Mathematics
2 years ago

New Mathematical Discovery Challenges Fundamental Laws of Group Operations

arXiv (Cornell University)
Antiassociative Groupoids
Milton Braitt, David Hobby, D. M. Silberger

Paper Summary

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The article explores groupoids that are antiassociative, meaning the order of operations matters. They show that for any number of elements greater than or equal to 3, there are groupoids where different ways of grouping elements always give different results. This finding has implications for understanding how certain mathematical structures behave when combined in different ways.