most recent 30 from http://mathoverflow.net 2013-05-23T19:35:26Z http://mathoverflow.net/feeds/question/17817 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/17817/can-a-corollary-follow-a-conjecture mathnewb 2010-03-11T04:04:47Z 2010-04-23T15:32:47Z

<p>It is typical to find a corollary that following theorems, but is it right to use the word corollary for a statement following a conjecture, where the statement is true only if the unproven conjecture is true?</p>

http://mathoverflow.net/questions/17817/can-a-corollary-follow-a-conjecture/17818#17818 Douglas S. Stones 2010-03-11T04:12:49Z 2010-03-11T04:12:49Z

<p>I think it's generally bad form to have a corollary dependent on an earlier conjecture. I recommend one of the following:</p> <p><strong>Theorem</strong>: Assuming Conjecture A, properties X, Y and Z are true.</p> <p>or </p> <p><strong>Theorem</strong>: Conjecture A implies X, Y and Z.</p> <p>Most importantly, it should be crystal clear that the result is dependent on the conjecture.</p>

http://mathoverflow.net/questions/17817/can-a-corollary-follow-a-conjecture/17820#17820 David Speyer 2010-03-11T04:19:09Z 2010-03-11T04:19:09Z

<p>I would write "Proposition Z: If X holds, then Y is true." Even if the deduction of Y from X were trivial, I think labelling this a corollary would be confusing. (After all, what is the statement "X implies Y" a corollary of?) However, I wouldn't have a problem writing something like "as we saw above, Y would be a corollary of X" later on. (The subjunctive voice is important here!)</p>

http://mathoverflow.net/questions/17817/can-a-corollary-follow-a-conjecture/17831#17831 Theo Johnson-Freyd 2010-03-11T06:16:29Z 2010-03-11T06:16:29Z

<p>I'm reminded of the following story that I posted on my personal web journal a couple years ago:</p> <blockquote> <p>At the Topology seminar yesterday, the speaker presented a theorem, which he immediately followed with a refinement: a statement that directly and obviously implies the theorem. He labeled his refinement a "corollary". I turned to Noah Snyder, and said that it was more an "uncorollary, or an anticorollary", but as soon as I said as much, the two of us simultaneously correctly labeled the refinement as a "rollary".</p> <p>There should be more rollaries in mathematical writing.</p> </blockquote>

http://mathoverflow.net/questions/17817/can-a-corollary-follow-a-conjecture/17832#17832 Noah Snyder 2010-03-11T06:27:15Z 2010-03-11T06:27:15Z

<p>Making a new Theorem environment that let you have the bolded part say "Corollary to Conjecture X" seems to me a good compromise of concise and unlikely to confuse anyone.</p>

http://mathoverflow.net/questions/17817/can-a-corollary-follow-a-conjecture/17850#17850 anton 2010-03-11T12:04:27Z 2010-03-11T12:04:27Z

<p>The correct term for such an item is CONJOLLARY. ;)</p>