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

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Posts: 2,777
Registered: 12/13/04
Re: Matheology S 224
Posted: Apr 20, 2013 11:13 AM
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On 20/04/2013 4:25 AM, Alan Smaill wrote:
> Frederick Williams <> 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)

Not important, just curious: Why would you think I didn't have some
of those backgrounds (about set theory axioms)?

There is no remainder in the mathematics of infinity.


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