Talk:Euler's identity: Difference between revisions
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:FWIW, the [https://en.wikipedia.org/wiki/Euler%27s_identity Wikipedia article] on the subject describes e<sup>ix</sup>=cos(x)+i.sin(x) as ''Euler's formula'' and agrees with the task author that e<sup>iπ</sup> + 1 = 0 is called ''Euler's identity''. I have no idea whether this is correct terminology or not. --[[User:PureFox|PureFox]] ([[User talk:PureFox|talk]]) 14:48, 9 August 2021 (UTC) |
:FWIW, the [https://en.wikipedia.org/wiki/Euler%27s_identity Wikipedia article] on the subject describes e<sup>ix</sup>=cos(x)+i.sin(x) as ''Euler's formula'' and agrees with the task author that e<sup>iπ</sup> + 1 = 0 is called ''Euler's identity''. I have no idea whether this is correct terminology or not. --[[User:PureFox|PureFox]] ([[User talk:PureFox|talk]]) 14:48, 9 August 2021 (UTC) |
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:Somewhat inconsistently used AKA's. However, if we adopt "formula" for the general case, and "identity" for the special case, and the task here is regarding the special case (which must necessarily pre-assume the validity of the general case), then as per Nigel the "proof" is trivial - boils down to "proving" that -1 + 1 = 0 (to the limit of IEEE 754 for the "-1" in most non-symbolic languages), right? --[[User:Davbol|Davbol]] ([[User talk:Davbol|talk]]) 16:10, 9 August 2021 (UTC) |
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Revision as of 16:11, 9 August 2021
Euler's identity is actually eix=cos(x)+i.sin(x). The example given is a special case when when x=π. cos π is -1 and sin π is 0. Thus eiπ is obviously -1.--Nigel Galloway (talk) 14:31, 9 August 2021 (UTC)
- FWIW, the Wikipedia article on the subject describes eix=cos(x)+i.sin(x) as Euler's formula and agrees with the task author that eiπ + 1 = 0 is called Euler's identity. I have no idea whether this is correct terminology or not. --PureFox (talk) 14:48, 9 August 2021 (UTC)
- Somewhat inconsistently used AKA's. However, if we adopt "formula" for the general case, and "identity" for the special case, and the task here is regarding the special case (which must necessarily pre-assume the validity of the general case), then as per Nigel the "proof" is trivial - boils down to "proving" that -1 + 1 = 0 (to the limit of IEEE 754 for the "-1" in most non-symbolic languages), right? --Davbol (talk) 16:10, 9 August 2021 (UTC)