On Fri, 27 Apr 2012 14:17:48 +0200, Kiuhnm wrote: >>> Define your terms: what do you mean by "equal"? >> >> a and b are equal iff > > Nope. What I meant is that we can talk of equality whenever... > >> a = a >> a = b => b = a >> a = b and b = c => a = c >> If some of this properties are violated, we're talking of something >> else.
Sorry, that won't do it. You haven't defined equality, or given any way of deciding whether two entities are equal. What you have listed are three *properties* of equality, namely: - reflexivity (a = a) - symmetry (if a = b then b = a) - transitivity (if a = b and b = c then a = c) But those three properties apply to any equivalence relation, not just equality. Examples: "both are odd" (of integers) "have the same birthday" (of people) "is congruent to" (of triangles) "is in the same tax bracket" (of tax payers) "has the same length" (of pieces of string) "both contain chocolate" (of cakes) For example, if we define the operator "~" to mean "has the same genes" (to be precise: the same genotype), then if Fred and Barney are identical twins we have: Fred ~ Fred Fred ~ Barney and Barney ~ Fred Identical triplets are rare (at least among human beings), but if we clone Barney to get George, then we also have: Fred ~ Barney and Barney ~ George => Fred ~ George. So "have the same genes" meets all your conditions for equality, but isn't equality: the three brothers are very different. Fred lost his arm in a car crash, Barney is a hopeless alcoholic, and George is forty years younger than his two brothers. -- Steven -- http://mail.python.org/mailman/listinfo/python-list
