```Date: Jan 29, 2013 6:47 PM
Author: Virgil
Subject: Re: Matheology � 203

In article <f5702bc4-f905-4e60-94c5-a503f3d9d887@n2g2000yqg.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> "All" and "every" in impredicative statements about infinite sets.> > Consider the following statements:> > A) For every natural number n, P(n) is true.> B) There does not exist a natural number n such that P(n) is false.> C) For all natural numbers P is true.> > A implies B but A does not imply C.D) For all natural numbers n , P(n) is trueBut A does imply D.> > Examples for A:> 1) For every n in N, there is m in N with n < m.> 2) For every n in N, the set (1, 2, ..., n) is finite.> 3) For every n in N, the construction of the first n nodes of the> Binary Tree adds n paths to the Bibary Tree.False! At least for binary  non-Bibary trees. The first 3 nodes produce only 2 paths in a finite biNary tree.The first 7 nodes  produce only 4 paths in a finite binary tree. The first 15 nodes produce only 8  paths in a finite binary tree. > 4) For every n in N, the anti-diagonal of a Cantor-list is not in the> lines L_1 to L_n. Thus not anywhere in the list!--
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