Set Theory and Logic

    

Infinite Numbers in Mathematics

Authors: Weike Xu

A method named `motional construction' is introduced in this article. Questions involving continuum hypothesis and incompleteness theorems of formal systems are answered, but a major concern of this article is a nature of infinity: Infinity implies paradoxes.Many conclusions contradicting orthodox mathematics are proved, such as: a set of real numbers does not exist, Lebesgue measure of any set is zero, ZF axioms are not logically consistent, etc. Unreliable results are common in sub-fields of mathematics where infinite sets are used intensively.A valid mathematical conclusion describes finiteness in essence.When infiniteness is clear, the third mathematical crisis shall be over.

Comments: 49 Pages. The sequence of sections in this article is carefully arranged for correct understandings. It is recommended for professionals to read in order.

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[v1] 2024-12-22 04:26:36

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