Is a decision problem of determining if something belongs to a non-recursive language.

Or in other words: there is no Turing machine that always halts for every input with the yes/no output.

Every undecidable problem must obviously have an infinite number of "possibilities of stuff you can try": if there is only a finite number, then you can brute-force it.

Some undecidable problems are of recursively enumerable language, e.g. the halting problem.

Coolest ones besides the obvious boring halting problem:

- mortal matrix problem
- Diophantine equation existence of solutions: undecidable Diophantine equation problems

- Recursive language | 19, 302, 7
- Formal language theory | 0, 383, 12
- Computer science | 260, 3k, 77
- Computer | 138, 25k, 608
- Information technology | 0, 25k, 617
- Technology | 15, 43k, 991
- Ciro Santilli's Homepage | 262, 197k, 3k

- Computable problem | 34
- Halting problem | 9
- Mortal matrix problem | 18
- The beauty of mathematics | 313, 748, 7