Re: 2 questions about AC

On Thu, 09 Jun 2005 12:54:47 GMT, "big.ass"
<big.ass.invalid@xxxxxxxxxxxx> wrote:

>>>
>>> My first question is: extending axiom of pair to infinite is equivalent
>>> to [accept] AC?
>>>
What do you mean by "extending [the] axiom of pair[s] to infinite"?

>>>
>>> The second question is about the nature of the choice function.
>>> Considering Russell'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...
>>>
Which one? And how?
>>>
>>> ...seems not so inacceptable to me.
>>>
>> That's not a definition of a function.
>>
Indeed!

>
> Yes, but I can think of a function in such terms:
>
You are defining not a function but a relation!

>
> [...] f c S x T, f = {(X,x) | X e S, x e X}.
>
> Maybe the problem is in the statement "such that x in X",
> but I don't see essential flaws... please, help me finding
> what's wrong.
>
f is (in general) not a function, but a relation. Consider A = {a,b,c},
A e S. Then f (as defined above) contains (A, a), (A, b), (A, c).

Your definition does not "pick exactly one" x e {a,b,c}, to "pair" it
with A, that's the problem.


F.

.

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