It sounds like we can too determine its practical effect, which is zero. No real-world machine learning algorithm can use the real numbers. We can not obtain them to feed them as input, our real-world machines can not process them if we could, and if we got real-number-based answers, we could not use them. Whether the universe itself is or is not based on real numbers, we do not have access to them either way. Our real-world machines only have access to the computable numbers (and only a subset of them, at that).
I'm only speaking to the practical impact.
It's possible someone will find some way work this down into something practical, but I'd be fairly surprised. Real machine learners get finite data, for which the continuum hypothesis is irrelevant.
(I assume the original authors fully understand this.)
I'm only speaking to the practical impact.
It's possible someone will find some way work this down into something practical, but I'd be fairly surprised. Real machine learners get finite data, for which the continuum hypothesis is irrelevant.
(I assume the original authors fully understand this.)