[FOM] "Mathematician in the street" on AC

Vaughan Pratt pratt at cs.stanford.edu
Wed Aug 26 00:57:34 EDT 2009

Daniel Méhkeri wrote:
> For that matter, could the real numbers be the union of a countable family 
> of countable sets? 

No, because the latter is a countable union of null sets and hence 
itself null.

A better question would be, could the Cantor middle-third set be a 
countable union of countable sets?

(In both sentences, "could be" means "holds in some equiconsistent 
extension of ZF.")

Vaughan Pratt

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