The article says:
"If the machine prints NPRNPR, it has printed a false statement. But if the machine never prints NPRNPR, then NPRNPR is a true statement that the machine never prints."
This part seems logically true:
"If the machine prints NPRNPR, it has printed a false statement." It seems logically true, and I wont say why because I view it as obvious =/
This part seems logically false:
"if the machine never prints NPRNPR, then NPRNPR is a true statement" I don't understand the logic of "If it is not printed, it is true." I was under the impression that the only true statement was "If it prints, then it is true", and of course the contrapositive: "If it is not true, it doesn't print". The statement taken from the article is NOT the contrapositive. It is the inverse, and because the converse of a statement is not always true, the inverse is not always true because the inverse is always equal to the converse. "if the machine never prints NPRNPR, then NPRNPR is a true statement" That statement is the inverse of the original if-then statement, and the inverse/converse is FALSE because it allows opportunities which violate the original if-then statement.
I logically concluded that the statement in the proof:
"if the machine never prints NPRNPR, then NPRNPR is a true statement" is a false statement. And therefore the proof is incorrect.
Okay. If I am wrong, can someone please tell me where?