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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:
  • 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: