User blog comment:Ikosarakt1/Uncountable function cannot exists/@comment-1605058-20130707061148/@comment-1605058-20130708195421

You must understand one thing - we can't diagonalize through FGH directly, as it has uncountably many functions. We can't define such function too, because its existence is very likely independent of ZFC. By the way, any algorithm can find sequences for only countably many ordinals.