bounded

1. 1
   verb

   Simple past and past participle of bound.

   The hikers bounded down the trail, eager to reach the lake.

   Her enthusiasm was bounded only by the time she had available.

   Note

   The regular past form of two quite different senses of bound. One means to leap: the hikers bounded down the trail. The other means to form the edge of: a field bounded by hedges, which is often passive. Bounded is never the past of bind. That verb's past is bound itself, so write "the prisoners were bound", not "bounded".

2. 2
   adjective

   Able to be enclosed within a ball of finite radius.

   Like a planet's orbit that never strays beyond a fixed distance from its star.

   The interval from zero to one is bounded, since every point lies within a finite distance.

   Analysts confirmed the sequence was bounded before showing that it converged.

   Oppositeunbounded

   Note

   Analysis judges boundedness by distance. A set qualifies when some ball of finite radius can hold all of it. The word is said of sets, and it often comes up beside compactness, because a compact set must be bounded. The order-theory meaning looks for least and greatest members. Here no ordering is needed, only a way to measure how far apart points lie.

3. 3
   adjective

   Having a least element and a greatest element, so that every member lies between the two.

   Like a calendar month, which always has a first day and a last day with every date in between.

   The set is bounded, with its members ranging between a fixed minimum and a fixed maximum.

   Mathematicians showed the ordered collection was bounded by identifying its least and greatest elements.

   Oppositeunbounded

   Note

   Order theory's version is said of a partially ordered set. The condition holds only when the set itself contains a bottom element and a top one, with everything else falling between them. The bounds are members, not markers outside the set. Because the order may be partial, those two extremes must still sit below and above every element, even elements that cannot be compared with one another.

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