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