Well, I tried with matlab and discovered its boolean systems are just rubbish. I also tried to use some didactic software from various philosophy departments, but none of them had any real automatic use. Could someone please help with this? I'm running out of ideas save spending a month expanding the bloody thing out... Here it is, as corrected... General conditions: Let X be some set. Let g be some function which returns some set over the domain of all subsets of X, including X. Let f be some function such that for any of the subsets Y of X, including X, f(Y) is equal to the intersection of Y and g(Y) [that is, the set of all elements of Y which are also elements of g(Y)]. Let n be some natural number. _______________________________________________________________________________ Rational (I)(n): g is rational (I)(n) on X if and only if; ------------------------------------------------------------------------------- For any of the subsets Y of X, including X, for any of the subsets Z of X, including X, for any of the subsets W of X, including W; If; f(Y) is any of the subsets of Z, including Z, AND W is any of the subsets of Y, including Y, AND the cardinality of W [number of elements in W] is greater than or equal to n, AND the cardinality of Z is greater than or equal to n, AND; f(V) is any of the subsets of W, including W, OR f(V) is any of the subsets of f(Z), including f(Z), where V is equal to the union of W and f(Z) [that is, the set of all elements of W or f(Z)]; Then it must be that; f(V) is equal to f(Z), where V is equal to the union of W and f(Z). ------------------------------------------------------------------------------- _______________________________________________________________________________ _______________________________________________________________________________ Rational (II)(n): g is rational (II)(n) on X if and only if; ------------------------------------------------------------------------------- For any of the subsets Y of X, including X, for any of the subsets Z of X, including X; If; f(Y) is any of the subsets of Z, including Z, AND the cardinality of Y [number of elements in Y] is greater than or equal to n, AND the cardinality of Z is greater than or equal to n, AND; f(V) is any of the subsets of Y, including Y, OR f(V) is any of the subsets of f(Z), including f(Z), where V is equal to the union of Y and f(Z) [that is, the set of all elements of Y or f(Z)]; Then it must be that; f(V) is equal to f(Z), where V is equal to the union of Y and f(Z). ------------------------------------------------------------------------------- _______________________________________________________________________________ _______________________________________________________________________________ THEOREM: g is rational (II)(n) on X implies g is rational (I)(n) on X _______________________________________________________________________________ I'm having BIG problems proving/disproving this theorem... Could someone give me a hand? Thanks, David
