Re: P1788 response to Motion 13
Michel Hack wrote:
[Nate Hayes]
This leads to the family of relations depicted in Fig. 2, and also
gives: A \prec B iff A \preceq B and not ( A = B ).
This makes no sense to me, as \prec would differ from \preceq
in only one degenerate case, namely when A and B are the same
singleton. If A and B are equal but not singleton then
NOT (A \preceq B)
because (a1 < a2 <= b1 < b2) is incompatible with a1=b1 and a2=b2.
I agree with Michel.
As he points out (and I mention in my post, to some incoherent extent),
trying to use algebraic rules to define one relation in terms of the others
always appears to lead to some different, if not astonishing, result.
Now, this isn't really a bad thing. For example, in Table 2 it allows to
distinguish between "interior" from "proper subset" from "subset" quite
easily, etc. But there is a level of complexity, and users have to be
careful, for example, not to write code like
( A \preceq B ) and not ( A = B )
if they really are just looking for A \prec B.
However, this is ultimately why I came to the conclusion we should include
all the relations and definitions in Table 1.
Sincerely,
Nate