关于定义和交叉的表达式:的超实体和它们的分值计算
Jan A Bergstra1, John V Tucker2
1Informatics Institute, University of Amsterdam, Science Park 900, 1098 XH Amsterdam, The Netherlands.
Entropy (Basel, Switzerland)
|January 24, 2025
概括
这项研究引入了一个新的代数与符号无限和未定义的值,以简化计算和交叉. 这种方法解决了0log20的问题,并改善了概率论的数学基础.
科学领域:
- 信息理论 信息理论
- 数学基础数学基础的基础
- 可能性理论概率理论.
背景情况:
- 标准和交叉公式涉及未定义的运算,如0log20.
- 这些未定义的运算导致了计算的不确定性和逻辑分析的复杂性.
研究的目的:
- 开发一种新的数学框架,以解决信息理论计算中的未定义运算.
- 为了表达,交叉和相关的分歧,而不依赖于公约或案例分割.
主要方法:
- 引入了对实数的新代数,包括符号表示符号无限 (±∞) 和未定义值 ().
- 在这个新的代数系统中重新定义核心信息理论措施.
主要成果:
- ,交叉,库尔巴克-莱布勒分歧和香农分歧可以使用新代数一致地表达.
- 消除有问题的子表达式,如0log20和相关的计算不确定性.
结论:
- 拟议的代数为信息理论计算提供了一个统一和无约定的方法.
- 这一框架为概率理论更广泛地提供了潜在的基础.
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