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We know that topics like
finite field arithmetic do not require induction. We feel (intuitively?) that topics like
analysis are consistent with induction. Are there any examples of mathematical/logical systems which are "infinite" in some sense, but for which induction does not work? That is, has anyone created a (more-or-less consistent) system in which induction was intentionally broken, on purpose, but the system still somehow acheives a notion of infinity? Should I be asking this question on the
Peano's axioms talk page instead?
linas05:40, 7 September 2005 (UTC)reply
This article is within the scope of WikiProject Philosophy, a collaborative effort to improve the coverage of content related to
philosophy on Wikipedia. If you would like to support the project, please visit the project page, where you can get more details on how you can help, and where you can join the general discussion about philosophy content on Wikipedia.PhilosophyWikipedia:WikiProject PhilosophyTemplate:WikiProject PhilosophyPhilosophy articles
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of
mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join
the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
This article has been given a rating which conflicts with the
project-independent quality rating in the banner shell. Please resolve this conflict if possible.
We know that topics like
finite field arithmetic do not require induction. We feel (intuitively?) that topics like
analysis are consistent with induction. Are there any examples of mathematical/logical systems which are "infinite" in some sense, but for which induction does not work? That is, has anyone created a (more-or-less consistent) system in which induction was intentionally broken, on purpose, but the system still somehow acheives a notion of infinity? Should I be asking this question on the
Peano's axioms talk page instead?
linas05:40, 7 September 2005 (UTC)reply