Publisher's Synopsis
Your introductory Real Analysis textbook does not make complete sense and suddenly mathematics is so counterintuitive. Modern mathematics is based on Cantor's infinite set theory and the concept of an actual infinity. It is full of counterintuitive results and seeming contradictions. Almost all real numbers are supposed to be irrational but at the same time we don't know the exact numerical value of a single irrational number. Irrational numbers must be denoted with symbols leading to the absurdity that almost all members of the set of real numbers cannot be written as numbers. Two infinities with Cantor's Diagonalization Argument, and infinite infinities with Cantor's theorem, how can all this be true? It isn't! The theory of mathematics is wrong and this book shows you exactly why.The Law of Excluded Middle and proof by contradiction has been misapplied to conclude that the collection of natural numbers is an infinite set. The way one-to-one correspondence is established between two infinite sets is faulty. These two wrong assumptions lead to a series of cascaded incorrect results, each one more and more egregious than the previous. The empty set cannot be a set and the existence of the Power set does not follow from the existence of a set which makes Cantor's theorem meaningless for finite sets and not defined for infinite sets.There aren't infinite infinities. Not even one!There is no such thing as an infinite set!!The axiom of infinity in mathematics is a flawed assumption and is the root cause of all counterintuitive results in mathematics!An object can only be potentially infinite as per Aristotle.The only other science where such abstractions come directly into play is physics. A different theory of mathematics may lead to different theories in physics. The unsuccessful attempts at a unified theory of physics may be due to the underlying mathematics. Certain conclusions about imperfections in the real small world of quantum mechanics, like the Heisenberg Principle, may instead be pointing to an imperfection in the underlying mathematics.
