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Let $S$ be a set with a partial ordering $\leq$ and let $T$ be a subset of $S$ An upper bound for $T$ is an element $z \in S$ such that $x \leq z$ for all $x \in T$ We say that $T$ is bounded from above if there exists an upper bound for $T$
Lower bound, and bounded from below are defined in a similar manner.
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"upper bound" is owned by djao. [ full author list (2) | owner history (1) ]
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| Also defines: |
bound, lower bound, bounded, bounded from above, bounded from below |
- Attachments:
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tight (Definition) by mps
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Cross-references: similar, subset, partial ordering
There are 184 references to this entry.
This is version 4 of upper bound, born on 2001-10-21, modified 2004-03-20.
Object id is 450, canonical name is UpperBound.
Accessed 28562 times total.
Classification:
| AMS MSC: | 06A06 (Order, lattices, ordered algebraic structures :: Ordered sets :: Partial order, general) |
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Pending Errata and Addenda
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