Set Theory and Logic

Several Questions About Infinity

Authors: Jincheng Zhang
Comments: 15 Pages.

What is infinity? What principles should be adhered to when researching infinity? For a predicate on a natural number system, is it true that finite holds, and infinite holds? This paper reexamines the nature of infinity and proposes two opposite infinite axioms (δ+1=δ or δ+1≠δ). Based on these two infinite axioms, the "infinite induction" of the identity formula is proved; it is found that the infinite axioms in the ZF system do not satisfy the equality axiom, and there are many contradictions in the reasoning of the Cantor ordinal number. The ordinal theory of set theory ZF system is not strict. It is hoped that the mathematics community will pay attention to these questions and give a convincing answer.
Category: Set Theory and Logic