# User:Ivan

From Encyclopedia of Mathematics

## Some notes on style

- There are legacy images (e.g., m06542010.png) in this wiki with a lower ellipsis where one might expect a midline ellipsis instead. I used to write
`\ldots`

in order to preserve style, however, the printed Encyclopaedia of Mathematics does use midline ellipses and there are also legacy images where the multiplication dot is corrupted to a lower dot. To do:- Replacing
`\ldots`

where appropriate. - Proper spacing with differentials, consistent use of
`\quad`

and`\qquad`

(cf. Mathematics into Type, pages 37ff.).

- Replacing
- According to ISO 80000-2:2009, explicitly defined, context-independent functions, mathematical constants and well-defined operators are printed in roman (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.) The Unicode and ISO/IEC 10646 name of the character U+2213 is MINUS-OR-PLUS SIGN, not MINUS-PLUS SIGN.
- 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.

**How to Cite This Entry:**

Ivan.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Ivan&oldid=44340