terms from foreign languages used in mathematics (html version) TermsFromForeignLanguagesUsedInMathematics 2006-06-13 15:54:26 2008-09-23 06:37:47 Topic a fortiori a priori ad absurdum ad infinitum Ansatz cf. confer doh eigen espace et al. et alii \'etale \'etal\'e e.g. exempli gratia ibid. ibidem i.e. id est inter alia logarithmus binaris binary logarithm logarithmus generalis general logarithm logarithmus naturalis natural logarithm loc. cit. loco citato mutatis mutandis N.B. NB nota bene op. cit. opere citato p.p. presque partout sine qua non stufe urelement ur-element viz videlicet Zahlen Zentrum % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} \usepackage[T2A]{fontenc} \usepackage[russian, english]{babel} % there are many more packages, add them here as you need them % define commands here \PMlinkescapeword{point} This entry is best viewed in html \PMlinkescapetext{mode}. For the page \PMlinkescapetext{images} version, \PMlinkname{click here}{TermsFromForeignLanguagesUsedInMathematicsPageImagesVersion}. Following are \PMlinkescapetext{terms} from foreign \PMlinkescapetext{languages} that appear in mathematical literature. Each \PMlinkescapetext{chart} (TeX \PMlinkescapetext{object} tabular) contains \PMlinkescapetext{terms} from the foreign \PMlinkescapetext{language} indicated. The foreign \PMlinkescapetext{languages} are ordered according to how many \PMlinkescapetext{terms} appear in its corresponding \PMlinkescapetext{chart}. In each \PMlinkescapetext{chart}, the \PMlinkescapetext{terms} are listed in alphabetical \PMlinkescapetext{order}. \section{Latin} \begin{center} \begin{tabular}{|c|c|c|c|} \hline abbr. & \PMlinkescapetext{term} & literal \PMlinkescapetext{translation} & mathematical usage \\ \hline & {\em a fortiori} & with stronger reason & used in logic to denote an \PMlinkescapetext{argument} to the effect that because one ascertained fact exists; therefore another which is included in it or analogous to it and is less improbable, unusual, or surprising must also exist \\ \hline & {\em a priori} & from the former & already known/assumed \\ \hline & {\em ad absurdum} & to absurdity & an assumption is made in hopes of obtaining a contradiction [reductio ad absurdum is also used] \\ \hline & {\em ad infinitum} & to infinity & endlessly, infinitely \\ \hline & {\em casus irreducibilis} & not-reducible case & roots real but not expressible via real \PMlinkname{radicals}{Radical5} \\ \hline cf. & {\em confer} & compare & used to suggest that another work might also be consulted in \PMlinkescapetext{relation} to that \PMlinkescapetext{argument} \\ \hline et al. & {\em et alii} & and others & used in multi-author references but it is customary to include all the authors in the first citation and/or in the bibliography \\ \hline e.g. & {\em exempli gratia} & for example's sake & for example \\ \hline ibid. & {\em ibidem} & in the same \PMlinkescapetext{place} & relates to the immediately prior \PMlinkescapetext{source} \\ \hline i.e. & {\em id est} & that is & that is \\ \hline inf & {\em inferior}, {\em infimum} & lowest & limit inferior; greatest lower bound \\ \hline & {\em inter alia} & among other things & among other things \\ \hline loc. cit. & {\em loco citato} & in the \PMlinkescapetext{place} already mentioned & relates to \PMlinkescapetext{sources} before the immediately prior citation [probably less frequent than op. cit.] \\ \hline lb & {\em logarithmus binaris} & binary logarithm & log. in base 2 \\ \hline lg & {\em logarithmus generalis} & general logarithm & log. in base 10 \\ \hline ln & {\em logarithmus naturalis} & natural logarithm & log. in base $e$ \\ \hline & {\em mutatis mutandis} & once changing thing to be changed & repeat the \PMlinkescapetext{similar argument} for the related case \\ \hline N.B. & {\em nota bene} & note well & the following is important \\ \hline op. cit. & {\em opere citato} & in the work already mentioned & relates to \PMlinkescapetext{sources} before the immediately prior citation [probably more frequent than loc. cit.] \\ \hline QED & {\em quod erat demonstrandum} & which was to be demonstrated & end of proof \\ \hline QEF & {\em quod erat faciendum} & which was to be done & end of construction \\ \hline & {\em regula falsi} & rule of false position & Newton's method \\ \hline & {\em sine qua non} & without which it could not be & an essential condition or element; an indispensable thing \\ \hline sup & {\em superior}, {\em supremum} & uppermost & limit superior; \PMlinkname{least upper bound}{LowestUpperBound} \\ \hline viz & {\em videlicet} & that is to say, namely & a keynote abbreviation \\ \hline \end{tabular} \end{center} \section{German} \begin{center} \begin{tabular}{|c|c|c|c|} \hline abbr. & \PMlinkescapetext{term} & literal \PMlinkescapetext{translation} & mathematical usage \\ \hline & {\em Ansatz} & approach, attempt & assumed form for an expression \\ \hline & {\em eigen} & \PMlinkescapetext{characteristic}, typical & eigenvalue; eigenvector \\ \hline & {\em Gr\"osse, Gr\"o\ss e} & size, magnitude & Gr\"ossencharacter \\ \hline & {\em Faltung} & folding & convolution \\ \hline & {\em im kleinen} & in the small & connected im kleinen \\ \hline & {\em Nullstellensatz} & zero point \PMlinkescapetext{theorem} & zero point \PMlinkescapetext{theorem} \\ \hline & {\em Stufe} & stair, \PMlinkescapetext{level} & stufe of a field\\ \hline & {\em Urelement} & primeval element & set element which is not a set \\ \hline $V$, $K_4$ & {\em Vierergruppe} & four-group & Klein 4-group \\ \hline $\mathbb{Z}$ & {\em Zahlen} & numbers & integers \\ \hline $Z$ & {\em Zentrum} & \PMlinkname{center}{GroupCentre} & \PMlinkname{center (of a group)}{GroupCentre} \\ \hline \end{tabular} \end{center} \section{French} \begin{center} \begin{tabular}{|c|c|c|c|} \hline abbr. & \PMlinkescapetext{term} & literal \PMlinkescapetext{translation} & mathematical usage \\ \hline & {\em espace} & space & (topological) space [see Espace \'Etal\'e] \\ \hline & {\em \'etale} & slack & \'etale fundamental group; \PMlinkname{\'etale morphism}{Etale}; \'etale site \\ \hline & {\em \'etal\'e} & spread out, displayed & \PMlinkname{\'Etal\'e space}{EtaleSpace3} \\ \hline p.p. & {\em presque partout} & almost everywhere & \PMlinkname{almost everywhere}{AlmostSurely} \\ \hline \end{tabular} \end{center} \section{Russian} \begin{center} \begin{tabular}{|c|c|c|c|} \hline abbr. & \PMlinkescapetext{term} & literal \PMlinkescapetext{translation} & mathematical usage \\ \hline $\partial$ & italic ``\cyrd'' [may be pronounced ``doh''] & letter ``d'' & e.g. in $\frac{\partial f}{\partial x}$ [see partial derivative] \\ \hline \end{tabular} \end{center}