Induction and Recursion

Version of April 5, 2013; 29 pages of size a5, slightly edited from the last version (the reduction in the number of pages is due to the removal of vertical space between paragraphs).

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Version of November 12, 2012; 31 pages of size a5.

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Version of March 14, 2012; 30 pages of size a5.

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The article (in the March version) is published in the De Morgan Journal (volume 2 [2012], issue 1). The November version corrects two mathematical errors:

1. In §2, the cancellative property of addition needs not only induction, but also the injectivity of the successor map.
2. In §6, ℕ is the smallest collection of sets that is closed under succession and contains 1 (not 0).

Also a few typos are corrected. An attempt to clarify a comment is made by inclusion of a Figure 2 to supplement Figure 1.