Henry writes:
<<
Computer languages are just as bad.
"from m to n" now means [m..n] inclusive, although English
was never so unambiguous prior to computer languages. Fortran
never took a stand, as it simply used "1,N", and didn't use
an English word.
I have always advocated "from m upto n" for the non-inclusive [m..n),
since this matches 0-origin indexing much better than the "to" form:
"from 0 upto length(vector)".
>>
Now, I don't think it's such a bad thing that math or computer languages
use ambiguous English to mean unambiguous things. Virtually any English
word is somewhat ambiguous (multibiguous?), and it seems wworthwhile
to use English words & phrases in math and computer languages instead
of making up a new word for every concept or operation.
In computer languages, you just have to learn them, that all there is to it.
In math, there are a number of cases where "standardized" language really isn't
standard, even for the simplest things. Does "the natural numbers N" mean
{1,2,3,...} or {0,1,2,3,...}? Depends who you ask.
(On the other hand, I don't know if I think using "upto" to denote
"up to but not including" is all that unambiguous; it's almost unambiguous for
the opposite meaning: If in English someone says "He took care of those files up to Q, but no further", it would seem quite clear that Q was included.)
--Dan
