Let's try fixing grandparent's argument: let p be the decoder function, Cantor -> Integer. We can define it as the length of the initial run of zeroes (treat the initial bit as sign). This almost works.
Where it fails is the infinite sequence of zeroes: p would count forever; f.p and g.p are not decidable.
So grandparent's argument in fact shows that OpenCantor -> y does not have decidable equality (where OpenCantor is Cantor with the zero sequence - or by extension, any one computable element - excluded). One special element makes all the difference!
Where it fails is the infinite sequence of zeroes: p would count forever; f.p and g.p are not decidable.
So grandparent's argument in fact shows that OpenCantor -> y does not have decidable equality (where OpenCantor is Cantor with the zero sequence - or by extension, any one computable element - excluded). One special element makes all the difference!