Publisher's Synopsis
Real Analysis does not make sense. Infinite set theory is counterintuitive and full of results that are profoundly unbelievable. Mathematics is based on precise definitions and logically correct proofs, and is taken to be thoroughly rigorous. It isn't! The theory of mathematics is wrong and this book shows you exactly why.Definitions and axioms need to be not only meticulous but also consistent. Infinite set theory was lax on the former and failed to ensure the latter. The axioms of infinity and of power set are both shown to violate prior established principles. Both are wrong and lead to most of the contradictions in infinite set theory. No matter how much rigor is employed subsequently, it cannot make amends for the initial mistakes.The existence of the fixed infinite sets of natural numbers N and real numbers R are just assumptions in mathematics. The set N contains a non-terminating sequence of finite elements 1, 2, 3 ..., and is neither fixed finite nor fixed non-finite. These two have been assumed in mathematics as the only available choices. Instead it is something in between which is non-fixed finite. It is a fundamental mistake to call N and R sets. The logical, proof-by-contradiction arguments based on the unproven Law of Excluded Middle are shown to be effectively useless as a tool for proving theorems.There aren't infinite actual infinities. Not even one!There is no such thing as an infinite set!!It's time to debunk the axioms and not accept a flawed theory on faith anymore!!!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.
