File:Peano-9.pdf

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DescriptionPeano-9.pdf	English: Nonstandard-model of the Peano axioms, except for axiom 9 (induction). The horizontal vectors at the bottom denote the standard part, i.e. zero (leftmost, shown in glaring red) and its infinitely many -direct and indirect- successors. However, there is an additial nonstandard ("junk") part, viz. the cycle at the top, consisting of 48 members, none of which are reachable from zero via successor application. — See File:Domino effect visualizing exclusion of junk term by induction axiom.jpg for a 3d-graphic of the corrersponding domino effect. — See File:Peano-7.pdf and File:Peano-8.pdf for a nonstandard model violating just Peano axiom 7 and 8, respectively.
Date	21 February 2015
Source	Own work
Author	Jochen Burghardt

LaTeX source code

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