IANAMathematician, but it's "true" in the sense that we primarily use a set of axioms (ZF/ZFC) which produce this result. But in a sense one of the axioms is th

IANAMathematician, but it's "true" in the sense that we primarily use a set of axioms (ZF/ZFC) which produce this result. But in a sense one of the axioms is that these things exist (powerset axiom), so this result is a bit less illuminating than one might hope. My understanding is that we can reason about these sorts of non-constructible sequences but we can't really know if they "really exist" because it's not clear what that even means if their existence has no implications for physical reality (which is possible but not known). So now we're into the territory of whether there is such a thing as abstract truth independent of reality. I wrote a blog post in the past about my reading on this topic, and I can't claim that's it's accurate but at least I tried to talk about this subject: https://blog.kevmod.com/2022/04/09/do-the-real-numbers-exist/ https://blog.kevmod.com/2022/04/09/do-the-real-numbers-exist...