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A few years ago I had published a mathematics journal article where for one of the results I had imposed extremely strong assumptions to ensure that given conclusion is true. Figuratively speaking, I now realise that I have used a hydraulic press to crack a peanut. Indeed, the same conclusion can be obtained with minimal assumptions.

Needless to say, I am deeply ashamed by this sloppiness, but I am not sure if this merits publishing an erratum. One co-author strongly opposes publishing an erratum, saying that we should simply add a remark to a follow-up paper we are writing, while the other couldn't care less. As the original result isn't strictly incorrect, I'm not sure what the appropriate approach is.

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    If only mathematicians had a time machine so they could go back and "fix" their "sloppiness" when they realize their results hold in greater generality than they first thought....This is how math works, and it is glorious. You prove what you need, then someone (possibly yourself) makes you look like an idiot by one-upping you with a more beautiful and elegant result that you can't for the life of you explain how you didn't think of the first time around. So, yeah, I say go with Mac's answer: make a new paper either for it or containing it and carry on. – zibadawa timmy Mar 9 '17 at 9:09
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In my opinion, an erratum is an erratum. I mean you should use it if you really discovered a flaw in a result and you want to patch it when the patch is not evident.

In your case, in some sense you improved your previous result and this either necessitate a new paper if the improvement is substantial or just a remark in some follow-up paper.

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    Nice. I wanted to post the same answer. An erratum or corrigendum (plurals: errata, corrigenda) (comes from Latin: errata corrige) is a correction of a published text. The OP wants an improvement not a correction because the result is correct. – PsySp Mar 9 '17 at 7:55
  • I agree. If he has found his nutcracker (not that you'd need one for a peanut) it's probably worthy of a publication in its own right. An erratum, at worst, would muddle up exactly when the new solution was found and in what context. – Weckar E. Mar 9 '17 at 11:35
  • I agree as well. Either a remark or a short paper would be a better idea. – TryingToGraduate Mar 9 '17 at 16:53

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