Definition talk:Singleton

Sorry, but if we need a rigorous formalization of this, it needs to go on its own page, and deduce it from the Axiom of Pairing. --prime mover 00:39, 13 September 2011 (CDT)

Tarski has a slightly different definition of a singleton, is it different enough to be worth adding?

$\left\{{A}\right\} \text{consists of exactly one element} := \exists A \in \left\{{A}\right\} \land \left(A \in \left\{{A}\right\} \land B \in \left\{{A}\right\}\right) \implies A = B$ --GFauxPas 08:20, 25 December 2011 (CST)

As we've said before, once we have established "Tarski's axioms" or whatever they were, we can create all the various definitions that he formulated on their own separate pages, then link to that from here. --prime mover 18:11, 25 December 2011 (CST)

Okay. I haven't forgotten by the way, I've just had very little luck finding it. --GFauxPas 18:21, 25 December 2011 (CST)

Tarski's Axioms are now on PW. I saw nothing that had anything to do with what we're defining here. I think his definition is equivalent, but we should probably make sure we can prove their equivalence before we put it up. --GFauxPas 10:44, 29 January 2012 (EST)