upper bound
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upper bound
Let be a set with a partial ordering , and let be a subset of . An upper bound for is an element such that for all . We say that is bounded from above if there exists an upper bound for .
Lower bound, and bounded from below are defined in a similar manner.
Defines:
bound, lower bound, bounded, bounded from above, bounded from below
Type of Math Object:
Definition
Major Section:
Reference
Groups audience:
Mathematics Subject Classification
06A06 Partial order, general11A07 Congruences; primitive roots; residue systems
Comments
Notation for upper bound
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.
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Victor Porton - http://www.mathematics21.org
* Algebraic General Topology and Math Synthesis
* Category Theory - new concepts
Re: Notation for upper bound
I don't know of anything standard, but
X \leq a
seems to tell the whole story pretty concisely.
Cam