[FOM] "Mathematician in the street" on AC
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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