5

Does anyone know of a list of math terms that have (slightly) different meanings in different countries?

For example, "positive" could mean $\geq 0 $ in some places, and "strictly positive" means $>0$ - See Dutch wikipedia page on Positive numbers, which states "In Belgium, it is a number that is greater than or equal to 0".

Another common example is Domain and range, which is even ambiguous at the author level.

I'd also be interested in distinct math terms that different countries use. E.g. Divisors and factors in American vs British school systems, but this will easily get very long.

Since this is now CW, please add an answer for each term that you are aware of.

Community
  • 1
Calvin Lin
  • 68,864
  • Things may have changed, but I learnt both divisor and factor in school (in the U.S.). – Brian M. Scott Jul 18 '13 at 19:16
  • @BrianM.Scott I grew up (in singapore) knowing both too, along with GCD=HCF. However, I've come to notice, that many students do not treat these terms as interchangeable. Several even think that one of the terms refers exclusively to prime numbers, e.g. US is used to Divisors, and some think that factors are prime, with the opposite happening in UK. I'm not certain if this is a result of bad teaching, or a genuine concept. – Calvin Lin Jul 18 '13 at 19:20
  • 1
    Not totally unrealated, there are unusual translations. For example a field is a Körper in German whereas the respective literal translations would be Feld and body. – Hagen von Eitzen Jul 18 '13 at 19:23
  • HCF is definitely unusual in the U.S. On the other hand, it’s completely normal (to me, at least) to speak of cancelling common factors, pulling out a common factor, being off by a factor of $2$, etc. I don’t know whether it’s just me or something more widespread, but I think that I tend to use divisor when the notion of division is more prominent and factor when the notion of multiplication is more prominent. (That is, of course, more than a bit fuzzy!) – Brian M. Scott Jul 18 '13 at 19:26
  • Whole numbers strictly meant positive integers before I came to the us. whenever one wrote $log$ it meant to the base 10 and $ln$ to the base e. I haven't seen many people using $ln$ here, It doesn't matter but I have that 3 seconds of confusion once in a while. – felasfa Jul 18 '13 at 19:49
  • @abiyo: Your usage of $\log$ and $\ln$ is the one that I learned in the U.S. I simply can’t remember whether whole number meant positive integer or non-negative integer when I was in grade school, and I’ve not really used the term since then. – Brian M. Scott Jul 18 '13 at 19:55
  • @Brain, interesting. I guess then it differs from schools to schools in the US. It makes sense since the educational system here is decentralized as opposed to countries that have fixed text books and curriculum. – felasfa Jul 18 '13 at 20:04
  • U.S.: to factor. British: to factorize – Brian M. Scott Jul 18 '13 at 20:27
  • Trapezium & Trapezoid (American and English) (see http://en.wikipedia.org/wiki/Trapezoid). – Oleg567 Jul 18 '13 at 21:25
  • @Oleg567 Oh wow, I wasn't aware of that. I thought everyone used trapezium. Ooops – Calvin Lin Jul 18 '13 at 21:32
  • @Oleg567,@Calvin Lin: In Catalan we use trapezi (that is "trapezium") for a quadrilateral with only two parallel sides while trapezoide (that is "trapezoid") refers to a quadrilateral with no parallel sides at all. The same happens with the Spanish words trapecio and trapezoide. – A. Bellmunt Nov 08 '13 at 09:12
  • The most serious discrepancy I'm aware of is that the French define the notion of limit differently from the rest of the world: For $\lim_{x\to\xi} f(x)$ they look also at $f(\xi)$ when it is defined. – Christian Blatter Nov 08 '13 at 09:34
  • @CalvinLin: I've converted this to CW. Let me know if you object. – robjohn Nov 08 '13 at 19:00
  • @robjohn No objections. I wasn't aware about CW when I created this question in the past. – Calvin Lin Nov 08 '13 at 20:19
  • 1
    In French, variété stands for a manifold. And you need to really say variété algébrique to eliminate the confusion. – johnny Nov 09 '13 at 16:17
  • @johnny Please add that as a CW answer, instead of a comment. Also, please include an explanation of the difference. – Calvin Lin Nov 09 '13 at 16:19
  • *Moderator Note* Feel free to place another bounty on this question if you feel that it deserves one, but please skip nonsense in the custom reason. Thank you. – Tim Post Nov 14 '13 at 08:13

4 Answers4

4

(Expanding on Oleg's comment, taken from Mathworld's Trapezium.)

There are two common definitions of the trapezium. The American definition is a quadrilateral with no parallel sides; the British definition is a quadrilateral with two sides parallel (e.g., Bronshtein and Semendyayev 1977, p. 174)--which Americans call a trapezoid.

Definitions for trapezoid and trapezium have caused controversy for more than two thousand years.

Euclid (Book 1, Definition 22) stated, "Of quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right-angled but not equilateral; a rhombus that which is equilateral but not right-angled; and a rhomboid that which has opposite sides and angles equal to one another but is neither equilateral nor right angled. And let quadrilaterals other than these be called trapezia."

Proclus (also Heron and Posidonius) divided quadrilaterals into parallelograms and non-parallelograms. For the latter, Proclus assigned trapezium to "two sides parallel," and trapezoid to "no sides parallel." Archimedes also defined a trapezium as having precisely two parallel sides (Heath 1956, pp. 188-190).

According to the Oxford English Dictionary, the confusion of trapezium and trapezoid between the United States and Great Britain dates back to an error in Hutton's Mathematical Dictionary in 1795, the first work of its kind in the United States, which directly reversed the accepted meanings. Hutton assigned trapezium to "no sides parallel" and trapezoid to "two sides parallel" (Simpson and Weiner 1992, p. 2101).

After 1795 in the United States, the Hutton definitions became standard, while in the British empire, the Proclus definitions remained standard. Two hundred years later, the controversy remains. Country by country, region by region, and even teacher by teacher, the definitions of trapezoid and trapezium are commonly swapped.

It is perhaps therefore best to tread extremely carefully into questions of definition for these two simple plane figures. W. E. Greig (pers. comm., Mar. 10, 2007) has proposed that the American trapezoid (i.e., the British trapezium) be dubbed the "trapeziam" (with the -am suffix indicating "American"), but adding yet another term to the word soup seems unlikely to help resolve the confusion.

Calvin Lin
  • 68,864
1

"Positive" could mean $\geq 0 $ in some places, and "strictly positive" means $>0$ - See Dutch wikipedia page on Positive numbers, which states (translated) "In Belgium, it is a number that is greater than or equal to 0".

Calvin Lin
  • 68,864
1

There is a declining but still existent tendency in French to not assume fields are commutative,

English (field, division ring) = French (corps commutatif, corps)

zyx
  • 35,436
1

I find the following very confusing:

French: Groupe de type fini means (in English) a finitely generated group. For instance, for such a group $H_2(G)$ can have infinite rank.

English: Group of finite type means something much stronger, a group $G$ so that the group ring $ZG$ admits a finite projective resolution by finitely-generated $ZG$-modules. This, in particular, implies that $H_k(G)$ has finite rank for all $k$. Groups of finite type tend to be finitely presented.

Moishe Kohan
  • 97,719