 Undecidable problem

An undecidable problem is a decision problem for which no algorithm can be constructed that always leads to a correct yes-or-no answer for all possible inputs. In other words, there is no computational method that can determine the answer to these problems in a finite amount of time for every possible case. One of the most famous examples of an undecidable problem is the **Halting Problem**.

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.

Lists of undecidable problems.

Coolest ones besides the obvious boring halting problem: