There is a club called Undecidable, but they don't let in just any old question. In order to be admitted to the Undecidable Club, a question has to prove that she's seriously hard. How hard? Well, let's talk about the membership process.
First, the applicant needs a sponsor (Let's call the sponsor S
). Your sponsor is some question who's already in the club (so you know they're hard). In order to get into the club, an applicant has to show she's just as hard as her sponsor (Let's call the applicant A
). How does A
prove her difficulty? She has to show that if some Turing Machine could solve A
's problem, it could solve S
's problem as well. Since we know S
is hard (he's in the club already!), A
's problem must be just as hard.
These problems are all known to be hard. You can choose whichever you like to be your sponsor.
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