User talk:KarlFrei

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Cheers! prime mover (talk) 03:51, 6 September 2018 (EDT)

New proofs of existing results
Hi

Please note that when you develop a new proof of a result which has already got a proof for it, this should be added as a separate proof. Please do not replace an existing proof.

This is specifically with reference to Inverse of Positive Real is Positive. --prime mover (talk) 08:31, 18 September 2018 (EDT)


 * Sorry. I did not view this as a new proof but only as a constructive version of an existing proof (basically just reorder the lines). However, I've now realized that it doesn't even work, so I've gone back to the previous version. Again, apologies! KarlFrei (talk) 08:43, 18 September 2018 (EDT)

New proofs of existing results
Hi

Please do not just replace an existing proof with a new one, even if the new one does look better to you than the one it replaces.

I have reversed out your latest edit, and I will now do the job of re-incorporating the new one as a separate proof. --prime mover (talk) 07:41, 23 September 2018 (EDT)


 * ... There. Like that. --prime mover (talk) 07:51, 23 September 2018 (EDT)


 * Sorry, I am really not trying to be difficult, but in this case I thought the replacement I did was obvious.


 * The old proof was essentially A -> B -> C -> D and D -> C -> B -> A (wrapped in two proofs by contradiction). I replaced this by A <-> B <-> C <-> D. Surely this kind of change is unproblematic?? What is the point of keeping the two directions separate? KarlFrei (talk) 11:14, 23 September 2018 (EDT)


 * Also, it seems you could at least keep in the proofs by contraposition which I put in (and which you have been allowing so far). I really don't see what is so problematic about these minor edits. KarlFrei (talk) 11:18, 23 September 2018 (EDT)


 * Your new proof remains in place. As for the one you changed from being a proof by contradiction to a proof by contraposition, I can't see what you're complaining about. You deleted it. --prime mover (talk) 16:14, 23 September 2018 (EDT)

Even if a proof is supposed to replace another because it is "better" in some relevant way, it is usually good to have this idea checked by other contributors. We have merged two proofs of the same result on occasion, when the differences were deemed sufficiently negligible. However it should be noted that these were exceptions. &mdash; Lord_Farin (talk) 16:43, 23 September 2018 (EDT)


 * OK, I see. I have put the better version of Proof 1 back in and added an official suggestion to delete it (as I believe we only need proof 2). Please do assess this suggestion (at some point). Thank you! KarlFrei (talk) 02:46, 24 September 2018 (EDT)


 * It is only your assessment that your version of Proof 1 is "better" than the one that was there originally. I still remain unconvinced that a proof by contraposition is inherently "better" than a proof by contradiction. Both proof forms are valid. In fact, there is no reason why both forms should not both exist on this site.


 * I need to understand your motivation in reducing site content. You seem insistent on changing things to match your preferences, rather than adding your own valid content. This site attempts to document all approaches.


 * A longer, more discursive proof is friendlier to a newer and more inexperienced mathematician than a minimalist and compact proof, however more elegant and sophisticated the latter may appear. As the philosophy of this site is to allow intellectual accessibility to all, no matter where they are on their mathematical journey, it needs to be demonstrated rigorously that shorter and less explanatory proofs are just as effective as communicating the knowledge as the longer proof before the longer form is directly replaced by a shorter one. --prime mover (talk) 03:11, 24 September 2018 (EDT)


 * Hang on, I started off by adding some new content! Then I just came across this missing proof of contraposition (which was also an addition, come to think of it) and started to fix it (in my opinion).


 * I honestly thought that I was actually making things easier for the reader. All I am doing (in my view) is removing some unnecessary steps. I would not say that this is "reducing site content". I want the proofs to be accessible. And I know that each additional logical step potentially loses some readers.


 * "Reducing site content" was deleting a proof to make way for another one. --prime mover (talk) 04:53, 24 September 2018 (EDT)


 * I am sorry. I understand what you mean now. I guess the point is that I simply did not see this as deleting a proof, but merely combining both directions into one. KarlFrei (talk) 05:07, 24 September 2018 (EDT)


 * The proofs I have been changing are proofs by contraposition (OK, once or twice I had to make a very minor change to turn it into one). By this I mean that the assumption which is contradicted in the proof by contradiction is not needed anywhere in the proof until the final line. Look for instance at Path in Tree is Unique/Necessary_Condition. If you compare the two versions side by side, you will see that it actually contains more lines now.

https://proofwiki.org/w/index.php?title=Path_in_Tree_is_Unique/Necessary_Condition&oldid=159202 https://proofwiki.org/w/index.php?title=Path_in_Tree_is_Unique/Necessary_Condition&oldid=366870


 * I still need to be convinced that your way is better than the original way. A proof by contradiction is NOT a proof by contraposition until it is turned into one. Whether you prefer it to be a proof by contraposition or not, does not mean it is a proof by contraposition until it is turned into it. I confess that I don't care enough for it to be an issue. --prime mover (talk) 04:53, 24 September 2018 (EDT)
 * We should probably end this discussion here, but allow me to explain that intuitively, I would say that a proof by contradiction is a proof which starts off with an assumption and uses it to create a contradiction. The proofs I have been editing could put this assumption right before the last line as they do not use it (except that this would look really strange). All I am trying to do is save on logical steps. KarlFrei (talk) 05:07, 24 September 2018 (EDT)
 * But once you delete a proof (preferring a different approach), you can't really expect the one you deleted to be restored to the version you changed it to. (I refer to Preimages All Exist iff Surjection/Proof 1.) You deleted it. You didn't want it any more. So I restored the earlier one. If you didn't want it, why complain that I put the old one back? --prime mover (talk) 04:53, 24 September 2018 (EDT)
 * As I wrote in the comments for my last edit there, if we must have this proof on ProofWiki, I would prefer to have the one which has fewer logical steps. KarlFrei (talk) 05:07, 24 September 2018 (EDT)
 * Or look at Condition for Edge to be Bridge. (old version: https://proofwiki.org/w/index.php?title=Condition_for_Edge_to_be_Bridge&oldid=342171) All I had to do here was remove the initial step "Let e be a bridge of G" for the necessary direction, and "Let e not lie on a circuit" for the sufficient direction. These are steps which do not add anything to the proof. They are not needed inside (until the end). I hope that it is OK to make these kinds of changes.


 * Let me also add that I am all in favor of having multiple proofs for the same result! Having a repository is great, which is why I opened an account here. I recently saw a paper with about 30 proofs of the divergence of the harmonic series, and I added my favorite to the site. But having versions of a proof which only differ in 2-3 lines does not really contribute anything, I would say.


 * Finally, I do realize that I wrote down Preimages_All_Exist_iff_Surjection/Proof_2 in a very brief way. I can of course expand it to use more words. Then perhaps the correspondence to Proof 1 will be clearer as well.


 * I have made this change now. As an afterthought, I am 100% convinced that direct proofs are easier to understand (more accessible) than proofs by contradiction OR contraposition. I would be interested to hear an opposing view. KarlFrei (talk) 04:31, 24 September 2018 (EDT)


 * Hope this helps, KarlFrei (talk) 04:17, 24 September 2018 (EDT)

Well yes, it is okay to amend your own proof, but in this case I can't see why you would. It says exactly the same as the one you replaced, except that it does it in words instead of symbols. As such, it possibly merits inclusion as a separate proof in its own right.

As for me, I prefer proofs using symbols to those using words, for what are to me obvious reasons, but I understand others prefer words (possibly because they do not find it easy to learn symbols, maybe because of visual impairment).

I'm not going to argue tediously over whether Proof By Contradiction is better than Proof By Contraposition, as I have other things to do.


 * I am glad to hear it. But I really do want to ask your opinion about direct proofs. Can we come to a consensus that they are easier to understand than proofs that use a contradiction (in whatever form)? I ask because you stated earlier that (paraphrasing) shorter proofs are only better if they are easier to understand.


 * Whether a direct proof is easier to understand than an indirect proof is unimportant. What is important is that it is different from an indirect proof. If someone has written an indirect proof, and someone else has written a direct proof, there is no reason why both should not stay. --prime mover (talk) 08:31, 24 September 2018 (EDT)


 * I guess I just don't understand this community's insistence on keeping everything around if possible. Possibly this is because of my Wikipedia background, which of course has almost the opposite culture. (I tried to create a page there once. Oh boy!)


 * We are not Wikipedia. Let me repeat that: we are very not Wikipedia. Let me add further emphasis: we are very, very, very not Wikipedia.


 * Unless a page is genuinely wrong, or says the same as another page, we do not delete anything. Two different proofs are not the same. And even if a page is wrong, it does not get deleted unless it cannot be corrected. See -- we even have a page on squaring the circle! --prime mover (talk) 08:31, 24 September 2018 (EDT)

However this may eventuate, the suggestion is made that rather than retread a whole body of existing proofs, maybe you might like to consider where there are gaps that may need to be filled? There are plenty of entries in the Wanted Proofs cateogory. --prime mover (talk) 04:41, 24 September 2018 (EDT)


 * I have seen that list :-) Unfortunately, I did not immediately spot a theorem that I had a ready proof for. Abel-Ruffini would be a huge undertaking... KarlFrei (talk) 04:57, 24 September 2018 (EDT)


 * I gave you the link to the wrong category: Category:Proof Wanted --prime mover (talk) 08:23, 24 September 2018 (EDT)


 * Oh wow. Indeed, I had not seen that page yet... KarlFrei (talk) 11:05, 24 September 2018 (EDT)