```Date: Feb 17, 2013 4:35 PM
Author: Graham Cooper
Subject: Re: I Bet \$25 to your \$1 (PayPal) That You Can’t P<br>	rove Naive Set Theory Inconsistent

On Feb 16, 7:56 am, Charlie-Boo <shymath...@gmail.com> wrote:> Agreement:>> I, the owner of email account shymathgu...@aol.com, do hereby agree to> wager \$25 against \$1 from anyone, payable through PayPal, that they> cannot prove Naïve Set Theory inconsistent, subject to the condition> that the person states here that they enter into this wager within 24> hours after this offer appears and they are the first to give their> proof as part of this wager.>> C-BHere is a Small Depth Limited Formal Set Theory in PROLOG!*** t( THEOREM , LEVEL )  ***t(1,z(1)).not(0).*** PREDICATE CONSTRUCTION ***if(   and(X,Y)                ,    or(X,Y)            ).if(   and(not(X),Y)           ,    or(X,Y)            ).if(   and(X,not(Y))           ,    or(X,Y)            ).if(   and(not(X),not(Y))      ,    not(or(X,Y))       ).if(   and(not(X),not(Y))      ,    not(and(X,Y))      ).if(   and(not(X),Y)           ,    not(and(X,Y))      ).if(   and(X,not(Y))           ,    not(and(X,Y))      ).if(   and(X,Y)                ,    if(X,Y)            ).if(   and(not(X),not(Y))      ,    if(X,Y)            ).if(   and(not(X),Y)           ,    if(X,Y)            ).if(   and(X,not(Y))           ,    not(if(X,Y))       ).if(   and(X,Y)                ,    iff(X,Y)           ).if(   and(not(X),not(Y))      ,    iff(X,Y)           ).if(   and(not(X),Y)           ,    not(iff(X,Y))      ).if(   and(X,not(Y))           ,    not(iff(X,Y))      ).*** NEGATION ***if(   not(and(X,Y))           ,    or(not(X),not(Y))  ).if(   not(or(X,Y))            ,    and(not(X),not(Y)) ).if(   not(xor(X,Y))           ,    iff(X,Y)           ).if(   not(not(X))             ,    X                  ).if(   X                       ,    not(not(X))        ).*** TRANSITIVE RELATIONS ***if(   and(if(A,B),if(B,C))    ,    if(A,C)            ).if(   and(or(A,B),if(B,C))    ,    or(A,C)            ).if(   and(and(A,B),if(B,C))   ,    and(A,C)           ).*** ASSOCIATIVE RELATIONS ***if(   and(A,B)                ,    and(B,A)           ).if(   or(A,B)                 ,    or(B,A)            ).*** THEOREMHOOD ***t(if(X,Y),z(1)) :- if(X,Y).t(not(X),z(1)) :- not(X).t(X,z(Z)) :- t(X,Z).*** CARTESIAN JOIN ON THEOREM PAIRS ***t(  and(X,Y)           , z(Z))  :-  t(X,Z), t(Y,Z).t(  and(X,not(Y))      , z(Z))  :-  t(X,Z), not(Y).t(  and(not(X),Y)      , z(Z))  :-  not(X), t(Y,Z).t(  and(not(X),not(Y)) , z(Z))  :-  not(X), not(Y).*** SETHOOD ***t(e(A,B),z(1)) :- e(A,B).*** DEMO SET ***if( e(X,X) , e(X,selfish) ).e( ideas, abstract ).e( abstract, abstract ).e( dog, animals ).e( cat, animals ).*** ARITHMETIC ***add(1,2,3).t(add(M,N,S),z(1))  :- add(M,N,S).t(bigger(N,M),z(1)) :- bigger(N,M).if(  bigger(N,M)       ,    not(bigger(M,N))   ).if(  not(bigger(N,M))  ,    bigger(M,N)        ).if(  add(M,N,SUM)      ,    bigger(SUM,M)      ).if(  add(M,N,SUM)      ,    bigger(SUM,N)      ).if(  add(M,N,SUM)      ,    add(N,M,SUM)       ).*** MODUS PONENS ***t(R,z(Z)) :- if(L,R) , t(L,Z).*** DEMO QUERIES ***?- t( e(X,selfish) , z(z(1)) ).if( not(e(X,X)) , e(X,rusl) ).if( e(X,russell) , not(e(X,X)) ).not(e(rusl,rusl)).?- t( not(e(rusl,rusl)) , z(1) ).?- t( e(rusl,rusl) , z(z(1)) ).************************The output is:abstractYESYESe.g. the last 2 queries?- t( not(e(rusl,rusl)) , z(1) ).READS:  Is it a theorem that russells set is not an element ofrussells set with 1 deduction?YES?- t( e(rusl,rusl) , z(z(1)) ).READS: Is it a theorem that russells set is an element of russells setwith 2 or less deductions?YESTherefore|- rusl e ruslAND|- not( rusl e rusl)which satisifies the conditions of an Inconsistent System!Herc--Next Week :  Proving 1+1=4 in an Inconsistent System!www.BLoCKPROLOG,.com
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