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Definition. Idempotence (of binary operators) [dm-000D]

  • Liam O'Connor

A binary operator \bullet is idempotent iff, for all x, x \bullet x = x.

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    Corollary. Properties of \sqcup [dt-0018]

    • Liam O'Connor

    When lubs exist, the binary \sqcup operator is idempotent, commutative, and associative. Also, we have that x \sqsubseteq y iff x \sqcup y = y.