2012/7/10 Leif Halvard Silli <[email protected]>: > Philippe Verdy, Tue, 10 Jul 2012 13:50:03 +0200: >> 2012/7/10 Leif Halvard Silli: >>> Asmus Freytag, Mon, 09 Jul 2012 19:32:47 -0700: >>>> The European use (this is not limited to Scandinavia) >>> >>> Thanks. It seems to me that that this tradition is not without a link >>> to the (also) European tradition of *not* using the DIVISION SIGN (÷) >>> for division. >> >> Why European ? > > We have 3 accounts which say that is European: I, Jukka and Asmus. It > might be spread wider ... But perhaps your point was that it is more > narrow? ;-)
Certainly more narrow. which is probably only for Nordic (Baltic?) European countries. I just discovered this usage in this discussion. At least in France we have never learnt that DIVISION SIGN (÷) could be used for noting the substraction (we have very little interaction with Nordic European languages, as all other languages around France apparently have the same conventions for noting operators in their languages : English, Dutch, German, Italian, Spanish ; and even Arabic when it is still a large minority language in Metropolitan France or in French overseas of the Indian Ocean). I also doubbt that Russian even uses this Nordic convention. At school (in the 1970's when I was a child) the DIVISION SIGN (÷) was the first symbol ever tought for noting a division in an horizontal formula. Long before the slash (/, independapntly of its encoding and visual length), and then much later with the top-bottom notation using an horizontal line. The division sign denotes in fact this long horizontal linen where the dots are visually indicating the placements of the operands. But the first notation taught was this one: : dividend | divisor : - partial product +------------------- : ---------------------- | quotient : intermediate remainder | : ... | : remainder | which was used to learn how to compute manually a division, whose computed result could then be given using the horizontal formula with the DIVISION SIGN (÷). We did not have calculators (they were initially banned in French schools, we had to use paper and pen, or learn to compute in our heads...) The first calculators were authorized at end of the 1970's in secondary schools (but they were stictly limited as their cost was still too expensive at this time for many families). All calculators appeared in France using the DIVISION SIGN (÷). This is still true today (much more frequent than the slash which is only seen and used on mechanical PC keyboards, but not even on virtual keyboards on-screen used by calculator applications on PC or on smartphones, even when they are localized in French). The minus sign has always been taught as an horizontal line matching the metrics of the plus sign (notations of neative numbers between parentheses was used up to the end of the 1960's in some professional accountings, but the traditional presentation does not even use negative numbers but separate columns for debit/credits, so that all numbers are positive only). Using (÷) in French for the substraction would cause severe confusions (in France, Belgium, Luxembourg, Switzerland, North Africa, the French overseas in several continents, and in Canada) ! French and English probably have always used the same conventions in mathematics (and it may be true as well for German, Dutch, Spanish, and Italian), if we ignore minor typographic differences (such as spacing and kerning or historical ligatures).
