分类: 计算机科学 >> 计算机科学技术其他学科 分类: 生物学 >> 分子生物学 分类: 数学 >> 逻辑 提交时间: 2024-07-01
摘要: Polymer aggregates and molecular polymers are written as computable numbers, resulting in a unity between cells and universal Turing machines with the Entscheidungsproblem. However, whether the Entscheidungsproblem of cells really exists remains elusive. Alan Turing found universal Turing machines read only computable numbers written by humans who further differentiate transcendental numbers from the set of computable numbers by Georg Cantor’s diagonal process. It follows that the decidability of the Entscheidungsproblem derived from humans eliminates the independence of computable numbers from each other and enables computable numbers to be fused with each other into the set of computable numbers, with the result that humans are endowed with a capacity to read of the fusion of computable numbers with each other into the set of computable numbers by humans to read the set of computable numbers bearing computable numbers by being endowed with a capacity to write computable numbers. Accordingly, it is shown here how humans are invited to write cell backbones as complex numbers read by artificial intelligence machines emulated by cells by writing polyribonucleotides as computable numbers read by universal Turing machines emulated by extracellular ribosomes to extend Georg Cantor’s continuum hypothesis by being invited to extend Alan Turing’s work on the Entscheidungsproblem, resulting in a unity between cells and artificial intelligence machines without the Entscheidungsproblem.
分类: 数学 >> 数学(综合) 分类: 数学 >> 逻辑 提交时间: 2023-06-20
摘要: The aim of this paper is to study well-connected residuated lattices and residually finite residuated lattices. So far, well-connected residuated lattices not only a main tool for studying RLsi but also a subdirect irreducible representation object of residuated lattices. In this paper we both investigate the above two aspects by using some di#11;erent methods. Finally, we introduce the residually finite residuated lattices and characterize them from algebraic, logical and topological perspectives, respectively.
摘要: 为了从根本上消灭存在于数学基础中的各种悖论,使数学建筑在高度可靠的基础上,发现形式逻辑只能用于同一律,矛盾律和排中律这三大规律都成立的讨论域 (称为可行域) 内,否则就会产生包括悖论在内的各种错误,而在形式逻辑的适用范围即可行域内,只要前提可靠,推导严格,悖论是不存在的。根据该结论,分析了说谎者悖论和理发师悖论等一些历史上比较著名的悖论的形成原因,同时指出了数学基础中皮亚诺公理的应用和康托尔定理、区间套和对角线法证明中的一些逻辑错误,提出了能够避免这些错误的统一的定义自然数、有理数和无理数的建议。