At 09:14 PM 4/19/2006, you wrote:
This seems to be a question about word usage, rather than a mathematically precise question. ...
yes
In a programming context, non-transitively can happen by accident in an object-oriented language, if one creates two classes that know how to compare themselves to a third, but not to each other. E.g., Rational, Float, and Integer; 2/1 = 2, 2.0 = 2, but 2/1 != 2.0.
yes, but that works by overloading ==.
Another programming example is where one has two String classes, one using case sensitive compares, and one using case insensitive compares. If one implements comparisons between the two classes as either a case sensitive or a case insensitive compare, the result will not be transitive. I think other strange things can happen with case insensitive compares in some systems.
yes, we came up with something like that in our study group tonight, involving strings in different languages or from different code pages, but could not think of any other. i was hoping for a counter example from math that might end up in a random application. thanks
Franklin T. Adams-Watters
-----Original Message----- From: dasimov@earthlink.net
Ray Tayek writes:
<< hi, reading junit recipies by martin fowler. talking about equality as an equivalence relation on objects. ... he conjectures that this idea of "close enough" is the *only* case ... does anyone have a counter example?
It's hard to know what is meant here by "an equals relation", ... It's easy to come up with a relation having the first two ... properties but not transitivity: ... I don't know what it would mean to say this is or is not a "close enough" example. ...
--- vice-chair http://ocjug.org/