On 4 Jan., 19:47, fom <fomJ...@nyms.net> wrote: > The rationals > are not complete. So much so, in fact, that they are a set > of measure zero. > > But, wait.
No reasonable reason to wait. "Measure zero" is a nonsense expression because it presupposes aleph_0 as a meaningful notion. There are convergent sequences, but the limit is never assumed, not "after aleph_0 steps".
> A set of measure zero presumes a sigma algebra generated > from the open sets of the topology (or the compact sets if you > prefer). > > > > > Cantor's list establishes the uncountability of distinguishable and > > hence constructable reals. > > Constructible real has a definite sense that you > do not abide by. You should talk of nameable reals and > Frege's notion of definite symbols.
Constructible reals are a subset of nameable reals. (Every prescription for a construction is a name.) Therefore I do not make an error.