Timeline for Questions about proofs
Current License: CC BY-SA 4.0
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| Feb 15, 2022 at 6:15 | history | edited | ryang | CC BY-SA 4.0 |
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| Feb 14, 2022 at 12:06 | history | edited | ryang | CC BY-SA 4.0 |
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| Feb 11, 2022 at 7:41 | comment | added | user21820 | @DaveLRenfro: For whatever reason, I have never needed to write a proof that goes via a chain of equivalences to something trivial like "$1=1$". And regarding doing proofs backwards, I think it is pedagogically more instructive to learn the concepts of canonicalization and reductions, which actually suffice all high-school trigonometry. But of course, I completely agree with the point that both of you make, namely that correct proofs must be recognized as correct even if it looks silly, and likewise wrong proofs shouldn't be accepted. =) | |
| Nov 27, 2021 at 17:30 | comment | added | Dave L Renfro | @Daniel R. Collins: In high school, for harder trig. identity proofs, I would often do them backwards and then reverse the order of the steps. A couple of my mathy friends also did this when they took the class (after I did, as I took it earlier), having discovered it independently (i.e. I didn't tell them what I had done), so I would imagine some others here did the same thing. Of course, this can lead to some highly non-intuitively discoverable proofs, where (for example) you might wind up replacing $\sin x$ with $1\cdot \sin x,$ followed by $(\sin^2 x + \cos^2 x)\cdot \sin x \; \ldots$ | |
| Nov 27, 2021 at 15:27 | comment | added | Daniel R. Collins | Re: "It's even valid to start with the desired result then work towards 1=1": it should be noted that a good number of textbooks explicitly prohibit this practice, e.g., as in this question here: matheducators.stackexchange.com/questions/12586/… | |
| Nov 27, 2021 at 14:54 | history | edited | ryang | CC BY-SA 4.0 |
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| Nov 27, 2021 at 14:47 | history | answered | ryang | CC BY-SA 4.0 |