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Revision as of 15:17, 6 March 2006

Three forms of mathematical induction

This redundant article serves no purpose. (1) and (2) are covered by Mathematical induction; (3) is covered by complete induction. These relationships are already explored in detail at Mathematical induction. In 30 months, the article has accumulated as many edits; I attempted to merge it but was reverted. Melchoir 01:44, 6 March 2006 (UTC)

• Keep. Melchoir's hostility seems gratuitous; I don't know where it comes from. His attempt to "merge" material into mathematical induction amounted to (1) paraphrasing a fragment of this article in a way that made clear that he understood none of it and didn't care to; and (2) putting it into a randomly chosen place in that article. Michael Hardy 01:49, 6 March 2006 (UTC)
  • I do not understand why it is necessary to insult me to this degree. I have made nothing but good-faith edits; I understand the articles a little better than not at all, and I make sure that I understand what I'm doing before I do it. You can't possibly think my choice of position was random. And I merged a "fragment" because there is exactly one sentence in this article that can't be found in a more relevant place. Melchoir 02:07, 6 March 2006 (UTC)
    • They did not look at all like good-faith edits. I did not insult; I accused. And your writings above on this votes-for-deletion page clearly show that you have no understanding of this article. You say that (1) is covered somewhere and (2) is covered somewhere, and (3) can also be covered somewhere, and that misses the point. This is not about three disparate topics, each of which should be covered somewhere; it's about a triad and the relationship---in particular the contrast and the commonality---among the three things. You write "there is exactly one sentence in this article that can't be found in a more relevant place"; that makes it clear that you think each of the three things should be covered somewhere, possibly separately, so that you've missed the point that it's about a relationship. And yes, it does appear that you put it in a random place. The place where you put it within the article is utterly inappropriate and very stupidly so in a way that shows reckless disregard for what part of the article it is in. It also fails to convey the information. The subsection into which you inserted it was devoted to pointing out that the starting value could be any integer. Why would you put it there, of all places? And you began by saying "Such a strategy can also be useful to prove a statement for all n. That's what the whole article is about, unless by "all n" you mean something other than all n in a sequence with a first element, a second, a third, and so on. "Such a strategy"?? "Useful"?? The point was the splitting into three. Where is that in what you wrote? That small fragment would clearly fit better into the section on transfinite induction. But that would mislead: this particular form is obviously not used only in transfinite induction. Moreover, the sentence you wrote is incomprehensible; it is impossible to tell whether there is a "then" at any of the various semicolons you put into the sentence. I invite any mathematician here to look at Melchoir's edit at and see whether it conveys any of the meaning. Don't just look at what he wrote; look at whether it's in an appropriate place by reading the short section into which he inserted it. Michael Hardy 02:31, 6 March 2006 (UTC)
      • Mathematical induction is the place to explore relationships between types of mathematical induction, and it already does. The semicolons are not mine, and if you think you can improve the wording, you should try it. Finally, you continue to insult me with such accusations as "very stupidly". This is not constructive; please stop. Melchoir 02:39, 6 March 2006 (UTC)
    • Mathematical induction does not explain the contrast between these three forms. It mentions two of the three (#1 and #3, but not #2) but not in a way that calls explicit attention to the contrast between the three. It gives only two exmample (and that's one thing that this present article needs). One of the two is somewhat deficient in that only a small part of the induction hypothesis is used and the example lacks detail. The very fact that more examples, with more detail, should be added to mathematical induction, is one reason why this article should be separate from it: so that the two sorts of discussion will not interfere with each other (when you're paying attention to either of them, the other becomes noise). The examples that need to be added to the present article should be done in a different way from the examples in mathematical induction: the emphasis in examples in this should be on something other than details of the proofs. The edit history does make it look as if the semicolons were Melchoir's. Melchoir, I naturally presume that anyone who takes an interest in these topics is capable of judiciously choosing an appropriate place in the article and otherwise understanding and writing clearly; your failure to do any of those was so complete that it looked like recklessness rather than lack of any ability; that is why I accused you of that. It is of course possible that my accusation was incorrect, but saying you did something stupidly when you had the ability to do otherwise is an accusation, rather than an insult. Michael Hardy 03:25, 6 March 2006 (UTC)
      • I believe it is possible, reasonable, necessary, and consistent with the existing article to contrast forms of mathematical induction in Mathematical induction. The incompleteness of Mathematical induction is unfortunate, and Three forms of mathematical induction does not help.

As for "...understanding and writing clearly; your failure to do any of those was so complete...", perhaps I need to quote Misplaced Pages:No personal attacks here: "Comment on content, not on the contributor". My writing skills are not on trial here. And I am not aware of a definition of "insult" that excludes accusations of stupidity. Please focus on the articles. Melchoir 03:41, 6 March 2006 (UTC)

• Keep It's also cool having the 3 types right there clean and consisely MadCow257 01:51, 6 March 2006 (UTC)
• Delete per Melchoir. --Allen 02:11, 6 March 2006 (UTC)
• Merge any original information. Royboycrashfan 02:13, 6 March 2006 (UTC)
• Merge per nom. No clear reason for this topic to have its own article. dbtfz 03:37, 6 March 2006 (UTC).
  • Or delete, if the content isn't worth preserving. (I share Deville's concerns.) dbtfz 05:37, 6 March 2006 (UTC)
• Delete essentially per nom, as I don't see anything in here to merge. This may be the first example of mathcruft I've seen. How is (2) functionally different from (1)? Whatever your answer is, then please articulate why there should be the explicit case where one has to prove n=1,2 by hand and then start the induction at 2? And etc.? In any case, this article contains absolutely zero mathematical content not contained in other articles. --Deville (Talk) 05:17, 6 March 2006 (UTC)
• Delete, content isn't worth preserving. --Mmx1 06:31, 6 March 2006 (UTC)
• Delete; no offense to Michael, but this just doesn't strike me as an encyclopedia article. It would be a good sort of observation to include in a textbook, maybe for a discrete math course. --Trovatore 06:55, 6 March 2006 (UTC)
• 'Delete as per Melchoir. If the article's originator can work up a merge, then please go for it.Vizjim 12:13, 6 March 2006 (UTC)
• Delete. Comparison of different variations on induction belongs at mathematical induction. This article seems like it might be about using induction for a certain group of problems. If this topic really does deserve an article, it probably needs a better title, and it should at least have an introduction which makes the topic clear. JPD (talk) 12:17, 6 March 2006 (UTC)
• Merge and Delete. Whatever new content here should be merged and this article deleted. -- Alpha269 14:39, 6 March 2006 (UTC)
  • Comment I don't think you can really do that, in general, because of the GFDL. Certainly we wouldn't want to just stick literal text from the article somewhere else and then delete the record of who wrote it. Possibly if the text were paraphrased first we'd be technically OK; I'm really not sure what the rules on that are. --Trovatore 15:17, 6 March 2006 (UTC)
• Keep per MadCow257. --Siva1979 14:52, 6 March 2006 (UTC)