And yet there is a correct algorithm — it's either the const yes algorithm or the const no algorithm.
We don't _know_ which algorithm it is, but that's not relevant to the definition of undecidability, which only requires that the algorithm exist.
We don't _know_ which algorithm it is, but that's not relevant to the definition of undecidability, which only requires that the algorithm exist.
This is slightly bizarre now I think about it: the definition of decidability allows the algorithm selection to be undecidable!