2014/12/06 by Guang-Liang Li, Li, Guang-Liang, Victor O. K. Li +1
Mathematics · Physics and Astronomy · #60A05 #Calculus (dental) #Computer science #Constructive #Contradiction #Data mining #Discrete mathematics #Epistemology #FOS: Mathematics #General Mathematics (math.GM) #Ideal (ethics) #Mathematical economics #Mathematical proof #Mathematics #Measure (data warehouse) #Philosophy #Probability and Statistical Research #Probability measure #Process (computing) #Quantum Mechanics and Applications #Statistical Mechanics and Entropy #math.GM #msc:60A05
paper · pdf · doi:10.48550/arxiv.1412.5411
14 pages, 1 figure
arxiv created 2014/12/06 · openalex publication_date 2014/12/06 · arxiv updated 2014/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We reveal a contradiction in measure-theoretic probability. The contradiction is an "equation" 1/2 = 0 with its two sides representing probabilities. Unlike known paradoxes in mathematics, the revealed contradiction cannot be explained away and actually indicates that measure-theoretic probability is inconsistent. Appearing only in the theory, the contradiction does not exist in the physical world. So practical applications of measure-theoretic probability will not be affected by the inconsistency as long as "ideal events" in the theory (which will never occur physically) are not mistaken for real events in the physical world. Nevertheless, the inconsistency must be resolved. Constructive mathematics can avoid such inconsistency. There is no contradiction reported in constructive mathematics.