|
This
level-3 vital article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
|
This page has archives. Sections older than 90 days may be automatically archived by Lowercase sigmabot III when more than 5 sections are present. |
The result was: rejected by
Theleekycauldron (
talk) 10:57, 25 December 2022 (UTC)
Created by Slaythe ( talk). Self-nominated at 01:05, 24 December 2022 (UTC).
This article uses 3 different notations for multiplication. IMO, either must be replaced with or must be replaced by in any case, some occurrences of should be removed, especially in exponents. As I have no clear opinion on the best choice, I wait for a consensus here. For clarification (see the preceding thread), I have added an explanatory footnote. D.Lazard ( talk) 10:28, 9 January 2023 (UTC)
In the section:
[...]
and the imaginary part of z satisfies
-π < Im (z) < π [this does not make sense to me: Isn't it a condition on the Arg(z) or equivalently on the Im(log(z))? Since log(z)=log(|z|)+i(Arg(z)+2nπ), n in Z and the principal value of log(z) can be defined as Log(z) when chosing -π < Im(log((z))=Arg((z)) < π, i.e. n=0]
[...] 217.10.52.10 ( talk) 09:52, 20 April 2023 (UTC)
In the top of the page, the article demonstrates how exponents of rational numbers correspond to nth-roots by proving that b^(1/2) == sqrt(b). Part of this proof relies upon the property that (b^M)*(b^N) == b^(M+N) (see excerpt pasted below). However, the article only proved this property based on the definition that natural-number exponents are equivalent to repeated multiplication. This proof does not apply when M or N are rational because rational exponents are not defined as a repeated multiplication.
Therefore, the article needs to have a separate proof that (b^M)*(b^N) == b^(M+N) when M and N are rational numbers.
Proving this property holds true for rational numbers is a fair bit more complicated than proving it holds true for natural numbers, but it's not so complicated as to be out of the scope of a wiki article. One such proof can be found on this stack overflow page [1]. unfortunately i do not know of any proofs that meet wikipedia's credibility requirements.
this is the specific excerpt from the wiki article that i take issue with: "Using the fact that multiplying makes exponents add gives b^(r+r) == b". It is located at the top of the page. Snickerbockers ( talk) 16:14, 24 November 2023 (UTC)
取らぬタヌキ (
talk) 21:41, 4 January 2024 (UTC)
These will help you understand the following:
If it is a real number domain, the square root cannot take a negative value, so .
Also,
取らぬタヌキ (
talk) 19:37, 5 January 2024 (UTC)
We must understand correctly that a exponentiation is a multivalued function.
The following formula transformation is important.
|
This
level-3 vital article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
|
This page has archives. Sections older than 90 days may be automatically archived by Lowercase sigmabot III when more than 5 sections are present. |
The result was: rejected by
Theleekycauldron (
talk) 10:57, 25 December 2022 (UTC)
Created by Slaythe ( talk). Self-nominated at 01:05, 24 December 2022 (UTC).
This article uses 3 different notations for multiplication. IMO, either must be replaced with or must be replaced by in any case, some occurrences of should be removed, especially in exponents. As I have no clear opinion on the best choice, I wait for a consensus here. For clarification (see the preceding thread), I have added an explanatory footnote. D.Lazard ( talk) 10:28, 9 January 2023 (UTC)
In the section:
[...]
and the imaginary part of z satisfies
-π < Im (z) < π [this does not make sense to me: Isn't it a condition on the Arg(z) or equivalently on the Im(log(z))? Since log(z)=log(|z|)+i(Arg(z)+2nπ), n in Z and the principal value of log(z) can be defined as Log(z) when chosing -π < Im(log((z))=Arg((z)) < π, i.e. n=0]
[...] 217.10.52.10 ( talk) 09:52, 20 April 2023 (UTC)
In the top of the page, the article demonstrates how exponents of rational numbers correspond to nth-roots by proving that b^(1/2) == sqrt(b). Part of this proof relies upon the property that (b^M)*(b^N) == b^(M+N) (see excerpt pasted below). However, the article only proved this property based on the definition that natural-number exponents are equivalent to repeated multiplication. This proof does not apply when M or N are rational because rational exponents are not defined as a repeated multiplication.
Therefore, the article needs to have a separate proof that (b^M)*(b^N) == b^(M+N) when M and N are rational numbers.
Proving this property holds true for rational numbers is a fair bit more complicated than proving it holds true for natural numbers, but it's not so complicated as to be out of the scope of a wiki article. One such proof can be found on this stack overflow page [1]. unfortunately i do not know of any proofs that meet wikipedia's credibility requirements.
this is the specific excerpt from the wiki article that i take issue with: "Using the fact that multiplying makes exponents add gives b^(r+r) == b". It is located at the top of the page. Snickerbockers ( talk) 16:14, 24 November 2023 (UTC)
取らぬタヌキ (
talk) 21:41, 4 January 2024 (UTC)
These will help you understand the following:
If it is a real number domain, the square root cannot take a negative value, so .
Also,
取らぬタヌキ (
talk) 19:37, 5 January 2024 (UTC)
We must understand correctly that a exponentiation is a multivalued function.
The following formula transformation is important.