On 3 October 2011 15:15, Wolfgang Laun
<wolfgang(_dot_)laun(_at_)gmail(_dot_)com> wrote:
Just think of the universal quantifier "forall" (every $x in X
satisfies P) as a conjunction over zero or more elements. Its
initialization must be true (as the initial value for a product must
be 1). Therefore, the "forall" for an empty set is true.
The quantifier "exists" (some $x in X satisfies P) is a disjunction
over elements, and its initialization must be false (as the initial
value for a sum must be 0). Hence, the "exists" for an empty set X is
false.
Thanks - the 'initialization' is how I saw it - deep-equal() / every
starts from a position of true and looks for a reason to be false, and
=/some starts from a position of false and looks for a reason to be
true.
Not such faulty logic after all.
--
Andrew Welch
http://andrewjwelch.com
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