At 08:14 PM 4/19/2006, you wrote:
Ray Tayek writes:
<< ...equality as an equivalence relation on objects. i.. some idea of "close enough" (i.e. within some epsilon).... 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", since in math the concept of an "equivalence relation" is defined by possessing reflexivity, symmetry, and transitivity.
yes. the topic is an equals() method that *should* be tranistive and is not.
It's easy to come up with a relation having the first two properties but not transitivity: ...
sure
I don't know what it would mean to say this is or is not a "close enough" example.
my reading of it is that there is always something like abs(x1-x0)<epsilon and he conjectere that there are no other examples. thanks --- vice-chair http://ocjug.org/