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What is Maximal and Minimal Elements in Posets about?

This document discusses properties of partially ordered sets (posets) including: 1) Every finite nonempty poset has at least one maximal and minimal element. 2) A poset with a greatest element has exactly one maximal element, which is also the greatest element. 3) A poset with a unique maximal element, that element is also the greatest element. It also introduces Hasse diagrams for visualizing posets and notes future discussions will involve chains and antichains in posets.

Author

Ross Hamilton

Language

EN