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Topic: Matheology S 224
Replies: 16   Last Post: Apr 21, 2013 6:53 PM

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Alan Smaill

Posts: 937
Registered: 1/29/05
Re: Matheology S 224
Posted: Apr 20, 2013 6:25 AM
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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.

(Much though it would be good for Nam to realise that
some background set theory axioms would be kind of useful here)

Alan Smaill

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