[ogogmad]

It seems that the authors are skeptical of real numbers (even computable ones???) while being perfectly comfortable with power series. I don't see how one of these can be acceptable and the other not. Sadly, their point of view seems incoherent.

Maybe it's a gut reaction because power series can seem so "nice" to them in their experience.

Maybe if someone explained Computable Topology to them, then they could be more accepting? But if their judgement comes from the gut, instead of intellectual integrity or reason, then I'm not sure it would be worth trying it.