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Hometerms from foreign languages used in mathematics (html version)

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# terms from foreign languages used in mathematics (html version)

This entry is best viewed in html mode. For the page images version, click here.

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

# 1 Latin

abbr. | term | literal translation | mathematical usage |

a fortiori | with stronger reason | used in logic to denote an 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 | |

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 radicals | |

cf. | confer | compare | used to suggest that another work might also be consulted in relation to that argument |

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 place | relates to the immediately prior source |

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 place already mentioned | relates to sources 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 similar argument 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 sources 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; least upper bound |

viz | videlicet | that is to say, namely | a keynote abbreviation |

# 2 German

abbr. | term | literal translation | mathematical usage |

Ansatz | approach, attempt | assumed form for an expression | |

eigen | characteristic, typical | eigenvalue; eigenvector | |

Grösse, Größe | size, magnitude | Grössencharacter | |

Faltung | folding | convolution | |

im kleinen | in the small | connected im kleinen | |

Nullstellensatz | zero point theorem | zero point theorem | |

Stufe | stair, level | 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 | center | center (of a group) |

# 3 French

abbr. | term | literal translation | mathematical usage |
---|---|---|---|

espace | space | (topological) space [see Espace Étalé] | |

étale | slack | étale fundamental group; étale morphism; étale site | |

étalé | spread out, displayed | Étalé space | |

p.p. | presque partout | almost everywhere | almost everywhere |

# 4 Russian

abbr. | term | literal translation | mathematical usage |
---|---|---|---|

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

Defines:

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, gen

Related:

TermsFromForeignLanguagesUsedInMathematicsPageImagesVersion, MathematicsVocabulary, ApplicationOfCauchyCriterionForConvergence

Type of Math Object:

Topic

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

00A99*no label found*00A20

*no label found*

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- Other useful stuff
- Corrections

## Comments

## stipulations

I ask two things of those who choose to edit this object:

1. Please put the term that you are adding in the "Defines:" section (near "Synonyms:", "Related:", etc.)

2. Please do not change the tabular. With the exception of array (which, to the best of my knowledge, only exists in math mode), tabular is the only chart-like object in TeX that I know how to create/edit.

If you have any questions as to how to add to this entry, please feel free to post or send me an e-mail (Wkbj79@aol.com).

Warren

## PM

Unfortunately, the string of posts that started with "Latin abbreviations" seems to have disappeared. I'm guessing that this is because I deleted the object, "e.g.", to which the first post (made by pahio) was attached. Is there any way that we can still access these?

In any case, since this is the surviving entry that is most closely related, it makes sense for me to post here.

Within the string of posts "Latin abbreviations", the user alozano was kind enough to post:

"...On the other hand, congratulations to Wkbj79 for the many quality entries she/he has contributed so far, plus the corrections filed.

Alvaro"

I am glad that you appreciate it. I would like to point out that being active in PM helps me. Adding entries helps cement mathematical concepts in my mind, and it also gives me practice using TeX, at which I was somewhat rusty a month ago.

One thing that I hope will happen is that people are able to access information that will help them understand mathematical concepts, give them ideas for how to explain mathematics (especially important in the case of teachers), and stimulate their curiosity in higher mathematics and/or fields of mathematics with which they might not be familiar. I see no reason why PM cannot attempt to achieve this.

One additional aspect that I appreciate about PM is that I feel that most of us who are active here are striving to become better mathematicians and are trying to help others become better mathematicians.

Warren

PS -- For the record, it's "he". :-)

## Re: PM

I feel much the loss of your entry, Warren. When I saw it, I observed that Silverfish and pahio had collaborated in including some abbreviations. Personally I had including the following abbreviations: a fortiori, cf., et al., ibid, loc. cit., op. cit., sine qua non and viz. I think that it was a useful entry since it helped in the redaction, references and in the bibliography of new entries. I am to your complete disposition if you wish to write your entry again.

Sincerely,

perucho

## Re: PM

Warren, your entry did not lose. When I did my first reply it appeared again but I don't know why.

perucho

## Re: PM

I forgot the Algeboy collaboration. Sorry my friend!

perucho

## italic Russian d

``doh'' (i.e. d and a long vowel o) is _one_way_ for pronouncing the italic Russian letter d in mathematical utterances, such as the partial derivative \frac{\partial f}{\partial x}. The way is much used e.g. in Finland. Thus the partial derivative can be read

"doh f doh x", as we read dy/dx "dee y dee x".

There may be alternative ways to read the italic Russian d in mathematics, but I don't know such. I don't even know whether the Cyrillic d is pronounced ``doh'' in some Slavic language. I have learned ``doh'' in 1961 of the famous number-theorist K. Inkeri (see http://users.utu.fi/taumets/inkeri.htm).

It were interesting to hear the alternative ways for pronouncing the mathematical ``doh'', especially in the English-speaking countries.

Jussi

## Re: PM

> I am glad that you appreciate it. I would like to point out

> that being active in PM helps me. Adding entries helps

> cement mathematical concepts in my mind, and it also gives

> me practice using TeX, at which I was somewhat rusty a month

> ago.

PlanetMath helps me in exactly the same ways. Long ago, I wrote in the wiki very similar words: I want PlanetMath to be the standard online reference in Algebra and Number Theory. At least, it will be my standard reference. As I do research, I take mental notes of results that I think particularly useful and then include them in PM. That way, I can always go back from any computer and check the result, in case I don't have the article/book with me. It is working!

(here: http://planetx.cc.vt.edu/AsteroidMeta//alozano )

> One thing that I hope will happen is that people are able to

> access information that will help them understand

> mathematical concepts, give them ideas for how to explain

> mathematics (especially important in the case of teachers),

> and stimulate their curiosity in higher mathematics and/or

> fields of mathematics with which they might not be familiar.

> I see no reason why PM cannot attempt to achieve this.

Many of us also share this view. You may also at some point become involved with organizational tasks here in PlanetMath. Those tasks are organized through the wiki:

http://planetx.cc.vt.edu/AsteroidMeta/HomePage

and through the google group:

http://groups.google.com/group/planetmath

Alvaro