Re: Set of irrationals closed under sum

In article <ddfts1$21nc$1@xxxxxxxxxxxxxxxxxx>, Arturo Magidin
<magidin@xxxxxxxxxxxxxxxxx> wrote:

> In article <3m18mcF14hotnU1@xxxxxxxxxxxxxx>,
> José Carlos Santos <jcsantos@xxxxxxxx> wrote:
> >Hi all,
> >
> >Let x be an irrational number and let A = {x,2x,3x,...}. Then A is countable
> >set of irrational
> >numbers such that A + A is a subset of A.
> >
> >My question is: is there an *uncountable* set A of irrational numbers such
> >that A + A is a
> >subset of A?
>
> Sure. Let B be a Hamel basis for R over Q. Let S be any uncountable
> subset of B which does not include a rational number (there is at most
> one rational number in B), and let A be the Z-span of S.

Better not take Z-span, since you get u and -u both in your set...
.