Talk:Exponentiation

message: This article uses 3 different notations for multiplication. IMO, either \times must be replaced with \cdot, or \cdot must be replaced by \times; in any case, some occurrences of \cdot 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)
replies: text: As you wrote in the first thread, the primary issue with using \cdot is that it becomes ambiguous whether this represents ellipses or multiplication (to be fair, it's not really ambiguous, because one could figure out from context that one dot means multiplication and three means ellipses). So, I think that defaulting to \times in this article is probably best, even though this notation feels quite elementary-school-y. Duckmather (talk) 15:20, 9 January 2023 (UTC)
replies: text: Now that I know what is meant, I would suspect that most uninitiated readers (in the UK at least) would recognize a \times sign as a multiplication sign, but that the \cdot sign for multiplication would be much less familiar, and might well be a source of confusion. Additionally, I have come to this article in following-up work on the biographical WP article on William Oughtred, and I find that the introduction of the \times sign, in W.O.'s Clavis Arithmeticae (1631), followed on very soon after, and in the context of, the description of logarithms (in the English edition of John Napier's Description of the Admirable Table of Logarithmes (S. Waterson, London 1618), Appendix, at p. 4 (Google)). (An explanation of the sign is given in William Forster's Forster's Arithmetick (1673), at pp. 43-44 and pp. 113-14 (Google).) Hence there is an historical association between Exponentiation and this \times usage which some readers may want to understand. I find some explanations in F. Cajori's History of Mathematics (Macmillan, New York/London 1919), at pp. 157-58 (Internet Archive). Perhaps the pedagogic example is the better for being elementary? Eebahgum (talk) 18:38, 9 January 2023 (UTC)
replies: text: I adjusted the intro to be consistent with /times. I left the rest of the article as is. Emschorsch (talk) 04:49, 24 July 2023 (UTC)
thread_title:  Three notations for multiplication 

message: In the section: 
==== Principal value ====
[...]
:
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)
replies: text: . D.Lazard (talk) 16:12, 21 April 2023 (UTC)
thread_title:  Definition of principal value of log(z) 

message: [...]
:
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)
replies: text: . D.Lazard (talk) 16:12, 21 April 2023 (UTC)
thread_title:  Principal value