Could the day ever come when mathematics proceeds in a purely mechanistic fashion - that it requires no genuinely new insights? This sounds like a good question for an afternoon's debate. But, strange as it may seem, there is actually a theorem in mathematics to the effect that this subject can never become routine! This result, called Godel's theorem, is one of the greatest discoveries in mathematics of the twentieth century. And - perhaps even more remarkable - the proof of this theorem can be understood by anyone, without any knowledge at all of mathematics. The statement and proof of Godel's theorem is the subject of this book. The idea is quite simple, but it requires thinking about things in a new way. The book includes homework problems and exams with solutions and comments.Games. Let us consider games of the following type. There are two players a call them axa and aoa. There is a board, visible to ... Whether there is a procedure for solving the problem asks whether one can give explicit instructions such that aanbsp;...
|Publisher||:||Minkowski Institute Press - 2013-05-21|