Re: Set of irrationals closed under sum
- From: "José Carlos Santos" <jcsantos@xxxxxxxx>
- Date: Fri, 12 Aug 2005 12:02:40 +0100
Arturo Magidin wrote:
>>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.
Thanks a lot.
Best regards,
Jose Carlos Santos
.
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