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We're thinking its:

$ A \subset B \leftrightarrow \forall x [x \in A \rightarrow x \in B] \land \exists x [x \notin A \land x \in B] $

is this OK?

Thanks,

z.

  • 2
    Yes, that works.2012-07-04

2 Answers 2

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As Brian says: Yes, that works. ${}{}{}{}{}{}{}{}{}{}{}{}{}{}$

  • 2
    An answer has to contain some minimum number of characters before the system will accept it. Since my first attempt to submit it had too few characters, I added some do-nothing TeX code to mollify the server.2012-07-04
1

You could use the axiom of extensionality to make a simpler definition: $A\subsetneq B =_\mathrm{def} (\forall x\in A. x\in B)\land \lnot(A=B).$

This is, of course, equivalent to yours.