2009/12/9 Richard O'Keefe
On Dec 10, 2009, at 2:58 AM, Roel van Dijk wrote:
I tried to be conservative with the choice of unicode symbols. I have defined the division sign (÷) to be (/). But it could just as well be defined as 'div'.
No it couldn't. One expects 3÷2 to be 1½, not 1. You will, for example, find this text on the web: "Mathematically, the division sign is equivalent to the forward slash. Thus, for example, 4 ÷ 5 = 4/5 = 0.8" This is actually historically backwards. When I was a nipper, 1/6 meant "one and six" or "eighteen pence" or at least three loaves of good bread. As far as I'm aware, the use of "/" instead of "÷" is a computerism introduced in the days of 6 bit character sets.
Another choice that could lead to some discussion is the definition of
(⊂) to be 'Data.Set.isProperSubsetOf' and (⊆) to be 'Data.Set.isSubsetOf'. An alternative choice would be to have (⊊) for 'isProperSubsetOf' and (⊂) for 'isSubsetOf'.
Mathematicians may use the plain horseshoe for either subset or proper subset, depending on the author. But I've never ever seen anyone use the horseshoe with an equals bar for proper subset; that would really make no sense.
The second notation uses a horseshoe with an equals bar and a _slash_ through it to indicate proper subset, and I have seen that several times before; however, I prefer the first notation style.
I suggest that you take the Z formal specification language as your guide (plain horseshoe is proper subset, horseshoe with equal bar is subset-or-equal). If you don't like Z, try B: same thing.
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