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1. • CommentRowNumber1.
   • CommentAuthorTobyBartels
   • CommentTimeAug 26th 2011
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   Author: TobyBartels
   Format: MarkdownItexAs reported elsewhere, Zhen Lin began [[recursion]]. I changed the section title "In classical mathematics" to "In general" since there didn't seem to be anything inherently classical about it. But maybe I'm missing something.

   As reported elsewhere, Zhen Lin began recursion. I changed the section title “In classical mathematics” to “In general” since there didn’t seem to be anything inherently classical about it. But maybe I’m missing something.

2. • CommentRowNumber2.
   • CommentAuthorZhen Lin
   • CommentTimeAug 27th 2011
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   Author: Zhen Lin
   Format: MarkdownI chose that heading because I wasn't sure the proof carried through in, say, intuitionistic mathematics. But then again, how could it not? (I suppose we'd just redefine what well-foundedness means so that it is true...)

   I chose that heading because I wasn't sure the proof carried through in, say, intuitionistic mathematics. But then again, how could it not? (I suppose we'd just redefine what well-foundedness means so that it is true...)

3. • CommentRowNumber3.
   • CommentAuthorMike Shulman
   • CommentTimeAug 27th 2011
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   Author: Mike Shulman
   Format: MarkdownItexIt's a good point; we do have to define "well-founded" correctly in intuitionistic mathematics if we want that proof to carry through. One of the classical definitions involves a lot of negations, and that one doesn't work so well intuitionistically.

   It’s a good point; we do have to define “well-founded” correctly in intuitionistic mathematics if we want that proof to carry through. One of the classical definitions involves a lot of negations, and that one doesn’t work so well intuitionistically.

4. • CommentRowNumber4.
   • CommentAuthorTobyBartels
   • CommentTimeAug 27th 2011
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   Author: TobyBartels
   Format: MarkdownItexYou (Zhen Lin) linked [[well-founded relation]], which has the proper definition, which you seemed to use.

   You (Zhen Lin) linked well-founded relation, which has the proper definition, which you seemed to use.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMay 11th 2012
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   Author: Urs
   Format: MarkdownItexI have added to _[[recursion]]_ a supposedly contentful paragraph in the Idea-section. (Or I will have done so as soon as the $n$Lab reacts to me pressing the "Submit" button. Which may take a while.) Previously there had been the following paragraph. I think I found the joke funny the first time that I read it, but since wiki entries stay there for a while, any jokes in them tend to become lame, don't they? Please let me know if anyone insists that the following is kept in the $n$Lab. Maybe we can find some compromise. --- [begin forwarded message] > To understand recursion, one must first understand recursion. > > — An old joke Joke as it may be, the quote above is very nearly the truth. The missing ingredient are conditions to _guarantee_ that the process terminates; formally, what we need are _base cases_ and a [[well-founded relation]] on the domain on which we are recursing.

   I have added to recursion a supposedly contentful paragraph in the Idea-section. (Or I will have done so as soon as the $n$Lab reacts to me pressing the “Submit” button. Which may take a while.)

   Previously there had been the following paragraph. I think I found the joke funny the first time that I read it, but since wiki entries stay there for a while, any jokes in them tend to become lame, don’t they? Please let me know if anyone insists that the following is kept in the $n$Lab. Maybe we can find some compromise.

   ---

   [begin forwarded message]

   To understand recursion, one must first understand recursion.

   — An old joke

   Joke as it may be, the quote above is very nearly the truth. The missing ingredient are conditions to guarantee that the process terminates; formally, what we need are base cases and a well-founded relation on the domain on which we are recursing.

6. • CommentRowNumber6.
   • CommentAuthorMike Shulman
   • CommentTimeMay 12th 2012
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   Author: Mike Shulman
   Format: MarkdownItexI'm glad to have the joke removed. I think the new Idea section is good, but in the general case it's not really correct to distinguish between the "initial value(s)" and the "rules to obtain other values" — they're one and the same sort of thing. I did a bit more editing, see what you think.

   I’m glad to have the joke removed. I think the new Idea section is good, but in the general case it’s not really correct to distinguish between the “initial value(s)” and the “rules to obtain other values” — they’re one and the same sort of thing. I did a bit more editing, see what you think.

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeMay 12th 2012
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   Author: Urs
   Format: MarkdownItexThanks, Mike. What you wrote is much better. I just changed "induction principle" to "recursion principle".

   Thanks, Mike. What you wrote is much better. I just changed “induction principle” to “recursion principle”.

8. • CommentRowNumber8.
   • CommentAuthorTobyBartels
   • CommentTimeMay 13th 2012
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   Author: TobyBartels
   Format: MarkdownItexThis is a classic joke, part of the mathematical culture, not something that one expects to stay fresh. In this case, however, I don't think that it made for a good Idea section; I actually don't understand "the quote above is very nearly the truth".

   This is a classic joke, part of the mathematical culture, not something that one expects to stay fresh. In this case, however, I don’t think that it made for a good Idea section; I actually don’t understand “the quote above is very nearly the truth”.