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Topic: Matheology § 203
Replies: 202   Last Post: Feb 10, 2013 3:34 AM

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mueckenh@rz.fh-augsburg.de

Posts: 14,973
Registered: 1/29/05
Matheology § 203
Posted: Jan 29, 2013 3:33 AM
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"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.

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.
4) For every n in N, the anti-diagonal of a Cantor-list is not in the
lines L_1 to L_n.

Regards, WM


Date Subject Author
1/29/13
Read Matheology § 203
mueckenh@rz.fh-augsburg.de
1/29/13
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William Hughes
1/29/13
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mueckenh@rz.fh-augsburg.de
1/29/13
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William Hughes
1/29/13
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mueckenh@rz.fh-augsburg.de
1/29/13
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William Hughes
1/29/13
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mueckenh@rz.fh-augsburg.de
1/29/13
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William Hughes
1/29/13
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mueckenh@rz.fh-augsburg.de
1/29/13
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William Hughes
1/29/13
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mueckenh@rz.fh-augsburg.de
1/29/13
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William Hughes
1/29/13
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mueckenh@rz.fh-augsburg.de
1/29/13
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William Hughes
1/29/13
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mueckenh@rz.fh-augsburg.de
1/29/13
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William Hughes
1/30/13
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mueckenh@rz.fh-augsburg.de
1/30/13
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William Hughes
1/30/13
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mueckenh@rz.fh-augsburg.de
1/30/13
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William Hughes
1/30/13
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mueckenh@rz.fh-augsburg.de
1/30/13
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William Hughes
1/30/13
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mueckenh@rz.fh-augsburg.de
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1/30/13
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mueckenh@rz.fh-augsburg.de
1/30/13
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1/30/13
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mueckenh@rz.fh-augsburg.de
1/30/13
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William Hughes
1/30/13
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mueckenh@rz.fh-augsburg.de
1/30/13
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William Hughes
1/30/13
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mueckenh@rz.fh-augsburg.de
1/30/13
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William Hughes
1/31/13
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mueckenh@rz.fh-augsburg.de
1/31/13
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1/31/13
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mueckenh@rz.fh-augsburg.de
1/31/13
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William Hughes
1/31/13
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mueckenh@rz.fh-augsburg.de
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William Hughes
1/31/13
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mueckenh@rz.fh-augsburg.de
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William Hughes
1/31/13
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mueckenh@rz.fh-augsburg.de
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2/1/13
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mueckenh@rz.fh-augsburg.de
2/1/13
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2/1/13
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mueckenh@rz.fh-augsburg.de
2/1/13
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2/1/13
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mueckenh@rz.fh-augsburg.de
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2/1/13
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mueckenh@rz.fh-augsburg.de
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2/1/13
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mueckenh@rz.fh-augsburg.de
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2/1/13
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mueckenh@rz.fh-augsburg.de
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William Hughes
2/1/13
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Virgil
2/2/13
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2/2/13
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2/2/13
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mueckenh@rz.fh-augsburg.de
2/2/13
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William Hughes
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Virgil
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fom
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mueckenh@rz.fh-augsburg.de
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2/2/13
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mueckenh@rz.fh-augsburg.de
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2/2/13
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William Hughes
2/3/13
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mueckenh@rz.fh-augsburg.de
2/3/13
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2/3/13
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mueckenh@rz.fh-augsburg.de
2/3/13
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Virgil
2/3/13
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2/3/13
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mueckenh@rz.fh-augsburg.de
2/3/13
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fom
2/4/13
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2/10/13
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fom
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2/4/13
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mueckenh@rz.fh-augsburg.de
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William Hughes
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mueckenh@rz.fh-augsburg.de
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William Hughes
2/4/13
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mueckenh@rz.fh-augsburg.de
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William Hughes
2/4/13
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mueckenh@rz.fh-augsburg.de
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William Hughes
2/4/13
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mueckenh@rz.fh-augsburg.de
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2/5/13
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William Hughes
2/5/13
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Virgil
2/5/13
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gus gassmann
2/5/13
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Virgil
2/5/13
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fom
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2/5/13
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Virgil
2/4/13
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2/4/13
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2/6/13
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2/1/13
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2/1/13
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2/1/13
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2/2/13
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2/2/13
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2/1/13
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1/31/13
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1/30/13
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1/30/13
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1/30/13
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mueckenh@rz.fh-augsburg.de
1/30/13
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Virgil
1/30/13
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Virgil
1/29/13
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1/29/13
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1/29/13
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1/29/13
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1/29/13
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1/29/13
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1/29/13
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2/4/13
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1/29/13
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1/29/13
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1/29/13
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fom
1/29/13
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1/29/13
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Virgil
1/30/13
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fom
1/30/13
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mueckenh@rz.fh-augsburg.de
1/30/13
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fom
1/30/13
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mueckenh@rz.fh-augsburg.de
1/30/13
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Virgil
1/31/13
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fom
1/30/13
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fom
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Virgil
1/31/13
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fom
1/29/13
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fom
1/29/13
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Virgil

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