The Infinity Tree: Representing Infinities of Real Numbers with Countably Infinite Tree Structures  

作　　者：Philip C. Jackson Philip C. Jackson(TalaMind LLC, Troy, MI, USA)

机构地区：[1]TalaMind LLC, Troy, MI, USA

出　　处：《Advances in Pure Mathematics》2023年第4期198-205,共8页理论数学进展（英文）

摘　　要：This paper discusses how the infinite set of real numbers between 0 and 1 could be represented by a countably infinite tree structure which would avoid Cantor’s diagonalization argument that the set of real numbers is not countably infinite. Likewise, countably infinite tree structures could represent all real numbers, and all points in any number of dimensions in multi-dimensional spaces. The objective of this paper is not to overturn previous research based on Cantor’s argument, but to suggest that this situation may be treated as a definitional or axiomatic choice. This paper proposes a “non-Cantorian” branch of cardinality theory, representing all these infinities with countably infinite tree structures. This approach would be consistent with the Continuum Hypothesis.This paper discusses how the infinite set of real numbers between 0 and 1 could be represented by a countably infinite tree structure which would avoid Cantor’s diagonalization argument that the set of real numbers is not countably infinite. Likewise, countably infinite tree structures could represent all real numbers, and all points in any number of dimensions in multi-dimensional spaces. The objective of this paper is not to overturn previous research based on Cantor’s argument, but to suggest that this situation may be treated as a definitional or axiomatic choice. This paper proposes a “non-Cantorian” branch of cardinality theory, representing all these infinities with countably infinite tree structures. This approach would be consistent with the Continuum Hypothesis.

关 键 词：INFINITY Countable DIAGONALIZATION Real Numbers Tree Structure Infinity Tree Continuum Hypothesis 

分 类 号：O17[理学—数学]