terms from foreign languages used in mathematics (page images version)

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Following are from foreign that appear in mathematical literature. Each (TeX tabular) contains from the foreign indicated. The foreign are ordered according to how many appear in its corresponding . In each , the are listed in alphabetical .

1 Latin

abbr.		literal	mathematical usage
	a fortiori	with stronger reason	used in logic to denote an
			to the effect that
			because one ascertained fact exists;
			therefore another which is
			included in it or analogous to is
			and is less improbable, unusual,
			or surprising must also exist
	a priori	from the former	already known/assumed
	ad absurdum	to absurdity	an assumption is made in hopes of
			obtaining a contradiction
			[reductio ad absurdum is also used]
	ad infinitum	to infinity	endlessly, infinitely
	casus irreducibilis	not-reducible case	roots real but not
			expressible via real http://planetmath.org/Radical5radicals
cf.	confer	compare	used to suggest that another
			work might also be consulted
			in to that
et al.	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
e.g.	exempli gratia	for example’s sake	for example
ibid.	ibidem	in the same	relates to the
			immediately prior
i.e.	id est	that is	that is
inf	inferior, infimum	lowest	limit inferior; greatest lower bound
	inter alia	among other things	among other things
loc. cit.	loco citato	in the already mentioned	relates to before the
			immediately prior citation
			[probably less frequent
			than op. cit.]
lb	logarithmus binaris	binary logarithm	log. in base 2
lg	logarithmus generalis	general logarithm	log. in base 10
ln	logarithmus naturalis	natural logarithm	log. in base $e$
	mutatis mutandis	once changing thing to be changed	repeat the
			for the related case
N.B.	nota bene	note well	the following is important
op. cit.	opere citato	in the work already mentioned	relates to before the
			immediately prior citation
			[probably more frequent
			than loc. cit.]
QED	quod erat demonstrandum	which was to be demonstrated	end of proof
QEF	quod erat faciendum	which was to be done	end of construction
	regula falsi	rule of false position	Newton’s method
	sine qua non	without which it could not be	an essential condition
			or element; an indispensable thing
sup	superior, supremum	uppermost	limit superior, http://planetmath.org/LowestUpperBoundleast upper bound
viz	videlicet	that is to say, namely	a keynote abbreviation

2 German

abbr.		literal	mathematical usage
	Ansatz	approach, attempt	assumed form for an expression
	eigen	, typical	eigenvalue; eigenvector
	Grösse, Größe	size, magnitude	Grössencharacter
	im kleinen	in the small	connected im kleinen
	Nullstellensatz	zero point	zero point
	Stufe	stair,	stufe of a field
	Urelement	primeval element	set element which is not a set
$V$, $K_4$	Vierergruppe	four-group	Klein 4-group
$\mathbb{Z}$	Zahlen	numbers	integers
$Z$	Zentrum	http://planetmath.org/GroupCentrecenter	http://planetmath.org/GroupCentrecenter (of a group)

3 French

abbr.		literal	mathematical usage
	espace	space	(topological) space [see Espace Étalé]
	étale	slack	étale fundamental group; http://planetmath.org/Etaleétale morphism; étale site
	étalé	spread out, displayed	http://planetmath.org/EtaleSpace3Étalé space
p.p.	presque partout	almost everywhere	http://planetmath.org/AlmostSurelyalmost everywhere

4 Russian

abbr.		literal	mathematical usage
$\partial$	italic ‘‘д’’ [may be pronounced ‘‘doh’’]	letter ‘‘d’’	e.g. in ${\displaystyle \frac{\partial f}{\partial x}}$ [see partial derivative]

Title	terms from foreign languages used in mathematics (page images version)
Canonical name	TermsFromForeignLanguagesUsedInMathematicspageImagesVersion
Date of creation	2013-03-22 16:06:45
Last modified on	2013-03-22 16:06:45
Owner	Wkbj79 (1863)
Last modified by	Wkbj79 (1863)
Numerical id	37
Author	Wkbj79 (1863)
Entry type	Topic
Classification	msc 00A20
Classification	msc 00A99
Related topic	TermsFromForeignLanguagesUsedInMathematics
Related topic	MathematicsVocabulary