/lit/ - Literature

>>17227527
I know the fraudulent "constructions" using Dedekind cuts and Cauchy sequences very well.
>there is nothing wrong with defining real numbers directly as their own axiomatic system
There is. Because that's not a definition of what the real numbers are, the axioms are just assertions which these supposed "real numbers" are asserted to satisfy, without any proof.
If there were nothing wrong with the axiomatic approach, the fraudulent "constructions" of the reals wouldn't be viewed as necessary.
>go full formalist and admit sets are defined by the rules of the inclusion relation (see Bourbaki for instance).
I've never seen a formalist, nor a platonist define what set is. As for Bourbaki, I downloaded their joke of a book "Theory of Sets". They start talking about sets only in page 65. To them, sets are synonymous with logical terms. Of course, that cannot be right, because two different logical terms can give rise to two equal terms. So then they have to define what it means for two sets (terms) to be equal. Of course, they don't do this, since this is impossible to do.
>If you really want to dig into logic way beyond the need for set theory, read Husserl and Łukasiewicz works on mereology.
I don't want to dig into anything, all I want is a proper definition of the real numbers. Sadly, as of now, it seems like there are none. The whole theory of analysis is based on sand.