I am reading an e-book called To Infinity and Beyond by Dr. Kent A Bessey. In the book the author makes the claim that Georg Cantor made a discovery "where half of a pie is as large as the whole".
In talking about it, he seems to claim that because half a pie can be broken into an infinite amount of pieces, and likewise a whole pie can be broken into an infinite amount of pieces they are infact the same size.
By the same concept, he states that if you took all of the pieces of the edge of a box you could create as many more boxes of whatever size you wanted using those pieces.
This seems undeniably false to me. I cannot help but draw a parallel between limits -> infinity. Where those limits may equal 2 or some other finite value. In my view, even if you were to break half a pie into an infinite amount of pieces the pieces could never add up to more than half a pie.
Am I misunderstanding? Can someone explain this concept better?