In mathematics, a meet on a set is defined either as the unique infimum (greatest lower bound) with respect to a partial order on the set, provided an infimum exists, or (abstractly) as a commutative and associative binary operation satisfying an idempotency law. In either case, the set together with the meet is a meet-semilattice. The two definitions yield equivalent results, except that in the partial order approach it may be possible directly to define meets of more general sets of elements.

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  • In mathematics, a meet on a set is defined either as the unique infimum (greatest lower bound) with respect to a partial order on the set, provided an infimum exists, or (abstractly) as a commutative and associative binary operation satisfying an idempotency law. In either case, the set together with the meet is a meet-semilattice. The two definitions yield equivalent results, except that in the partial order approach it may be possible directly to define meets of more general sets of elements. The most common context in which to find a meet is as one of the operations in a lattice. Usually, the meet of <math>x</math> and <math>y</math> is denoted <math>x \land y</math>.
  • 在数学中，在一个集合上的交(meet)有两种定义：关于在这个集合上的偏序的唯一下确界(最大下界)，假定下确界存在的话； 或者是满足幂等律的交换结合二元运算。在任何一个情况下，这个集合与交运算一起是半格。这两个定义产生等价的结果，除了在偏序方式中有可能直接定义更一般的元素的集合的交。最常见到交运算的领域是格。 通常把 <math>x</math> 和 <math>y</math> 的交指示为 <math>x \land y</math>。
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  • April 2009
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  • Talk:Join (mathematics) Merge proposal
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  • In mathematics, a meet on a set is defined either as the unique infimum (greatest lower bound) with respect to a partial order on the set, provided an infimum exists, or (abstractly) as a commutative and associative binary operation satisfying an idempotency law. In either case, the set together with the meet is a meet-semilattice. The two definitions yield equivalent results, except that in the partial order approach it may be possible directly to define meets of more general sets of elements.
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  • Meet (mathematics)
  • 交运算
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