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Re: Given a set , is there a disjoint set with an arbitrary cardinality?
Posted:
Dec 4, 2012 1:29 AM
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On Mon, 3 Dec 2012, forbisgaryg@gmail.com wrote:
> On Monday, December 3, 2012 6:21:05 AM UTC-8, jaakov wrote:
> > Given a set X and a cardinal k, is there a set Y such that card(Y)=k and
> >
> > X is disjoint from Y?
> >
> > Is there a proof of this fact that works without the axiom of regularity
> >
> > (= axiom of foundation) and does not assume purity of sets?
>
> Based upon some of your replies I have a question.
>
> Given your statment: "Given a set X and a cardinal k"
>
> 1. Are you referring to any set X or specifically a set of real numbers?
Any set or course.
> 2. Are you saying saying k isn't necessarily the cardinality of X?
That's right.
All that was said about the given cardinal k was card Y = k.
> Given your question "> Is there a proof of this fact that works without
> the axiom of regularity (= axiom of foundation) and does not assume
> purity of sets?
>
> 1. Are you referring to any set or specifical sets of real numbers?
Any set of course. No where was it stated or even suggested
that X or Y, is a subset of the reals. Where do you get this
notion that the discussion is about set of real numbers?
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