# Undecidable problem | ðŸ—– nosplit | â†‘ parent "Recursive language" | 129, 2, 174

decision problem 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