m

ha ha ha ha ha

[laughing intensifies]

test

$0_{\Bbb N}=\emptyset$

$\leftrightarrow$

$\forall a(\lnot(a\in0_{\Bbb N}))$

$0_{\Bbb Z}=\{(a,b)|a\in\Bbb N\land b\in\Bbb N\land a=b\}$

$0_{\Bbb Z}=\{(a,a)|a\in\Bbb N\}$

$0_{\Bbb Z}=\{\{\{a\},\{a,a\}\}|a\in\Bbb N\}$

$0_{\Bbb Z}=\{\{\{a\}\}|a\in\Bbb N\}$

$\forall a((a\in0_{\Bbb Z})\leftrightarrow(\forall b((b\in a)\leftrightarrow(\forall c((c\in b)\leftrightarrow(\forall d((c\in d)\leftrightarrow((\exists e((e\in d)\land(\forall f(\lnot(f\in e)))))\land(\forall e((e\in d)\rightarrow(\forall f((\forall g((g\in f)\leftrightarrow((g\in e)\lor(\forall h((h\in e)\leftrightarrow(h\in g))))))\rightarrow(f\in d)))))))))))))$