[FOM] "Mathematician in the street" on AC

Bill Taylor W.Taylor at math.canterbury.ac.nz
Thu Aug 27 00:00:03 EDT 2009

->> For that matter, could the real numbers be the union of a countable family 
->> of countable sets? 

Yes; it has been proved that there are such models.

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

False.  The countable union of null sets (being null) does itself use AC.
As always, in a rather hidden form, the way the proofs are usually written.

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

This is actually the same question, as there is a bijection between Cantor & R.

Lots of traps for young players!

-- Bill Taylor

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