[om] Bug in definition of `strict_order'
ocaprott at risc.uni-linz.ac.at
Thu Jul 10 11:20:37 CEST 2003
Scott L. Burson wrote:
> I just now learned about OpenMath as I was using Google to look for some
> I seem to have found a bug in the definition of `strict_order', or more
> precisely, in that of `antireflexive' on which it depends. A strict order
> is irreflexive, meaning `forall(x) ~R(x, x)'. The current definition of
> `antireflexive', however, says
> forall(x, y) R(x, y) -> R(y, x) -> x = y
> But this definition does not work as part of the definition of
> `strict_order', because by irreflexivity and transitivity, there are no x, y
> such that `R(x, y) & R(y, x)'.
Yes, this is what the definition of strict order implies and it is the
goal of the definition to make sure that an order relation R is such
that if Rxy then ~Ryx, like < (less than).
It could be written instead as something
> forall(x, y) (R(x, y) = R(y, x)) -> x = y
> and then it would work for both reflexive and irreflexive relations.
> Please CC: me in replies as I am not on the mailing list.
> -- Scott
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