[math-fun] equality of floating point numbers.

hi, reading junit recipies by martin fowler. talking about equality as an equivalence relation on objects. if one of the fields of the objects that is in included in the equals method has a floating point number, then one uses some idea of "close enough" (i.e. within some epsilon). this is clearly reflexive and symmetric, but not transitive. he conjectures that this idea of "close enough" is the *only* case (in the space of equals methods for object) of having a equals relation that is symmetric and reflexive and not transitive. does anyone have a counter example? thanks --- vice-chair http://ocjug.org/