Source: cirosantilli/undecidability-requires-infinitely-many-inputs
= Undecidability requires infinitely many inputs
If there are infinitely many inputs, we can always construct a (potentially exponentially huge) <Turing machine> that hardcodes the outcome for every possible input, so the problem is never <undecidable>.
The problem is of course deciding and proving the outcome for each possible input, notably as it is possible that calculation for some of the inputs may be <independent (mathematical logic)> from <ZFC>.