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upper bound (Definition)

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.



"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

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tight (Definition) by mps
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Cross-references: similar, subset, partial ordering
There are 148 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 24183 times total.

Classification:
AMS MSC: 06A06 (Order, lattices, ordered algebraic structures :: Ordered sets :: Partial order, general)
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Notation for upper bound by porton on 2008-02-29 11:45:24
Is there any conventional math symbol which means "a is an upper bound of X"?

Or maybe there is some symbol which means "the set of all upper bounds of X"?

What I want is to write phrase "a is an upper bound of X" symbolically (not by English words).

And dually for lower bounds.
--
Victor Porton - http://www.mathematics21.org
* Algebraic General Topology and Math Synthesis
* Category Theory - new concepts
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