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# upper bound

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.

Defines:

bound, lower bound, bounded, bounded from above, bounded from below

Type of Math Object:

Definition

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Reference

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## Mathematics Subject Classification

06A06*no label found*11A07

*no label found*

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## 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.

--

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