Re: counting the elements of finite sets

In article <4542da99$0$29167$afc38c87@xxxxxxxxxxxxxxxxxxxx>,
Peter Webb <webbfamily-diespamdie@xxxxxxxxxxxxxxx> wrote:


Set theory defines {x} and {x,x} as equal in the axiom of
regularity.

I believe you mean the axiom of extension.

If you
want to create something different where {x,x} <> {x} you are welcome to;
but don't use any results of set theory (which depend on this axiom) or call
your structures "sets".

There's the notion of "multisets" already floating around, for one.


--
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"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
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Arturo Magidin
magidin-at-member-ams-org

.

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