2003-03-28 11:12:26, Marco Cimarosti <marco.cimarosti@...> wrote:

>Nicholas Bodley wrote:
>
>> Europe would show [decimal 1/4] as [0,25] ; the USA, as [0.25].
>
>This is not exact. English-speaking European countries use the dot as well.
>These presentation conventions are more linked to the language than to the
>geographical location.

Thank you! It's so easy to learn incomplete information.

>Moreover, the symbol used for separating the decimal part of the number is
>often dependent on what is being counted. The generic dot (or comma) it is
>often substituted with a symbol for the relevant unit of measure (e.g., "m"
>for "meter" or "$" for "dollar").

In electronics, where in the USA we would write "4.7k", in most other parts of the
world they write "4k7". (For "4.7", it's "4R7", the "R" probably signifying
"radix". Over the several decades I have been in the field, electronics has become
increasingly international.

I'm reasonably sure that astronomers and surveyors write fractions of angles
(seconds of arc only?) by substituting the unit glyph for the decimal point.
( 3.6" (seconds) would be 3"6 .)

>While the decimal separator has a mathematical significance (it establishes
>the "scale" of the number), the so-called "grouping separator" only has the
>linguistic purpose of making it easier to translate of written number into
>linguistic units, so it is even more strictly connected to language.

[...]

>Consequently, Indians write 12345678901 as "1234,5678,901" because, in
>Indian English, the number corresponds to this phrase:
>
> "One thousands two hundreds thirty-four (1234) crores
> five thousands six hundreds seventy-eight (5678) lakhs
> nine hundreds and one (901)"

*Most* interesting!

>> Topic for another time: Mathematical notation is often akin to slang!

>Numbers written grouping digits are hardly mathematical notation: they are a
>just a sort shorthand for a particular kind of phrases that it would be too
>fatiguing to spell out in letters.

Agreed, but I was referring to such forms as [arc sine of x], which is often
written as "sin[] x", with a superscripted [minus one] where the [] are.
By convention, superscripted integers make lots of sense when they represent
powers, such as x³ for x cubed. As well, negative superscripted integers also make
sense. But, when you put a superscripted [minus one] as a suffix for "sin", that's
just ridiculous, but it is understood universally, afaik.
(Just in case: ³ is a superscripted 3.)

(Arc sine is also called "inverse sine", a more accurate term, afaik. Given a
number, the arc sine of the number is an angle. The sine of that angle is the
original number. My condolences to people who had inept math. teachers. I was
lucky.)

Thanks, again, for some very enlightening comments.

Nicholas Bodley |@| Waltham, Mass.
Crocuses are coming up!
I detest arrogance.