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Often when I see a question I think it's probably a duplicate of some earlier question, but it's hard to know. The software always suggests related questions, but that only helps if the titles are informative. So I've taken on a little project to make the titles of the induction problems more informative by adding to the title (if it's not already there) something about the result OP wants to prove by induction. For example, if the title is "Proof by induction," and the person is asking about the formula for $1^2+3^2+\cdots+(2n-1)^2$, I might change the title to "Proof by induction ($1^2+3^2+\cdots+(2n-1)^2$)."

I don't want to flood the front page, so I'll only do a few at a time.

To turn this announcement of intentions into a question, I'll ask: is there any reason why I shouldn't proceed as indicated?

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  • $\begingroup$ Sounds good. I've long since changed my MSE bookmarks to sort by "newest" instead of "active", so you won't be flooding this peon's front page... $\endgroup$
    – The Chaz 2.0
    Commented Mar 8, 2012 at 5:13
  • $\begingroup$ Why not add "Proof by Induction" to the "List of Generalized Question"? $\endgroup$
    – Nobody
    Commented Mar 8, 2012 at 5:14
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    $\begingroup$ @scaaahu, I'm not sure that works, since the details of induction proofs can vary considerably. $\endgroup$
    – Gerry Myerson
    Commented Mar 8, 2012 at 6:23
  • $\begingroup$ @Gerry, I respect you very much ever since I saw you on sci.math many years ago. That said, allow me to ask, what's the difference between math.stackexchange.com/q/117780/17111 and math.stackexchange.com/q/72636/17111 ? $\endgroup$
    – Nobody
    Commented Mar 8, 2012 at 6:49
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    $\begingroup$ @scaaahu, not much difference - both ask to prove a formula for a sum, and both are solved by adding the next term and doing some algebra. But induction goes far beyond that. You can use induction to prove that you can always list the participants in a round-robin tournament in such a way that each one won the match against the next one. You can prove the Unique Factorization Theorem. You can prove $n\ge18$ implies $4a+7b=n$ has a solution in non-negative integers. They're all proofs by induction, but aside from that they have little in common. $\endgroup$
    – Gerry Myerson
    Commented Mar 8, 2012 at 11:39
  • $\begingroup$ ... and not to mention the difference between transfinite induction and the usual principle of mathematical induction, and the topological continuity principle, or the bootstrap/induction-by-energy arguments of partial differential equations. Induction is not so much a solution method but a frame of mind. $\endgroup$
    – Willie Wong Mod
    Commented Mar 8, 2012 at 12:10
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    $\begingroup$ +1: I don't want to flood the front page, so I'll only do a few at a time. $\endgroup$
    – GEdgar
    Commented Mar 8, 2012 at 13:41
  • $\begingroup$ I don't really agree. I think a title is only necessary to attract the right people, not to give a complete explanation of the problem. Of course, this means that in some cases a more verbose title is needed. $\endgroup$
    – user1120
    Commented Mar 8, 2012 at 16:49
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    $\begingroup$ For example, I don't agree with the changed title of my own post: math.stackexchange.com/questions/117883/… The original title would attract people that know something about special functions. People that don't know anything about those will not be more informed with the new title anyway. $\endgroup$
    – user1120
    Commented Mar 8, 2012 at 16:51
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    $\begingroup$ Quite a large collection of questions whose titles could use some improvement (not only because they appear more than once) is listed in this thread $\endgroup$
    – t.b.
    Commented Mar 8, 2012 at 17:19
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    $\begingroup$ @Jonas, I'm not trying to give a complete explanation of any problem, I'm just trying to make it easier to spot duplicates. If next year someone asks about $1^2+3^2+\cdots$ I want to be able to spot the earlier occurrence without having to open every question titled "Prove by induction". $\endgroup$
    – Gerry Myerson
    Commented Mar 8, 2012 at 23:00
  • $\begingroup$ @Gerry: Okay, sorry. I didn't completely understand. $\endgroup$
    – user1120
    Commented Mar 8, 2012 at 23:00
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    $\begingroup$ @GerryMyerson While the latter title is much better in a list, it's no more searchable than the original title; for your example I might go with 'Proof by induction of a sum of odd squares' so that someone searching 'sum of squares' or 'odd squares' might find it... $\endgroup$
    – Steven Stadnicki
    Commented Sep 6, 2012 at 19:38

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While people are thinking about this issue, remember that the best way to deal with this is to fix the titles early on while the question is still on the front page. People are rightfully somewhat nervous about editing content of questions, but I think editing titles should be done more freely as new users don't necessarily understand what a SE question title is supposed to be.

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    $\begingroup$ Also, feel free to fix a question when it returns to the front page for some other reason. $\endgroup$
    – GEdgar
    Commented Feb 4, 2014 at 14:23

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