[FOM] "Mathematician in the street" on AC

freek freek at cs.ru.nl
Sat Aug 15 01:55:05 EDT 2009


>For a concrete example, if a student asks a professor,
>"My classmate said that there exist non-measurable sets.
>Is that true?"  Almost surely, the professor will say yes
>without hesitation.

I would ask "is the union of a countable number of countable
sets countable?"

Of course only a weak version of AC is needed for that,
but I would be surprised if in the answer to that question
"a mathematician in the street" would be even aware that
AC is involved.

Or I would ask about the different notions of infinity that
one gets without AC.

That you need AC to get non-measurable sets "everyone
knows", so I think that the existence of non-measurable
sets is too surprising a property to get a clear "yes,
of course that's true" answer.


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