Re: Power and ur-elements

On May 3, 8:28 am, LauLuna <laureanol...@xxxxxxxx> wrote:
On May 3, 12:20 pm, zuhair <zaljo...@xxxxxxxxx> wrote:





Hi all,

Three questions:

In any set theory T which allows for P(x) to be a proper subset of x,
or for P(x) to be a member of x; are the following statements true?

1) Any set x that has its power as a proper subset of it, should
contain ur-elements.

P(x) proper subset_of x -> Ey(y is a ur-element & yex).

2)If P(x) is a proper subset of x, then |P(x)|<|x|.

P(x) proper subset_of x -> |P(x)|<|x|.

3) If P(x) is a member of x , then xex.

P(x) e x -> xex.

Zuhair

Let me give you an extremely naive answer.

For all I know, there is no way in which the powerset of x could be a
subset of x or an element of x. So, 1), 2) and 3) are true only if you
understand them as material implications (the antecedent will always
be false).

Unless you are referring to some exotic non Cantorian set theory. Then
I can't help you.

NFU.

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