James Hall james at slohall.com
Wed Dec 9 19:08:39 EST 2009

```2009/12/9 Richard O'Keefe <ok at cs.otago.ac.nz>

>
> 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.
>
>
> _______________________________________________