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Re: Matheology S 224
Posted:
Apr 20, 2013 6:47 AM
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Alan Smaill wrote:
>
> Frederick Williams <freddywilliams@btinternet.com> writes:
>
> > Nam Nguyen wrote:
> >>
> >> On 19/04/2013 5:55 AM, Frederick Williams wrote:
> >> > Nam Nguyen wrote:
> >> >>
> >> >> On 18/04/2013 7:19 AM, Frederick Williams wrote:
> >
> >>
> >> >
> >> >>> Also, as I remarked elsewhere, "x e S' /\ Ay[ y e S' -> y e S]" doesn't
> >> >>> express "x is in a non-empty subset of S".
> >> >>
> >> >> Why?
> >> >
> >> > It says that x is in S' and S' is a subset of S.
> >>
> >> How does that contradict that it would express "x is in a non-empty
> >> subset of S", in this context where we'd borrow the expressibility
> >> of L(ZF) as much as we could, as I had alluded before?
> >
> > You really are plumbing the depths. To express that x is non-empty you
> > have to say that something is in x, not that x is in something.
>
> but the claim was that x *is in* a non-empty set --
> in this case S', which is non-empty, since x is an element of S',
> and S' is a subset of S.
Oh, I am so sorry, I did not see the "in" in "x is in a non-empty subset
of S", and it seems I didn't see it three or four times. My apologies
to Nam.
> (Much though it would be good for Nam to realise that
> some background set theory axioms would be kind of useful here)
--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting
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