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Topic: ZFC really really really sucks -- really!
Replies: 20   Last Post: Jan 20, 2013 6:30 AM

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Registered: 2/15/09
Re: ZFC really really really sucks -- really!
Posted: Jan 7, 2013 10:13 PM
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On Jan 7, 2:30 pm, Dan Christensen <Dan_Christen...@sympatico.ca>
> On Monday, January 7, 2013 4:51:47 PM UTC-5, david petry wrote:
> > On Monday, January 7, 2013 1:45:40 PM UTC-8, Dan Christensen wrote:
> > > On Monday, January 7, 2013 3:59:48 PM UTC-5, david petry wrote:
> > > > On Monday, January 7, 2013 11:14:57 AM UTC-8, Dan Christensen wrote:
> > > > > On Monday, January 7, 2013 8:50:09 AM UTC-5, david petry wrote
> > > > > > An article by Nic Weaver is worth a read:
> > > > > >http://arxiv.org/PS_cache/arxiv/pdf/0905/0905.1680v1.pdf
> > > > I suppose it is surprising to classically trained mathematicians, but it is not necessary to define a set of all continuous functions, nor even a set of all real numbers, to develop the mathematics used in science.
> > > That WOULD be surprising if it were true.
> > Once again, I recommend that you read Nik Weaver's article.
> IIUC, he hopes to do mathematics (e.g. real analysis) without sets (or any equivalent notion). If he wants to be taken seriously, he should just go ahead and do so. I have tried to do so for a number of years myself to no avail. I don't much care for the ZF axioms of regularity and infinity myself. I haven't found any use for them in my own work, and haven't incorporated them (or any equivalent) in my own simplified set theory. But I really don't see how you can do foundational work without a powerset axiom.
> Dan
> Download my DC Proof 2.0 software athttp://www.dcproof.com

Doesn't it follow from pairing and union?

Basically we know that any element of a set is a set via union.

Then, each of those as elements as a singleton subset, is a set, as
necessary via inductive recursion and building back up the sets.

Via pairing, the two-elements subsets are sets, via pairing, the three
element sets are sets, ..., via induction, each of the subsets are

Then all the subsets are each sets, via pairing, that's a set.

It follows from pairing and union.


Ross Finlayson

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