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It’s only an approximation after finitely many terms — the full series limit is exact.

I think the incongruity that the original commenter was pointing out is that Wildberger critiqued radicals by saying that they're imprecise approximations that rely on the problematic concept of infinity.

So setting aside the new method's practical implications, replacing an infinitely accurate approximation with a different infinitely accurate approximation doesn't feel any different.

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.

Indeed, this is what confuses me. But also, could you please elaborate on the practical implications? Why does this work better in practice?

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