User:Ivan

Ivan Panchenko

Some notes on style

• According to ISO 80000-2:2009, variables are italicized, while explicitly defined, context-independent functions, mathematical constants and well-defined operators are not (e.g., $\mathrm C^k_n$, $\mathrm dx$, $\mathrm e$^{$\mathrm i$π}). Note, however, that physical constants are written in italics, e.g., $m_\mathrm e$ for the electron mass and $e$ for the elementary charge. It may be argued that $\mathrm P$ clearly stands for probability; on the other hand, there are different probability measures and $P$ may be used as a variable for such a measure (just as $p$ is often used as a variable for a prime number). (ISO 3534-1:2006 uses italic $P$, so I will stick to that.)
• The standard document is pretty sloppily written. In the remark to item 2-13.2, a minus appears that looks rather like a hyphen. The spacing is inconsistent and $\mathrm{Ei}x$ as well as $\mathrm{li}x$ are found even though, according to the standard, there should be a thin space in such cases. $\bar x_a$ for the arithmetic mean (the subscript may be omitted) appears with an italic $a$ which barely makes any sense. (In the remarks row, there is talk about subscript h for the harmonic, subscript g for the geometric and subscript q or rms for the quadratic mean or root mean square; “h”, “g”, “q” and “rms” appear upright there, although the corresponding notations are not actually displayed.) In turn, the notations $\int\limits_\mathrm C$, $\int\limits_\mathrm S$ and $\int\limits_\mathrm V$ (integral over a curve $\mathrm C$, a surface $\mathrm S$, a three-dimensional domain $\mathrm V$) are mentioned – aren’t variables used here so that italic type is called for?
• In Writing Mathematical Expressions, Jukka Korpela states: “The standard says that the symbols $\sqrt{\color{white}a\!\!\!\!}$​$a$ and $\sqrt[n]a$ ‘should be avoided’. The exact meaning of this is not clear, and the standard itself uses the square root symbol in many examples.” In fact, the standard recommends to avoid $\sqrt{\color{white}a\!\!\!\!}$​$a$ and $^n\!\sqrt{\color{white}a\!\!\!\!}$​$a$. This clearly refers to notation without a vinculum.
• Korpela: “Congruence notations use the equals sign ($=$). The identify [sic] sign ($\equiv$) can, however, be interpreted as an allowed alternative.” The standard does, in fact, use an equivalence sign and not an equals sign ($n\equiv k\bmod m$) – unfortunately, neither with extra large space before the $\mathrm{mod}$ nor with parentheses.