Wiki143:Articles for deletion/Proof of mathematical induction

The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was no consensus. Mailer Diablo 17:12, 30 July 2006 (UTC)

Proof of mathematical induction

This article was PROD'd with the reason, "nonstandard presentation of trivial material". That didn't seem an appropriate reason for PROD, so I'm AfD-ing for further discussion. I have no preference regarding deletion. Thanks. RJH (talk) 20:15, 24 July 2006 (UTC)

Delete and merge the concepts into the section Mathematical induction#Proof or reformulation of mathematical induction . CMummert 22:12, 24 July 2006 (UTC)

• Delete for the reasons originally stated. -lethe ^{talk +} 22:13, 24 July 2006 (UTC)
• Keep: this can be merged without deletion; and if it is to be merged, and if it is to be merged the history should be kept. Septentrionalis 22:46, 24 July 2006 (UTC)
• Delete for the reasons originally stated. In WP jargon, "nonstandard presentation" is original research. Inasmuch as the content is standard it is adequately covered in mathematical induction. Also, lousy title. —Blotwell 00:50, 25 July 2006 (UTC)
• Delete. I'm not sure it is nonstandard, I think I have seen a proof along these lines before. However, it is a trivial proof, and trivial proofs usually do not belong in an encyclopaedia. As most participants are probably aware, there is also some discussion at Wikipedia talk:WikiProject Mathematics#Proving induction. -- Jitse Niesen (talk) 02:26, 25 July 2006 (UTC)
  • Abstain. If Ryan says it's important, then I guess it is. Furthermore, I forgot that I decided long ago not to bother about articles containing only a proof, even though I think they do not belong here. -- Jitse Niesen (talk) 01:41, 26 July 2006 (UTC)
• Keep and expand. I usually hate joining AfD's, but this one seems to me to be misguided on a reasonably important topic. I dispute that this presentation is nonstandard, first of all. I have here on my lap a copy of Kolmogorov and Fomin's book Introductory Real Analysis (ISBN 0-486-61226-0) which, on page 28, proves "strong" induction using precisely this argument. Since strong and weak induction are equivalent, the argument has seen print. Second, on page 29, they prove transfinite induction using the same technique. Now, regardless of your opinion of the axiomatic status of the principle of induction for the natural numbers, you will probably agree with me that said status is nonexistent for ordinals. It can, however, be proved that the ordinals are well-ordered and hence satisfy induction using this argument. However, the article is not so well-written. I think it should be improved, have transfinite induction included, and perhaps sourced (like, from Kolmogorov and Fomin) to avoid further accusations of originality. I also think the name is fine: the natural numbers have a pretty variable axiomatic status (you can define them from the ground up, with the Peano axioms, but you can also define them from the top down, as a subset of the real numbers, and in the latter case, well-ordering and induction need to be proven explicitly). Ryan Reich 20:38, 25 July 2006 (UTC)

  See talk page for relevant details. --KSmrq^T 15:06, 27 July 2006 (UTC)

• Merge or keep per Septentrionalis. -- nae'blis _(talk) 21:15, 25 July 2006 (UTC)

• Keep and improve. It may be fairly trivial stuff but it is also covered in books like Willard's 'General Topology' (and Munkres, I believe), along with the proof (based on well-ordering) of transfinite induction. Madmath789 11:52, 26 July 2006 (UTC)
• Keep- I have already seen an argument of this kind in the mathematical literature, the problem is to clarify the meaning and the details.--Pokipsy76 14:34, 26 July 2006 (UTC)
• Clean up and Merge. — Arthur Rubin | (talk) 20:55, 26 July 2006 (UTC)
• keep I look this sort of thing up on wikipedia from time to time(although this particular one has never been my goal) I hate when the present visual quality is enough to kill an article. i kan reed 15:10, 27 July 2006 (UTC)
• Merge and improve. Variations of this content are found in standard literature, so OR is not an issue, per se. To be interesting and meaningful, this cannot stand alone. It must be part of a wider discussion of induction and the different axiomatic ways it arises and finds use. In Peano axioms induction is "built in". Typical topos foundations have a natural numbers object. Axiomatic set theory can use choice/Zorn to prove every set is well-ordered, from which induction follows. All of this belongs in the article on induction where it can properly be discussed. --KSmrq^T 15:24, 27 July 2006 (UTC)

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.