2 questions about AC
- From: "big.ass" <big.ass.invalid@xxxxxxxxxxxx>
- Date: Thu, 09 Jun 2005 01:47:02 GMT
Hello,
AC for a finite set of sets is equivalent to the axiom of pair. In other
words if we consider the set
S={S_1, S_2, ... , S_k}
with S_i<>{} for all i, we know that there are s_1 in S_1, s_2 in s_2 etc.
such that (by axiom of pair):
{(S_1,s_1),(s_2,s_2), ... , (S_k,s_k)};
and this is a choice function.
If S is not finite, AC is not equivalent to any other axiom of ZF. My first
question is: extending axiom of pair to infinite is equivalent to accept AC?
The second question is about the nature of the choice function. Considering
Russel's socks example, we could comprehend that there is no acceptable law
that allows to choose one sock.
What is the "so inacceptable" thing with this method? At first glance, the
function defined by choosing only one element of a class (despite of
choosing "which" element is) seems not so inacceptable to me.
Thank you.
.
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