>>12462045>>12461995>Sure, try https://www.youtube.com/watch?v=3cI7sFr707sOkay, I have watched most of it (I skipped some of more long-winded stuff). I think it's a good representative sample, which illustrates my point accurately.
Wildberger points out the following characteristics of Cauchy-based real numbers (I skipped some secondary ones):
>1. The meaning of the term "infinite sequence of rationals".You can see an infinite sequence as a choice function or as an algorithm. Yes, that's correct. The standard view is the choice function, not the algorithm.
>1.1. There are no examples.Correct. The reals are uncountable and the things you can describe finitely are countable, so whatever you can describe is going to be a small subset of the full space.
>1.2. Any operations with such sequences must involve an infinite amount of time and memory, i.e. they are completely impossible.Indeed. The reals are uncountable, and you can't do arithmetic on uncountable things.
>2. The Cauchy requirement is ambiguous.No it isn't. Yes, checking the Cauchy would take an infinite amount of work, which is *inconvenient*, but that doesn't make it ambiguous. It's perfectly unambiguous.
>3. The meaning of "equivalence class" is ambiguous.No it isn't, same as point 2. Yes, checking whether two sequences are equivalent would take an infinite amount of work. No, that does not make the notion ambiguous.
>5. Show us the arithmatic!You cannot do arithmetic with uncountable things.
[continued 1/2]
