From: Kenneth Whistler (email@example.com)
Date: Tue Oct 12 2010 - 18:56:16 CDT
Karl Williamson asked:
> The Unicode standard only gives numeric values to rational numbers. Is
> the reason for this merely because of the difficulty of representing
> irrational ones?
No. Primarily it is because the Unicode Standard is a *character*
encoding standard, and not a standard for numeric values for
various mathematical constants that some characters might be
used to represent.
> In looking through the list of code points, I actually found only one
> case where a character totally unambiguously refers to a particular
> irrational number, and that is U+2107, EULER CONSTANT.
Well, U+2107 is classified as an uppercase letter. It isn't
classed as a number -- and only the numbers are systematically
given Numeric_Value values in the UCD, and that only because such
information is routinely required for their text processing --
particularly for the digits.
I consider "EULER CONSTANT" an unfortunate misnomer from the
very, very early days of the Unicode Standard. If we had it to
do over, particularly given the later addition of all the
styled mathematical alphanumerics, I would have favored:
2107 [insert stylename here] CAPITAL E
= Euler constant
Or something similar -- just to make the point clearer.
> says that U+03C0, GREEK SMALL LETTER PI is used for the ratio of a
> circle's circumference to its diameter, but it has other uses as well,
> and does not have the Math property.
Having the Math property basically has nothing to do with whether
a character is assigned a Numeric_Value or not.
> The various Math PI's don't seem
> that they necessarily mean this value either. Things like the two
> characters that have "Planck's constant" in their names, even if the
> code points always meant that, have different values in different
> measurement systems, so couldn't be said to refer to particular numbers.
> I'm curious if any thought was given to this, and what code points I'm
> missing in my analysis.
U+1D452 MATHEMATICAL ITALIC SMALL E (or merely U+0065 LATIN
SMALL LETTER E), also used for Euler's number. See also U+2147.
For that matter, why stop with irrationals? There is
also U+1D456 MATHEMATICAL ITALIC SMALL I (or merely U+0069 LATIN
SMALL LETTER I), used for the imaginary number, square root
of -1. See also U+2148 and U+2149.
Basically, there is no end to how mathematicians may end up
assigning odder and more exotic kinds of "numbers" to various
symbols available in the standard. And I think how they do
so and exactly what those values mean is basically out of
scope of the Unicode Standard.
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