Problem Undecidable?

[@EasyTheory]

Thanks to my supporters Yuri, vinetor, Ali (KZbin) and Bruno, Timmy, Micah (Patreon) for making this video possible! If you want to contribute, links are in the video description.

[@scottklosen2148]

bruh what. "because it is" is a wild statement

[@morgard211]

Very intuitive proof, nice. I like it more than other approaches.

[@teenfoe]

Put H in another program D which does the opposite of what H says. Then feed D it's own program which passes it to H. You have set up H for failure using a paradox.

[@SunShine-xc6dh]

That's a problem of program d not h. You can remove h, just have d by itself taking its output as input and the paradox (infine loop) already exists.

[@pedrogouveia3111]

Nice explanation

[@TheKk85]

Nice job

[@tarikhacialiogullari4627]

May Allah bless you with Islaam, this really was beneficial. Exam in a week :D

[@yassirsoukaki4111]

Ameen

[@potato8262]

So you assume A_tm is undecidable... That does not sound quite right to me. If "A_tm is undecidable" is a fact, your proof is completely correct, but you base it on a supposition. Proof by contradiction should be constructed based on facts and flip the argument that you want to prove wrong. This proof only shows 2 conclusions: either your supposition is incorrect, which A_tm is decidable, or HALT_tm is undecidable. The proof becomes meaningless unless you later prove A_tm is undecidable. (Edit: I noticed that your next video is the proof of A_tm, but it would complete the logic if you point it out at the end of this video.) Please clarify this, and please don't hesitate to point out any mistake I made. 😁

[@pedrogouveia3111]

But ATM is undecidable. There is a proof for it…. It’s a fact

[@joebrice]

@@pedrogouveia3111 But isn't this video supposed to show why ATM is undecidable? I thought thats what the video was going to be about but instead it seems he is saying the halting problem is undecidable because we know the halting problem is undecidable