"Paul McGuire" <[EMAIL PROTECTED]> writes: > > Usually, "for all X in S, PRED(x) is true" means: > > there does not exist X in S so that PRED(x) is false. > > > How do you get this "usually" stuff? I would agree that this is usually > implemented as a short-circuited loop through the list, that breaks out at > the first False value. But I would not be quick to equate "commonality of > implementation" with "meaning".
See <http://en.wikipedia.org/wiki/For_all>: Generally, then, the negation of a propositional function's universal quantification is an existential quantification of that propositional function's negation; symbolically, \lnot\ \forall{x}{\in}\mathbf{X}\, P(x) \equiv\ \exists{x}{\in}\mathbf{X}\, \lnot\ P(x) -- http://mail.python.org/mailman/listinfo/python-list
