Talk:Quantifier shift

Examples from calculus

In some metric space (M,d), let B(a,r) be the (metric) ball with center a and radius r.

• Convergence of $(x_{n})_{n\in \mathbb {N} }\subset M$ is

$\exists a\in M\forall \epsilon >0:x_{n}\in B(a,\epsilon ){\mbox{ for almost all }}n$

vs.

Cauchy-criterion (equivalent to the usual definition):

$\forall \epsilon >0\exists a\in M:x_{n}\in B(a,\epsilon ){\mbox{ for almost all }}n$

• Continuity on a set $U\subset M$ vs. uniform continuity on U is the better known example

$\forall x\in U\forall \epsilon >0\exists \delta >0:f(B(x,\delta ))\subset B(f(x),\epsilon )$

vs.

$\forall \epsilon >0\exists \delta >0\forall x\in U:f(B(x,\delta ))\subset B(f(x),\epsilon )$

--LutzL (talk) 16:58, 25 December 2012 (UTC)

Mother of all people

It says in the article: "It is fallacious to conclude that there is one woman who is the mother of all people." But Mitochondrial Eve is "the most recent woman from whom all living humans descend in an unbroken line purely through their mothers and through the mothers of those mothers, back until all lines converge on one woman". Therefore this conclusion in the article (and of Russel's) is false. I don't actually see what in the logic statement led someone to think that "It is fallacious to conclude that there is one woman who is the mother of all people", and clearly it isn't fallacious. Aarghdvaark (talk) 22:08, 9 August 2025 (UTC)